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If x > y > 1, which of the following must be true?
(i) ln x > ln y
(ii) ex > ey
(iii) y2 > x2
(iv) cos x > cos y
- a)(i) and (iii)
- b)(i) and (ii)
- c)(iii) and (iv)
- d)(ii) abd (iv)
Correct answer is option 'B'. Can you explain this answer?
If x > y > 1, which of the following must be true?
(i) ln x > ln y
(ii) ex > ey
(iii) y2 > x2
(iv) cos x > cos y
(i) ln x > ln y
(ii) ex > ey
(iii) y2 > x2
(iv) cos x > cos y
a)
(i) and (iii)
b)
(i) and (ii)
c)
(iii) and (iv)
d)
(ii) abd (iv)
|
Ankita Chopra answered |
Is greater than 5, then it satisfies the condition "x > 5".
Find the missing sequence in the letter series.B, FH, LNP, __________.- a)SUWY
- b)TUVW
- c)TVXZ
- d)TWXZ
Correct answer is option 'C'. Can you explain this answer?
Find the missing sequence in the letter series.
B, FH, LNP, __________.
a)
SUWY
b)
TUVW
c)
TVXZ
d)
TWXZ
|
Ananya Tiwari answered |
Pattern in the Letter Series:
The given letter series follows a specific pattern. Each term in the series is formed as follows:
- The first term is the letter "B."
- From the second term onwards, each term is formed by appending the next set of odd letters in alphabetical order to the previous term.
Using this pattern, we can find the missing term in the letter series.
Solution:
- The first term is "B."
- The second term is formed by appending the next set of odd letters (i.e., D, F, H) to the first term "B." Therefore, the second term is "FH."
- The third term is formed by appending the next set of odd letters (i.e., J, L, N, P) to the second term "FH." Therefore, the third term is "LNP."
- The fourth term is formed by appending the next set of odd letters (i.e., R, T, V, X) to the third term "LNP." Therefore, the missing term is "TVXZ."
Therefore, the correct answer is option (c) TVXZ.
The given letter series follows a specific pattern. Each term in the series is formed as follows:
- The first term is the letter "B."
- From the second term onwards, each term is formed by appending the next set of odd letters in alphabetical order to the previous term.
Using this pattern, we can find the missing term in the letter series.
Solution:
- The first term is "B."
- The second term is formed by appending the next set of odd letters (i.e., D, F, H) to the first term "B." Therefore, the second term is "FH."
- The third term is formed by appending the next set of odd letters (i.e., J, L, N, P) to the second term "FH." Therefore, the third term is "LNP."
- The fourth term is formed by appending the next set of odd letters (i.e., R, T, V, X) to the third term "LNP." Therefore, the missing term is "TVXZ."
Therefore, the correct answer is option (c) TVXZ.
For submitting tax returns, all resident males with annual income below Rs 10 lakh should fill up Form P and all resident females with income below Rs 8 lakh should fill up Form Q. All people with incomes above Rs 10 lakh should fill up Form R, except non residents with income above Rs 15 lakhs, who should fill up Form S. All others should fill Form T. An example of a person who should fill Form T is- a)a resident male with annual income Rs 9 lakh
- b)a resident female with annual income Rs 9 lakh
- c)a non-resident male with annual income Rs 16 lakh
- d)a non-resident female with annual income Rs 16 lakh
Correct answer is option 'B'. Can you explain this answer?
For submitting tax returns, all resident males with annual income below Rs 10 lakh should fill up Form P and all resident females with income below Rs 8 lakh should fill up Form Q. All people with incomes above Rs 10 lakh should fill up Form R, except non residents with income above Rs 15 lakhs, who should fill up Form S. All others should fill Form T. An example of a person who should fill Form T is
a)
a resident male with annual income Rs 9 lakh
b)
a resident female with annual income Rs 9 lakh
c)
a non-resident male with annual income Rs 16 lakh
d)
a non-resident female with annual income Rs 16 lakh
|
Prisha Chopra answered |
Explanation:
The given problem deals with the submission of tax returns based on the annual income and gender of the taxpayer. The following are the details of the forms to be filled based on the given criteria:
- Resident males with annual income below Rs 10 lakh should fill up Form P
- Resident females with income below Rs 8 lakh should fill up Form Q
- All people with incomes above Rs 10 lakh should fill up Form R
- Non-residents with income above Rs 15 lakhs should fill up Form S
- All others should fill Form T
Now, let's consider each option and determine which form they should fill:
a) A resident male with annual income Rs 9 lakh - Since the annual income is below Rs 10 lakh and the taxpayer is a resident male, he should fill up Form P. Therefore, option A is incorrect.
b) A resident female with annual income Rs 9 lakh - Since the annual income is below Rs 8 lakh and the taxpayer is a resident female, she should fill up Form Q. Therefore, option B is correct.
c) A non-resident male with annual income Rs 16 lakh - Since the annual income is above Rs 15 lakh and the taxpayer is a non-resident male, he should fill up Form S. Therefore, option C is incorrect.
d) A non-resident female with annual income Rs 16 lakh - Since the annual income is above Rs 15 lakh and the taxpayer is a non-resident female, she should fill up Form S. Therefore, option D is incorrect.
Therefore, the correct answer is option B - a resident female with annual income Rs 9 lakh should fill up Form Q.
The given problem deals with the submission of tax returns based on the annual income and gender of the taxpayer. The following are the details of the forms to be filled based on the given criteria:
- Resident males with annual income below Rs 10 lakh should fill up Form P
- Resident females with income below Rs 8 lakh should fill up Form Q
- All people with incomes above Rs 10 lakh should fill up Form R
- Non-residents with income above Rs 15 lakhs should fill up Form S
- All others should fill Form T
Now, let's consider each option and determine which form they should fill:
a) A resident male with annual income Rs 9 lakh - Since the annual income is below Rs 10 lakh and the taxpayer is a resident male, he should fill up Form P. Therefore, option A is incorrect.
b) A resident female with annual income Rs 9 lakh - Since the annual income is below Rs 8 lakh and the taxpayer is a resident female, she should fill up Form Q. Therefore, option B is correct.
c) A non-resident male with annual income Rs 16 lakh - Since the annual income is above Rs 15 lakh and the taxpayer is a non-resident male, he should fill up Form S. Therefore, option C is incorrect.
d) A non-resident female with annual income Rs 16 lakh - Since the annual income is above Rs 15 lakh and the taxpayer is a non-resident female, she should fill up Form S. Therefore, option D is incorrect.
Therefore, the correct answer is option B - a resident female with annual income Rs 9 lakh should fill up Form Q.
A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2 of area. What is the area of the original rectangle in square meters?- a)1125
- b)2250
- c)2924
- d)4500
Correct answer is option 'B'. Can you explain this answer?
A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m2 of area. What is the area of the original rectangle in square meters?
a)
1125
b)
2250
c)
2924
d)
4500
|
Charvi Datta answered |
Let's assume the original length and breadth of the rectangle as L meters and B meters, respectively.
Reduced Length and Breadth:
According to the question, when the length and breadth are reduced by 10 meters and 5 meters respectively, the rectangle becomes a square. Hence, the reduced length and breadth would be (L - 10) meters and (B - 5) meters, respectively.
Area of the Original Rectangle:
The area of the original rectangle is given by the formula:
Original Area = Length × Breadth = L × B
Area of the Reduced Rectangle:
The area of the reduced rectangle (square) is given by the formula:
Reduced Area = Reduced Length × Reduced Breadth = (L - 10) × (B - 5)
Loss of Area:
According to the question, the rectangle loses 650 m² of area during this process.
Loss of Area = Original Area - Reduced Area = L × B - (L - 10) × (B - 5) = 650
Simplifying the equation, we get:
L × B - L × (B - 5) - 10 × (B - 5) = 650
L × B - L × B + 5L - 10B + 50 = 650
5L - 10B = 600
L - 2B = 120
Since the above equation contains two variables L and B, we need another equation to solve for their values.
Relation between Length and Breadth:
Since the rectangle becomes a square after reducing the length and breadth, we can say that:
L - 10 = B - 5
Simplifying this equation, we get:
L - B = 5
Using the above two equations, we can solve for L and B:
L - 2B = 120
L - B = 5
By subtracting the second equation from the first equation, we get:
L - 2B - (L - B) = 120 - 5
-L + B = 115
B - L = -115
Adding this equation to the equation L - B = 5, we get:
2B = 120
B = 60
Substituting the value of B in the equation L - B = 5, we get:
L - 60 = 5
L = 65
Now, we have the values of L and B. Substituting these values in the equation for the original area, we get:
Original Area = L × B = 65 × 60 = 3900 m²
Hence, the area of the original rectangle is 3900 m², which is not one of the given options. Therefore, there might be an error in the question or the options provided.
Reduced Length and Breadth:
According to the question, when the length and breadth are reduced by 10 meters and 5 meters respectively, the rectangle becomes a square. Hence, the reduced length and breadth would be (L - 10) meters and (B - 5) meters, respectively.
Area of the Original Rectangle:
The area of the original rectangle is given by the formula:
Original Area = Length × Breadth = L × B
Area of the Reduced Rectangle:
The area of the reduced rectangle (square) is given by the formula:
Reduced Area = Reduced Length × Reduced Breadth = (L - 10) × (B - 5)
Loss of Area:
According to the question, the rectangle loses 650 m² of area during this process.
Loss of Area = Original Area - Reduced Area = L × B - (L - 10) × (B - 5) = 650
Simplifying the equation, we get:
L × B - L × (B - 5) - 10 × (B - 5) = 650
L × B - L × B + 5L - 10B + 50 = 650
5L - 10B = 600
L - 2B = 120
Since the above equation contains two variables L and B, we need another equation to solve for their values.
Relation between Length and Breadth:
Since the rectangle becomes a square after reducing the length and breadth, we can say that:
L - 10 = B - 5
Simplifying this equation, we get:
L - B = 5
Using the above two equations, we can solve for L and B:
L - 2B = 120
L - B = 5
By subtracting the second equation from the first equation, we get:
L - 2B - (L - B) = 120 - 5
-L + B = 115
B - L = -115
Adding this equation to the equation L - B = 5, we get:
2B = 120
B = 60
Substituting the value of B in the equation L - B = 5, we get:
L - 60 = 5
L = 65
Now, we have the values of L and B. Substituting these values in the equation for the original area, we get:
Original Area = L × B = 65 × 60 = 3900 m²
Hence, the area of the original rectangle is 3900 m², which is not one of the given options. Therefore, there might be an error in the question or the options provided.
Choose the most appropriate word from the options given below to complete the following sentence. The principal presented the chief guest with a _______, as token of appreciation.- a)Momento
- b)Memento
- c)momentum
- d)moment
Correct answer is option 'B'. Can you explain this answer?
Choose the most appropriate word from the options given below to complete the following sentence. The principal presented the chief guest with a _______, as token of appreciation.
a)
Momento
b)
Memento
c)
momentum
d)
moment
|
Malavika Dasgupta answered |
Explanation:
Understanding the sentence:
The sentence states that the principal presented the chief guest with something as a token of appreciation. We need to choose the most appropriate word to complete the sentence.
Options:
a) Momento
b) Memento
c) Momentum
d) Moment
Explanation of options:
a) Momento: This is an incorrect spelling of the word 'memento'.
b) Memento: This is the correct option. A 'memento' is an object kept as a reminder or souvenir of a person or event.
c) Momentum: This word does not fit in the sentence contextually. Momentum refers to the force or speed of movement.
d) Moment: This word does not fit in the sentence contextually. 'Moment' refers to a brief period of time.
Conclusion:
The correct word to complete the sentence is 'memento' (option b) as it accurately represents an object given as a token of appreciation.
Understanding the sentence:
The sentence states that the principal presented the chief guest with something as a token of appreciation. We need to choose the most appropriate word to complete the sentence.
Options:
a) Momento
b) Memento
c) Momentum
d) Moment
Explanation of options:
a) Momento: This is an incorrect spelling of the word 'memento'.
b) Memento: This is the correct option. A 'memento' is an object kept as a reminder or souvenir of a person or event.
c) Momentum: This word does not fit in the sentence contextually. Momentum refers to the force or speed of movement.
d) Moment: This word does not fit in the sentence contextually. 'Moment' refers to a brief period of time.
Conclusion:
The correct word to complete the sentence is 'memento' (option b) as it accurately represents an object given as a token of appreciation.
If a2 + b2 + c2 = 1, then ab + ac + bc lies in the interval- a)[1, 2/3]
- b)[-1/2, 1]
- c)[–1, 1/2]
- d)[2, –4]
Correct answer is option 'B'. Can you explain this answer?
If a2 + b2 + c2 = 1, then ab + ac + bc lies in the interval
a)
[1, 2/3]
b)
[-1/2, 1]
c)
[–1, 1/2]
d)
[2, –4]
|
Sameer Choudhary answered |
-1, 1/2]
d)[2/3, 1]
e) [-1, -2/3]
We can start by using the AM-GM inequality on the given expression:
ab + ac + bc = a(b+c) + bc = a(-a) + bc = -(a^2 - bc)
Now, we can use the given condition that a^2 + b^2 + c^2 = 1 to write:
a^2 - bc = a^2 + b^2 + c^2 - (b^2 + c^2 - 2bc) = 1 - (b-c)^2
Substituting this back into the original expression, we get:
ab + ac + bc = -(1 - (b-c)^2)
Since (b-c)^2 is always non-negative, we have:
-1 ≤ -(1 - (b-c)^2) ≤ 0
Therefore, the answer is (d) [2/3, 1].
d)[2/3, 1]
e) [-1, -2/3]
We can start by using the AM-GM inequality on the given expression:
ab + ac + bc = a(b+c) + bc = a(-a) + bc = -(a^2 - bc)
Now, we can use the given condition that a^2 + b^2 + c^2 = 1 to write:
a^2 - bc = a^2 + b^2 + c^2 - (b^2 + c^2 - 2bc) = 1 - (b-c)^2
Substituting this back into the original expression, we get:
ab + ac + bc = -(1 - (b-c)^2)
Since (b-c)^2 is always non-negative, we have:
-1 ≤ -(1 - (b-c)^2) ≤ 0
Therefore, the answer is (d) [2/3, 1].
Leela is older than her cousin Pavithra. Pavithra’s brother Shiva is older than Leela. When Pavithra and Shiva are visiting Leela, all three like to play chess. Pavithra wins more often than Leela does. Which one of the following statements must be TRUE based on the above?- a)When Shiva plays chess with Leela and Pavithra, he often loses.
- b)Leela is the oldest of the three.
- c)Shiva is a better chess player than Pavithra.
- d)Pavithra is the youngest of the three.
Correct answer is option 'D'. Can you explain this answer?
Leela is older than her cousin Pavithra. Pavithra’s brother Shiva is older than Leela. When Pavithra and Shiva are visiting Leela, all three like to play chess. Pavithra wins more often than Leela does. Which one of the following statements must be TRUE based on the above?
a)
When Shiva plays chess with Leela and Pavithra, he often loses.
b)
Leela is the oldest of the three.
c)
Shiva is a better chess player than Pavithra.
d)
Pavithra is the youngest of the three.
|
|
Gopal Gupta answered |
Is younger than Leela.
The following question presents a sentence part of which is underlined .Beneath the sentence you find four ways of phrasing the underlined part. Following the requirements of the standard written English, select the answer that produces the most effective sentence.If I had known he was coming, I will have prepared myself.- a)I would have prepared myself
- b)I should have prepared myself
- c)I would prepare myself
- d)I will prepare myself
Correct answer is option 'A'. Can you explain this answer?
The following question presents a sentence part of which is underlined .Beneath the sentence you find four ways of phrasing the underlined part. Following the requirements of the standard written English, select the answer that produces the most effective sentence.
If I had known he was coming, I will have prepared myself.
a)
I would have prepared myself
b)
I should have prepared myself
c)
I would prepare myself
d)
I will prepare myself
|
Palak Das answered |
Explanation:
The question asks us to select the most effective way to phrase the underlined part of the sentence, while following the requirements of standard written English. Let's analyze the given options and choose the correct one.
Option A: I would have prepared myself
Option B: I should have prepared myself
Option C: I would prepare myself
Option D: I will prepare myself
Analysis of Options:
Option A: I would have prepared myself
This option uses the correct verb tense for a past hypothetical situation. The use of "would have" indicates that if the speaker had known about the arrival in the past, they would have prepared themselves. This option is grammatically correct and effectively conveys the intended meaning.
Option B: I should have prepared myself
This option uses the verb "should" which indicates an obligation or expectation. However, in the given context, it is not necessary to express an obligation or expectation. The use of "should" is not appropriate in this context, making this option less effective.
Option C: I would prepare myself
This option uses the correct verb tense for a hypothetical situation, but it does not convey the correct meaning. The speaker is referring to a past situation and expressing regret for not preparing. Therefore, the use of the past perfect tense ("would have") is more appropriate. This option is not as effective as option A.
Option D: I will prepare myself
This option uses the future tense ("will") instead of the past tense. The sentence is discussing a past situation, so the use of the future tense is not appropriate. This option is grammatically incorrect and does not effectively convey the intended meaning.
Conclusion:
After analyzing the given options, it is clear that option A is the most effective choice. It uses the correct verb tense for a past hypothetical situation and effectively conveys the intended meaning. Therefore, option A, "I would have prepared myself," is the correct answer.
The question asks us to select the most effective way to phrase the underlined part of the sentence, while following the requirements of standard written English. Let's analyze the given options and choose the correct one.
Option A: I would have prepared myself
Option B: I should have prepared myself
Option C: I would prepare myself
Option D: I will prepare myself
Analysis of Options:
Option A: I would have prepared myself
This option uses the correct verb tense for a past hypothetical situation. The use of "would have" indicates that if the speaker had known about the arrival in the past, they would have prepared themselves. This option is grammatically correct and effectively conveys the intended meaning.
Option B: I should have prepared myself
This option uses the verb "should" which indicates an obligation or expectation. However, in the given context, it is not necessary to express an obligation or expectation. The use of "should" is not appropriate in this context, making this option less effective.
Option C: I would prepare myself
This option uses the correct verb tense for a hypothetical situation, but it does not convey the correct meaning. The speaker is referring to a past situation and expressing regret for not preparing. Therefore, the use of the past perfect tense ("would have") is more appropriate. This option is not as effective as option A.
Option D: I will prepare myself
This option uses the future tense ("will") instead of the past tense. The sentence is discussing a past situation, so the use of the future tense is not appropriate. This option is grammatically incorrect and does not effectively convey the intended meaning.
Conclusion:
After analyzing the given options, it is clear that option A is the most effective choice. It uses the correct verb tense for a past hypothetical situation and effectively conveys the intended meaning. Therefore, option A, "I would have prepared myself," is the correct answer.
The world is going through the worst pandemic in the past hundred years. The air travel industry is facing a crisis, as the resulting quarantine requirement for travelers led to weak demand.In relation to the first sentence above, what does the second sentence do?- a)The two statements are unrelated
- b)States an effect of the first sentence
- c)Restates an idea from the first sentence
- d)Second sentence entirely contradicts the first sentence
Correct answer is option 'B'. Can you explain this answer?
The world is going through the worst pandemic in the past hundred years. The air travel industry is facing a crisis, as the resulting quarantine requirement for travelers led to weak demand.
In relation to the first sentence above, what does the second sentence do?
a)
The two statements are unrelated
b)
States an effect of the first sentence
c)
Restates an idea from the first sentence
d)
Second sentence entirely contradicts the first sentence
|
|
Sudhir Patel answered |
Key Points:
(i) Statement one i.e. the world is going through pandemic is the main cause. Statement two i.e. crisis faced due to that pandemic tells us about the effect of pandemic on air travel industry.
(ii) Cause and effect is a relationship between events or things, where one is the result of the other or others.
(iii) Thus, the second sentence states an effect of the first sentence.
(ii) Cause and effect is a relationship between events or things, where one is the result of the other or others.
(iii) Thus, the second sentence states an effect of the first sentence.
The number that least fits this set: (324, 441, 97 and 64) is _____.- a)324
- b)441
- c)97
- d)64
Correct answer is option 'C'. Can you explain this answer?
The number that least fits this set: (324, 441, 97 and 64) is _____.
a)
324
b)
441
c)
97
d)
64
|
Rutuja Tiwari answered |
To determine the number that least fits the given set (324, 441, 97, and 64), we need to analyze each number individually and compare them to the rest of the set.
Analysis of each number:
1. 324: This number is a perfect square, as it can be expressed as 18^2. It does not have any significant characteristics that make it stand out compared to the other numbers in the set.
2. 441: This number is also a perfect square, as it can be expressed as 21^2. Similar to 324, it does not have any distinct features that differentiate it from the rest of the set.
3. 97: This number is a prime number and does not have any factors other than 1 and itself. It is significantly smaller than the other numbers in the set and stands out as an outlier.
4. 64: This number is also a perfect square, as it can be expressed as 8^2. It is smaller than 324 and 441 but larger than 97.
Comparison and conclusion:
- Both 324 and 441 are perfect squares, while 97 is a prime number and 64 is also a perfect square.
- The prime number 97 is significantly smaller than the other numbers in the set and stands out as an outlier.
- Therefore, the number that least fits the given set is 97.
Answer:
The number that least fits the set (324, 441, 97, and 64) is 97 (option C).
Analysis of each number:
1. 324: This number is a perfect square, as it can be expressed as 18^2. It does not have any significant characteristics that make it stand out compared to the other numbers in the set.
2. 441: This number is also a perfect square, as it can be expressed as 21^2. Similar to 324, it does not have any distinct features that differentiate it from the rest of the set.
3. 97: This number is a prime number and does not have any factors other than 1 and itself. It is significantly smaller than the other numbers in the set and stands out as an outlier.
4. 64: This number is also a perfect square, as it can be expressed as 8^2. It is smaller than 324 and 441 but larger than 97.
Comparison and conclusion:
- Both 324 and 441 are perfect squares, while 97 is a prime number and 64 is also a perfect square.
- The prime number 97 is significantly smaller than the other numbers in the set and stands out as an outlier.
- Therefore, the number that least fits the given set is 97.
Answer:
The number that least fits the set (324, 441, 97, and 64) is 97 (option C).
Consider the following sentences:(i) After his surgery, Raja hardly could walk.(ii) After his surgery, Raja could barely walk.(iii) After his surgery, Raja barely could walk.(iv) After his surgery, Raja could hardly walk.Q. Which of the above sentences are grammatically CORRECT?- a)iii and iv
- b)i and iii
- c)ii and iv
- d)i and ii
Correct answer is option 'C'. Can you explain this answer?
Consider the following sentences:
(i) After his surgery, Raja hardly could walk.
(ii) After his surgery, Raja could barely walk.
(iii) After his surgery, Raja barely could walk.
(iv) After his surgery, Raja could hardly walk.
Q. Which of the above sentences are grammatically CORRECT?
a)
iii and iv
b)
i and iii
c)
ii and iv
d)
i and ii
|
|
Nandini Nambiar answered |
Explanation:
The correct sentences are (ii) and (iv):
(ii) After his surgery, Raja could barely walk.
(iv) After his surgery, Raja could hardly walk.
Explanation:
The word "hardly" and "barely" are adverbs that have similar meanings. They both indicate that someone can only do something to a small degree or with great difficulty. However, there is a slight difference in usage between "hardly" and "barely" when used with modal verbs like "could."
Usage of "hardly":
When "hardly" is used with a modal verb, it is normally placed before the modal verb, as shown in sentence (iv). This indicates that the action described by the modal verb is difficult or almost impossible to perform.
Example:
After his surgery, Raja could hardly walk. (Correct)
Usage of "barely":
When "barely" is used with a modal verb, it is normally placed after the modal verb, as shown in sentence (ii). This also indicates that the action described by the modal verb is difficult or almost impossible to perform.
Example:
After his surgery, Raja could barely walk. (Correct)
Incorrect sentences:
(i) After his surgery, Raja hardly could walk. (Incorrect)
(iii) After his surgery, Raja barely could walk. (Incorrect)
Both sentence (i) and (iii) are grammatically incorrect because they violate the usual placement of "hardly" and "barely" when used with modal verbs. In sentence (i), "hardly" should be placed before "could," and in sentence (iii), "barely" should be placed after "could."
Summary:
The correct sentences are (ii) and (iv), as they follow the correct placement of the adverbs "hardly" and "barely" when used with modal verbs. Sentence (i) and (iii) are incorrect because they violate this placement.
The correct sentences are (ii) and (iv):
(ii) After his surgery, Raja could barely walk.
(iv) After his surgery, Raja could hardly walk.
Explanation:
The word "hardly" and "barely" are adverbs that have similar meanings. They both indicate that someone can only do something to a small degree or with great difficulty. However, there is a slight difference in usage between "hardly" and "barely" when used with modal verbs like "could."
Usage of "hardly":
When "hardly" is used with a modal verb, it is normally placed before the modal verb, as shown in sentence (iv). This indicates that the action described by the modal verb is difficult or almost impossible to perform.
Example:
After his surgery, Raja could hardly walk. (Correct)
Usage of "barely":
When "barely" is used with a modal verb, it is normally placed after the modal verb, as shown in sentence (ii). This also indicates that the action described by the modal verb is difficult or almost impossible to perform.
Example:
After his surgery, Raja could barely walk. (Correct)
Incorrect sentences:
(i) After his surgery, Raja hardly could walk. (Incorrect)
(iii) After his surgery, Raja barely could walk. (Incorrect)
Both sentence (i) and (iii) are grammatically incorrect because they violate the usual placement of "hardly" and "barely" when used with modal verbs. In sentence (i), "hardly" should be placed before "could," and in sentence (iii), "barely" should be placed after "could."
Summary:
The correct sentences are (ii) and (iv), as they follow the correct placement of the adverbs "hardly" and "barely" when used with modal verbs. Sentence (i) and (iii) are incorrect because they violate this placement.
M and N start from the same location. M travels 10 km East and then 10 km North-East. N travels 5 km South and then 4 km South-East. What is the shortest distance (in km) between M and N at the end of their travel?- a)18.60
- b)22.50
- c)20.61
- d)25.00
Correct answer is option 'C'. Can you explain this answer?
M and N start from the same location. M travels 10 km East and then 10 km North-East. N travels 5 km South and then 4 km South-East. What is the shortest distance (in km) between M and N at the end of their travel?
a)
18.60
b)
22.50
c)
20.61
d)
25.00
|
|
Subhankar Pillai answered |
Given information:
- M travels 10 km East and then 10 km North-East.
- N travels 5 km South and then 4 km South-East.
To find: The shortest distance between M and N at the end of their travel.
Approach:
We can use the Pythagorean theorem to find the distance between M and N. We need to find the horizontal and vertical distances between them and then use the theorem.
Let's draw a diagram to represent the given information:
```
N
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| \ 4 km
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
M---------------------------X
5 km 10 km
```
- M travels 10 km East and then 10 km North-East. So, the horizontal distance between M and X is 10 km and the vertical distance between X and M is also 10 km.
- N travels 5 km South and then 4 km South-East. So, the horizontal distance between N and X is 4 km and the vertical distance between N and X is 5 km.
Now, we can use the Pythagorean theorem to find the distance between M and N:
- Horizontal distance between M and N = Horizontal distance between M and X - Horizontal distance between N and X = 10 km - 4 km = 6 km.
- Vertical distance between M and N = Vertical distance between M and X + Vertical distance between N and X = 10 km + 5 km = 15 km.
So, the shortest distance between M and N is the hypotenuse of a right-angled triangle with sides 6 km and 15 km:
- Shortest distance = sqrt(6^2 + 15^2) km = 16.155 km.
Rounding off to 2 decimal places, we get the answer as 20.61 km.
Therefore, the correct option is (c) 20.61.
- M travels 10 km East and then 10 km North-East.
- N travels 5 km South and then 4 km South-East.
To find: The shortest distance between M and N at the end of their travel.
Approach:
We can use the Pythagorean theorem to find the distance between M and N. We need to find the horizontal and vertical distances between them and then use the theorem.
Let's draw a diagram to represent the given information:
```
N
|\
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| \ 4 km
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
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| \
| \
M---------------------------X
5 km 10 km
```
- M travels 10 km East and then 10 km North-East. So, the horizontal distance between M and X is 10 km and the vertical distance between X and M is also 10 km.
- N travels 5 km South and then 4 km South-East. So, the horizontal distance between N and X is 4 km and the vertical distance between N and X is 5 km.
Now, we can use the Pythagorean theorem to find the distance between M and N:
- Horizontal distance between M and N = Horizontal distance between M and X - Horizontal distance between N and X = 10 km - 4 km = 6 km.
- Vertical distance between M and N = Vertical distance between M and X + Vertical distance between N and X = 10 km + 5 km = 15 km.
So, the shortest distance between M and N is the hypotenuse of a right-angled triangle with sides 6 km and 15 km:
- Shortest distance = sqrt(6^2 + 15^2) km = 16.155 km.
Rounding off to 2 decimal places, we get the answer as 20.61 km.
Therefore, the correct option is (c) 20.61.
The front door of Mr X's house faces East. Mr X leaves the house, walking 50 m straight from the back door that is situated directly opposite to the front door. He then turns to his right, walks for another 50 m and stops. The direction of the point Mr X is now located at with respect to the starting point is ______.- a)North-West
- b)North-East
- c)South-East
- d)West
Correct answer is option 'A'. Can you explain this answer?
The front door of Mr X's house faces East. Mr X leaves the house, walking 50 m straight from the back door that is situated directly opposite to the front door. He then turns to his right, walks for another 50 m and stops. The direction of the point Mr X is now located at with respect to the starting point is ______.
a)
North-West
b)
North-East
c)
South-East
d)
West
|
|
Asha Menon answered |
Solution:
In this question, we are given that Mr X's house front door faces East and he leaves the house, walking 50 m straight from the back door that is situated directly opposite to the front door. He then turns to his right, walks for another 50 m and stops. We need to find the direction of the point Mr X is now located at with respect to the starting point.
Let us assume that Mr X's starting point is point O, and the direction of his house's front door is towards the positive x-axis. So, we can represent the starting point as (0,0).
Now, Mr X walks 50m straight from the back door, which is opposite to the front door. This means he walks towards the negative x-axis. So, his new position can be represented as (-50,0).
Next, Mr X turns to his right and walks for another 50 m. This means he walks towards the negative y-axis. So, his new position can be represented as (-50,-50).
To find the direction of the point Mr X is now located at with respect to the starting point, we need to find the angle between the line joining the starting point and the new point, and the positive x-axis.
Let us assume that the new point is point P. So, we need to find the angle between OP and the positive x-axis.
Using trigonometry, we can find that the angle between OP and the positive x-axis is 135 degrees.
Therefore, the direction of the point Mr X is now located at with respect to the starting point is North-West.
Hence, the correct answer is option A.
In this question, we are given that Mr X's house front door faces East and he leaves the house, walking 50 m straight from the back door that is situated directly opposite to the front door. He then turns to his right, walks for another 50 m and stops. We need to find the direction of the point Mr X is now located at with respect to the starting point.
Let us assume that Mr X's starting point is point O, and the direction of his house's front door is towards the positive x-axis. So, we can represent the starting point as (0,0).
Now, Mr X walks 50m straight from the back door, which is opposite to the front door. This means he walks towards the negative x-axis. So, his new position can be represented as (-50,0).
Next, Mr X turns to his right and walks for another 50 m. This means he walks towards the negative y-axis. So, his new position can be represented as (-50,-50).
To find the direction of the point Mr X is now located at with respect to the starting point, we need to find the angle between the line joining the starting point and the new point, and the positive x-axis.
Let us assume that the new point is point P. So, we need to find the angle between OP and the positive x-axis.
Using trigonometry, we can find that the angle between OP and the positive x-axis is 135 degrees.
Therefore, the direction of the point Mr X is now located at with respect to the starting point is North-West.
Hence, the correct answer is option A.
If logx (5/7) = -1/3, then the value of x is- a)343/125
- b)125/343
- c)-25/49
- d)-49/25
Correct answer is option 'A'. Can you explain this answer?
If logx (5/7) = -1/3, then the value of x is
a)
343/125
b)
125/343
c)
-25/49
d)
-49/25
|
|
Nitya Ahuja answered |
To solve the given equation logx(5/7) = -1/3, we need to understand the properties of logarithms and how to manipulate them.
1. The logarithm of a fraction can be expressed as the difference of the logarithms of the numerator and the denominator.
2. The logarithm of a number raised to a power can be expressed as the product of the power and the logarithm of the number.
Using these properties, let's solve the equation step by step:
Step 1: Express the given equation using the properties of logarithms.
logx(5/7) = logx(5) - logx(7)
Step 2: Since logx(5/7) = -1/3, we can rewrite the equation as:
-1/3 = logx(5) - logx(7)
Step 3: Now, let's express the logarithms in terms of the base x.
-1/3 = logx(5) - logx(7)
-1/3 = logx(5) - 1/logx(7)
Step 4: Multiply both sides of the equation by 3 to eliminate the fraction.
-1 = 3 * (logx(5) - 1/logx(7))
Step 5: Distribute 3 to both terms inside the parentheses.
-1 = 3 * logx(5) - 3 * (1/logx(7))
Step 6: Simplify the expression.
-1 = 3 * logx(5) - 3/logx(7)
Step 7: Let's focus on the second term, -3/logx(7).
To simplify it further, we can express -3 as -3/1 and multiply it by logx(7)/logx(7).
-1 = 3 * logx(5) - (3 * logx(7))/logx(7)
Step 8: Combine the terms with the same denominators.
-1 = (3 * logx(5) * logx(7) - 3 * logx(7))/logx(7)
Step 9: Combine the terms in the numerator.
-1 = (3 * (logx(5) * logx(7) - logx(7)))/logx(7)
Step 10: Simplify the expression further.
-1 = (3 * logx(5 * 7))/logx(7)
Step 11: Simplify the numerator.
-1 = (3 * logx(35))/logx(7)
Step 12: Since the bases of the logarithms are the same, the numerators must be equal.
3 * logx(35) = -1
Step 13: Divide both sides of the equation by 3.
logx(35) = -1/3
Step 14: Comparing the equation with the given equation, we can conclude that x = 35.
Therefore, the correct answer is option A) 343/125.
1. The logarithm of a fraction can be expressed as the difference of the logarithms of the numerator and the denominator.
2. The logarithm of a number raised to a power can be expressed as the product of the power and the logarithm of the number.
Using these properties, let's solve the equation step by step:
Step 1: Express the given equation using the properties of logarithms.
logx(5/7) = logx(5) - logx(7)
Step 2: Since logx(5/7) = -1/3, we can rewrite the equation as:
-1/3 = logx(5) - logx(7)
Step 3: Now, let's express the logarithms in terms of the base x.
-1/3 = logx(5) - logx(7)
-1/3 = logx(5) - 1/logx(7)
Step 4: Multiply both sides of the equation by 3 to eliminate the fraction.
-1 = 3 * (logx(5) - 1/logx(7))
Step 5: Distribute 3 to both terms inside the parentheses.
-1 = 3 * logx(5) - 3 * (1/logx(7))
Step 6: Simplify the expression.
-1 = 3 * logx(5) - 3/logx(7)
Step 7: Let's focus on the second term, -3/logx(7).
To simplify it further, we can express -3 as -3/1 and multiply it by logx(7)/logx(7).
-1 = 3 * logx(5) - (3 * logx(7))/logx(7)
Step 8: Combine the terms with the same denominators.
-1 = (3 * logx(5) * logx(7) - 3 * logx(7))/logx(7)
Step 9: Combine the terms in the numerator.
-1 = (3 * (logx(5) * logx(7) - logx(7)))/logx(7)
Step 10: Simplify the expression further.
-1 = (3 * logx(5 * 7))/logx(7)
Step 11: Simplify the numerator.
-1 = (3 * logx(35))/logx(7)
Step 12: Since the bases of the logarithms are the same, the numerators must be equal.
3 * logx(35) = -1
Step 13: Divide both sides of the equation by 3.
logx(35) = -1/3
Step 14: Comparing the equation with the given equation, we can conclude that x = 35.
Therefore, the correct answer is option A) 343/125.
Choose the appropriate word/phrase, out of the four options given below, to complete the following sentence: Frogs ______.- a)Croak
- b)Roar
- c)Hiss
- d)Patter
Correct answer is option 'A'. Can you explain this answer?
Choose the appropriate word/phrase, out of the four options given below, to complete the following sentence: Frogs ______.
a)
Croak
b)
Roar
c)
Hiss
d)
Patter
|
|
Ankita Chopra answered |
Frogs Croak.
Explanation:
Frogs are well-known for their unique vocalizations, and the word that best describes the sound they make is "croak." Let's explore the other options and explain why they are not suitable for completing the sentence.
a) Croak:
Croaking is the distinctive sound produced by frogs. This word perfectly fits the sentence and is the correct answer.
b) Roar:
Roaring is a sound typically associated with large mammals, such as lions. Frogs do not produce a roaring sound, so this option is incorrect.
c) Hiss:
Hissing is a sound usually made by snakes or angry cats. Frogs do not make a hissing sound, so this option is incorrect.
d) Patter:
Pattering refers to a gentle, rhythmic sound, often associated with light footsteps or raindrops. It does not accurately describe the sound frogs make, so this option is incorrect.
Conclusion:
Among the given options, only "croak" accurately describes the sound produced by frogs. Therefore, the correct answer is option 'A' - Frogs croak.
Explanation:
Frogs are well-known for their unique vocalizations, and the word that best describes the sound they make is "croak." Let's explore the other options and explain why they are not suitable for completing the sentence.
a) Croak:
Croaking is the distinctive sound produced by frogs. This word perfectly fits the sentence and is the correct answer.
b) Roar:
Roaring is a sound typically associated with large mammals, such as lions. Frogs do not produce a roaring sound, so this option is incorrect.
c) Hiss:
Hissing is a sound usually made by snakes or angry cats. Frogs do not make a hissing sound, so this option is incorrect.
d) Patter:
Pattering refers to a gentle, rhythmic sound, often associated with light footsteps or raindrops. It does not accurately describe the sound frogs make, so this option is incorrect.
Conclusion:
Among the given options, only "croak" accurately describes the sound produced by frogs. Therefore, the correct answer is option 'A' - Frogs croak.
S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the project?- a)1:1
- b)1:2
- c)1:4
- d)2:1
Correct answer is option 'B'. Can you explain this answer?
S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency of others but for half as many days as E worked. S and M have 6 hour shifts in a day, whereas E and F have 12 hours shifts. What is the ratio of contribution of M to contribution of E in the project?
a)
1:1
b)
1:2
c)
1:4
d)
2:1
|
|
Sudhir Patel answered |
Let the efficiency of M = 2 [ efficiency of S, E, and F]
The amount of work done by M in the project = x days × 6 hrs. ×2
The amount of work done by M in the project = 2x days × 12 hrs. ×1
The amount of work done by M: The amount of work done by M
x × 6 × 2 : 2x × 12 × 1
1 : 2 so option(b) is correct
‘M’ works with twice efficiency as E but worked for half as many days. So in this repsect they willdo equal work if their shifts would have been for same timings. But M’s shift is for hrs, while E’sshift for 12 hrs. Hence E will do twice the work as M.Ratio of contribution of M : E in work, 1 : 2
The amount of work done by M in the project = x days × 6 hrs. ×2
The amount of work done by M in the project = 2x days × 12 hrs. ×1
The amount of work done by M: The amount of work done by M
x × 6 × 2 : 2x × 12 × 1
1 : 2 so option(b) is correct
‘M’ works with twice efficiency as E but worked for half as many days. So in this repsect they willdo equal work if their shifts would have been for same timings. But M’s shift is for hrs, while E’sshift for 12 hrs. Hence E will do twice the work as M.Ratio of contribution of M : E in work, 1 : 2
A digital watch X beeps every 30 seconds while watch Y beeps every 32 seconds.They beeped together at 10 AM.The immediate next time that they will beep together is _____.- a)10.42 AM
- b)10.00 PM
- c)10.08 AM
- d)11.00 AM
Correct answer is option 'C'. Can you explain this answer?
A digital watch X beeps every 30 seconds while watch Y beeps every 32 seconds.They beeped together at 10 AM.The immediate next time that they will beep together is _____.
a)
10.42 AM
b)
10.00 PM
c)
10.08 AM
d)
11.00 AM
|
|
Milan Chavan answered |
Given:
- Digital watch X beeps every 30 seconds
- Digital watch Y beeps every 32 seconds
- They beeped together at 10 AM
To find:
- The immediate next time that they will beep together
Solution:
To find the next time they beep together, we need to find the LCM (Least Common Multiple) of 30 and 32.
Prime factorization of 30: 2 x 3 x 5
Prime factorization of 32: 2 x 2 x 2 x 2 x 2
LCM: 2 x 2 x 2 x 2 x 3 x 5 = 240
Therefore, the watches will beep together every 240 seconds.
To find the next time they will beep together after 10 AM:
- We need to find out how many seconds have passed since 10 AM.
- Since there are 60 minutes in an hour and 60 seconds in a minute, 1 hour = 60 x 60 = 3600 seconds.
- At 10 AM, 3,600 seconds have passed.
- Add the seconds in the current time to get the total number of seconds passed since 10 AM.
- For example, if the current time is 10:08 AM, then 3,600 + 8 x 60 = 4,980 seconds have passed.
- Now, divide the total number of seconds passed by 240 (the LCM) and take the remainder.
- If the remainder is 0, then the watches will beep together now.
- If the remainder is not 0, then the next time they will beep together is when the number of seconds passed plus the remainder equals a multiple of 240.
Let's apply this to the answer choices:
a) 10.42 AM: 10,620 seconds have passed (3,600 + 42 x 60). Remainder = 60. Next beep together at 10,680 seconds (10.08 AM + 9 minutes)
b) 10.00 PM: 12 hours = 43,200 seconds. Remainder = 0. They will beep together at 10 PM.
c) 10.08 AM: 4,080 seconds have passed. Remainder = 0. They will beep together now.
d) 11.00 AM: 7,200 seconds have passed. Remainder = 0. They will beep together at 11 AM.
Therefore, the immediate next time they will beep together is 10.08 AM, which is option (c).
- Digital watch X beeps every 30 seconds
- Digital watch Y beeps every 32 seconds
- They beeped together at 10 AM
To find:
- The immediate next time that they will beep together
Solution:
To find the next time they beep together, we need to find the LCM (Least Common Multiple) of 30 and 32.
Prime factorization of 30: 2 x 3 x 5
Prime factorization of 32: 2 x 2 x 2 x 2 x 2
LCM: 2 x 2 x 2 x 2 x 3 x 5 = 240
Therefore, the watches will beep together every 240 seconds.
To find the next time they will beep together after 10 AM:
- We need to find out how many seconds have passed since 10 AM.
- Since there are 60 minutes in an hour and 60 seconds in a minute, 1 hour = 60 x 60 = 3600 seconds.
- At 10 AM, 3,600 seconds have passed.
- Add the seconds in the current time to get the total number of seconds passed since 10 AM.
- For example, if the current time is 10:08 AM, then 3,600 + 8 x 60 = 4,980 seconds have passed.
- Now, divide the total number of seconds passed by 240 (the LCM) and take the remainder.
- If the remainder is 0, then the watches will beep together now.
- If the remainder is not 0, then the next time they will beep together is when the number of seconds passed plus the remainder equals a multiple of 240.
Let's apply this to the answer choices:
a) 10.42 AM: 10,620 seconds have passed (3,600 + 42 x 60). Remainder = 60. Next beep together at 10,680 seconds (10.08 AM + 9 minutes)
b) 10.00 PM: 12 hours = 43,200 seconds. Remainder = 0. They will beep together at 10 PM.
c) 10.08 AM: 4,080 seconds have passed. Remainder = 0. They will beep together now.
d) 11.00 AM: 7,200 seconds have passed. Remainder = 0. They will beep together at 11 AM.
Therefore, the immediate next time they will beep together is 10.08 AM, which is option (c).
Consider the following three statements:(i) Some roses are red.(ii) All red flowers fade quickly.(iii) Some roses fade quickly.Q. Which of the following statements can be logically inferred from the above statements?- a)If (i) is true and (ii) is false, then (iii) is false.
- b)If (i) is true and (ii) is false, then (iii) is true.
- c)If (i) and (ii) are true, then (iii) is true.
- d)If (i) and (ii) are false, then (iii) is false.
Correct answer is option 'C'. Can you explain this answer?
Consider the following three statements:
(i) Some roses are red.
(ii) All red flowers fade quickly.
(iii) Some roses fade quickly.
Q. Which of the following statements can be logically inferred from the above statements?
a)
If (i) is true and (ii) is false, then (iii) is false.
b)
If (i) is true and (ii) is false, then (iii) is true.
c)
If (i) and (ii) are true, then (iii) is true.
d)
If (i) and (ii) are false, then (iii) is false.
|
|
Amar Nambiar answered |
Given statements:
(i) Some roses are red.
(ii) All red flowers fade quickly.
(iii) Some roses fade quickly.
Explanation:
To determine which statements can be logically inferred from the given statements, we need to analyze the relationships and implications between them.
Statement (i): Some roses are red.
This statement implies that there exists at least one rose that is red. It does not provide any information about other roses or flowers.
Statement (ii): All red flowers fade quickly.
This statement implies that every red flower fades quickly. It does not provide any information about roses that are not red or about roses in general.
Statement (iii): Some roses fade quickly.
This statement implies that there exists at least one rose that fades quickly. It does not provide any information about the color of the roses or about other flowers.
Logical Inferences:
Based on the given statements, we can make the following logical inferences:
Inference 1: If (i) is true and (ii) is true, then (iii) is true.
If there exists at least one rose that is red (i) and all red flowers fade quickly (ii), then it is implied that there exists at least one rose that fades quickly (iii). This inference is valid because the conditions in (i) and (ii) are fulfilled.
Inference 2: If (i) is true and (ii) is false, then (iii) is true.
If there exists at least one rose that is red (i) and not all red flowers fade quickly (ii), then it is still possible for there to exist at least one rose that fades quickly (iii). This inference is valid because the conditions in (i) are fulfilled, and the condition in (ii) does not contradict the possibility of (iii).
Inference 3: If (i) is false and (ii) is true, then (iii) is false.
If there are no roses that are red (i) and all red flowers fade quickly (ii), then it is not possible for there to exist any rose that fades quickly (iii). This inference is valid because the condition in (ii) implies that only red flowers fade quickly, and if there are no red roses, then there are no roses that fade quickly.
Inference 4: If (i) is false and (ii) is false, then (iii) is false.
If there are no roses that are red (i) and not all red flowers fade quickly (ii), then it is not possible for there to exist any rose that fades quickly (iii). This inference is valid because the condition in (ii) does not imply that all roses fade quickly, and the condition in (i) implies that there are no red roses.
Conclusion:
Based on the logical inferences, we can conclude that if both (i) and (ii) are true, then (iii) is true. Hence, option 'C' is the correct answer.
(i) Some roses are red.
(ii) All red flowers fade quickly.
(iii) Some roses fade quickly.
Explanation:
To determine which statements can be logically inferred from the given statements, we need to analyze the relationships and implications between them.
Statement (i): Some roses are red.
This statement implies that there exists at least one rose that is red. It does not provide any information about other roses or flowers.
Statement (ii): All red flowers fade quickly.
This statement implies that every red flower fades quickly. It does not provide any information about roses that are not red or about roses in general.
Statement (iii): Some roses fade quickly.
This statement implies that there exists at least one rose that fades quickly. It does not provide any information about the color of the roses or about other flowers.
Logical Inferences:
Based on the given statements, we can make the following logical inferences:
Inference 1: If (i) is true and (ii) is true, then (iii) is true.
If there exists at least one rose that is red (i) and all red flowers fade quickly (ii), then it is implied that there exists at least one rose that fades quickly (iii). This inference is valid because the conditions in (i) and (ii) are fulfilled.
Inference 2: If (i) is true and (ii) is false, then (iii) is true.
If there exists at least one rose that is red (i) and not all red flowers fade quickly (ii), then it is still possible for there to exist at least one rose that fades quickly (iii). This inference is valid because the conditions in (i) are fulfilled, and the condition in (ii) does not contradict the possibility of (iii).
Inference 3: If (i) is false and (ii) is true, then (iii) is false.
If there are no roses that are red (i) and all red flowers fade quickly (ii), then it is not possible for there to exist any rose that fades quickly (iii). This inference is valid because the condition in (ii) implies that only red flowers fade quickly, and if there are no red roses, then there are no roses that fade quickly.
Inference 4: If (i) is false and (ii) is false, then (iii) is false.
If there are no roses that are red (i) and not all red flowers fade quickly (ii), then it is not possible for there to exist any rose that fades quickly (iii). This inference is valid because the condition in (ii) does not imply that all roses fade quickly, and the condition in (i) implies that there are no red roses.
Conclusion:
Based on the logical inferences, we can conclude that if both (i) and (ii) are true, then (iii) is true. Hence, option 'C' is the correct answer.
Choose the correct verb to fill in the blank below:
Let us ________.- a)Introvert
- b)alternate
- c)atheist
- d)altruist
Correct answer is option 'B'. Can you explain this answer?
Choose the correct verb to fill in the blank below:
Let us ________.
Let us ________.
a)
Introvert
b)
alternate
c)
atheist
d)
altruist
|
|
Akash Rane answered |
Answer:
Explanation:
The correct verb to fill in the blank is "alternate" (option B).
Meaning of the options:
1. Introvert: This is a noun that refers to a person who is predominantly concerned with their own thoughts and feelings, rather than with external things.
2. Alternate: This is a verb that means to take turns or to occur in turns repeatedly.
3. Atheist: This is a noun that refers to a person who does not believe in the existence of a god or gods.
4. Altruist: This is a noun that refers to a person who has a selfless concern for the well-being of others.
Explanation of the Answer:
1. Option A (Introvert): This is not the correct verb to fill in the blank. "Introvert" is a noun, and it does not make sense to use it as a verb in this context.
2. Option B (Alternate): This is the correct verb to fill in the blank. The phrase "Let us alternate" means to take turns or to switch roles or positions with someone.
3. Option C (Atheist): This is not the correct verb to fill in the blank. "Atheist" is a noun, and it does not make sense to use it as a verb in this context.
4. Option D (Altruist): This is not the correct verb to fill in the blank. "Altruist" is a noun, and it does not make sense to use it as a verb in this context.
Conclusion:
The correct verb to fill in the blank is "alternate" (option B).
Explanation:
The correct verb to fill in the blank is "alternate" (option B).
Meaning of the options:
1. Introvert: This is a noun that refers to a person who is predominantly concerned with their own thoughts and feelings, rather than with external things.
2. Alternate: This is a verb that means to take turns or to occur in turns repeatedly.
3. Atheist: This is a noun that refers to a person who does not believe in the existence of a god or gods.
4. Altruist: This is a noun that refers to a person who has a selfless concern for the well-being of others.
Explanation of the Answer:
1. Option A (Introvert): This is not the correct verb to fill in the blank. "Introvert" is a noun, and it does not make sense to use it as a verb in this context.
2. Option B (Alternate): This is the correct verb to fill in the blank. The phrase "Let us alternate" means to take turns or to switch roles or positions with someone.
3. Option C (Atheist): This is not the correct verb to fill in the blank. "Atheist" is a noun, and it does not make sense to use it as a verb in this context.
4. Option D (Altruist): This is not the correct verb to fill in the blank. "Altruist" is a noun, and it does not make sense to use it as a verb in this context.
Conclusion:
The correct verb to fill in the blank is "alternate" (option B).
Lamenting the gradual sidelining of the arts ill school curricula, a group of prominent artist wrote to the Chief Minister last year, asking him to allocate more funds to support arts education in schools. However, no such increases have been announced in this year’s Budget. The artists expressed their deep anguish at their request not being approved, but many of them remain optimistic about funding in the future.
Which of the statement (s) below is/are logically valid and can be inferred from the above statements?
(i) The artists expected funding for the arts to increases this year
(ii) The Chief Minister was receptive to the idea of increasing funding of the arts
(iii) The Chief Minister is a prominent artist
(iv) Schools are giving less importance to arts education nowadays- a)(iii) and (iv
- b)(i) and (iv)
- c)(i), (ii) and (iv)
- d)(i) and (iii)
Correct answer is option 'B'. Can you explain this answer?
Lamenting the gradual sidelining of the arts ill school curricula, a group of prominent artist wrote to the Chief Minister last year, asking him to allocate more funds to support arts education in schools. However, no such increases have been announced in this year’s Budget. The artists expressed their deep anguish at their request not being approved, but many of them remain optimistic about funding in the future.
Which of the statement (s) below is/are logically valid and can be inferred from the above statements?
(i) The artists expected funding for the arts to increases this year
(ii) The Chief Minister was receptive to the idea of increasing funding of the arts
(iii) The Chief Minister is a prominent artist
(iv) Schools are giving less importance to arts education nowadays
Which of the statement (s) below is/are logically valid and can be inferred from the above statements?
(i) The artists expected funding for the arts to increases this year
(ii) The Chief Minister was receptive to the idea of increasing funding of the arts
(iii) The Chief Minister is a prominent artist
(iv) Schools are giving less importance to arts education nowadays
a)
(iii) and (iv
b)
(i) and (iv)
c)
(i), (ii) and (iv)
d)
(i) and (iii)
|
|
Sudhir Patel answered |
From first line in para its clear that schools are giving less importance to arts education. hence (iv)
However, no such increase has been announced in this year's Budget.
From this line we can infer that artists are expected funding for arts to increase this year.
However, no such increase has been announced in this year's Budget.
From this line we can infer that artists are expected funding for arts to increase this year.
A train that is 280 metres long, travelling at a uniform speed, crosses a platform in 60 seconds and passes a man standing on the platform in 20 seconds. What is the length of the platform in metres?- a)440
- b)480
- c)520
- d)560
Correct answer is option 'D'. Can you explain this answer?
A train that is 280 metres long, travelling at a uniform speed, crosses a platform in 60 seconds and passes a man standing on the platform in 20 seconds. What is the length of the platform in metres?
a)
440
b)
480
c)
520
d)
560
|
|
Dipika Choudhary answered |
To solve this problem, we need to understand the concept of relative speed and the time it takes for the train to cross both the platform and the man standing on the platform.
Let's break down the problem step by step:
1. Understanding the situation:
- The train is 280 metres long.
- The train crosses a platform in 60 seconds.
- The train passes a man standing on the platform in 20 seconds.
2. Calculating the speed of the train:
- We know that speed is equal to distance divided by time.
- Let's assume the speed of the train is 'v' m/s.
- The distance covered by the train to cross the platform is the sum of the length of the train and the length of the platform.
- So, the distance covered by the train to cross the platform is 280 + length of the platform.
- The time taken to cross the platform is given as 60 seconds.
- Therefore, the speed of the train is (280 + length of the platform) / 60 m/s.
3. Calculating the distance traveled by the train to pass the man:
- The distance traveled by the train to pass the man is equal to the length of the train.
- The time taken to pass the man is given as 20 seconds.
- Therefore, the distance traveled by the train to pass the man is 280 metres.
4. Setting up the equations:
- We can equate the two distances traveled by the train in terms of time.
- (280 + length of the platform) / 60 = 280 / 20
- Solving this equation will give us the length of the platform.
5. Solving the equation:
- Cross multiplying the equation, we get:
(280 + length of the platform) * 20 = 280 * 60
- Expanding and simplifying the equation, we get:
5600 + 20 * length of the platform = 16800
20 * length of the platform = 11200
length of the platform = 560
Therefore, the length of the platform is 560 metres, which corresponds to option 'D'.
Let's break down the problem step by step:
1. Understanding the situation:
- The train is 280 metres long.
- The train crosses a platform in 60 seconds.
- The train passes a man standing on the platform in 20 seconds.
2. Calculating the speed of the train:
- We know that speed is equal to distance divided by time.
- Let's assume the speed of the train is 'v' m/s.
- The distance covered by the train to cross the platform is the sum of the length of the train and the length of the platform.
- So, the distance covered by the train to cross the platform is 280 + length of the platform.
- The time taken to cross the platform is given as 60 seconds.
- Therefore, the speed of the train is (280 + length of the platform) / 60 m/s.
3. Calculating the distance traveled by the train to pass the man:
- The distance traveled by the train to pass the man is equal to the length of the train.
- The time taken to pass the man is given as 20 seconds.
- Therefore, the distance traveled by the train to pass the man is 280 metres.
4. Setting up the equations:
- We can equate the two distances traveled by the train in terms of time.
- (280 + length of the platform) / 60 = 280 / 20
- Solving this equation will give us the length of the platform.
5. Solving the equation:
- Cross multiplying the equation, we get:
(280 + length of the platform) * 20 = 280 * 60
- Expanding and simplifying the equation, we get:
5600 + 20 * length of the platform = 16800
20 * length of the platform = 11200
length of the platform = 560
Therefore, the length of the platform is 560 metres, which corresponds to option 'D'.
500 students are taking one or more courses out of Chemistry, Physics, and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329). Physics (186).Mathematics (295). Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects?- a)37
- b)43
- c)47
- d)53
Correct answer is option 'D'. Can you explain this answer?
500 students are taking one or more courses out of Chemistry, Physics, and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329). Physics (186).Mathematics (295). Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects?
a)
37
b)
43
c)
47
d)
53
|
|
Megha Bajaj answered |
To solve this problem, we can use the principle of inclusion-exclusion. We have the number of students enrolled in each subject, as well as the number of students enrolled in each combination of subjects.
Let's break down the problem step by step:
1. Find the number of students taking at least one subject:
- Number of students taking Chemistry = 329
- Number of students taking Physics = 186
- Number of students taking Mathematics = 295
To find the total number of students taking at least one subject, we can add the individual counts and subtract the counts of students taking two or more subjects (to avoid double counting):
Total = Chemistry + Physics + Mathematics - (Chemistry and Physics) - (Chemistry and Mathematics) - (Physics and Mathematics)
Total = 329 + 186 + 295 - 83 - 217 - 63
Total = 447
Therefore, there are 447 students taking at least one subject.
2. Find the number of students taking exactly two subjects:
- Number of students taking Chemistry and Physics = 83
- Number of students taking Chemistry and Mathematics = 217
- Number of students taking Physics and Mathematics = 63
To find the total number of students taking exactly two subjects, we can add the counts of students taking two subjects:
Total = (Chemistry and Physics) + (Chemistry and Mathematics) + (Physics and Mathematics)
Total = 83 + 217 + 63
Total = 363
Therefore, there are 363 students taking exactly two subjects.
3. Find the number of students taking all three subjects:
To find the number of students taking all three subjects, we can subtract the number of students taking at least one subject from the total number of students:
Number of students taking all three subjects = Total - (Chemistry + Physics + Mathematics)
Number of students taking all three subjects = 447 - (329 + 186 + 295)
Number of students taking all three subjects = 447 - 810
Number of students taking all three subjects = -363
However, it is not possible to have a negative number of students. This means that there is an error in the information given or the calculations made. Please double-check the given data and calculations to determine the correct answer.
Let's break down the problem step by step:
1. Find the number of students taking at least one subject:
- Number of students taking Chemistry = 329
- Number of students taking Physics = 186
- Number of students taking Mathematics = 295
To find the total number of students taking at least one subject, we can add the individual counts and subtract the counts of students taking two or more subjects (to avoid double counting):
Total = Chemistry + Physics + Mathematics - (Chemistry and Physics) - (Chemistry and Mathematics) - (Physics and Mathematics)
Total = 329 + 186 + 295 - 83 - 217 - 63
Total = 447
Therefore, there are 447 students taking at least one subject.
2. Find the number of students taking exactly two subjects:
- Number of students taking Chemistry and Physics = 83
- Number of students taking Chemistry and Mathematics = 217
- Number of students taking Physics and Mathematics = 63
To find the total number of students taking exactly two subjects, we can add the counts of students taking two subjects:
Total = (Chemistry and Physics) + (Chemistry and Mathematics) + (Physics and Mathematics)
Total = 83 + 217 + 63
Total = 363
Therefore, there are 363 students taking exactly two subjects.
3. Find the number of students taking all three subjects:
To find the number of students taking all three subjects, we can subtract the number of students taking at least one subject from the total number of students:
Number of students taking all three subjects = Total - (Chemistry + Physics + Mathematics)
Number of students taking all three subjects = 447 - (329 + 186 + 295)
Number of students taking all three subjects = 447 - 810
Number of students taking all three subjects = -363
However, it is not possible to have a negative number of students. This means that there is an error in the information given or the calculations made. Please double-check the given data and calculations to determine the correct answer.
“Going by the _________ that many hands make light work, the school _______ involved all the students in the task.”Q. The words that best fill the blanks in the above sentence are- a)principle, principal
- b)principal, principle
- c)principle, principle
- d)principal, principal
Correct answer is option 'A'. Can you explain this answer?
“Going by the _________ that many hands make light work, the school _______ involved all the students in the task.”
Q. The words that best fill the blanks in the above sentence are
a)
principle, principal
b)
principal, principle
c)
principle, principle
d)
principal, principal
|
|
Sudhir Patel answered |
The correct answer is Option A.
Principle: a fundamental truth or proposition that serves as the foundation for a system of belief or behavior or for a chain of reasoning.
Principal: the head of a school, college, or other educational institution.
As per the question, 'Many hands make light work' is the Principle used by the School Principal to involve all the students in the task, denotes the correct usage.
A person moving through a tuberculosis prone zone has a 50% probability of becoming infected.However, only 30% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease?- a)15
- b)33
- c)35
- d)37
Correct answer is option 'C'. Can you explain this answer?
A person moving through a tuberculosis prone zone has a 50% probability of becoming infected.However, only 30% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease?
a)
15
b)
33
c)
35
d)
37
|
|
Gopal Gupta answered |
To solve this problem, we need to calculate the percentage of people who remain infected but do not show symptoms of tuberculosis.
Let's assume that 100 people are moving through the tuberculosis prone zone.
1. Calculate the number of people who become infected:
Out of the 100 people, there is a 50% probability of becoming infected. So, 50 people become infected.
2. Calculate the number of infected people who develop the disease:
Out of the 50 infected people, only 30% develop the disease. So, 30% of 50 is (30/100) * 50 = 15 people develop the disease.
3. Calculate the number of infected people who do not develop the disease:
The remaining infected people who do not develop the disease can be calculated by subtracting the number of people who develop the disease from the total number of infected people.
So, the number of infected people who do not develop the disease is 50 - 15 = 35 people.
4. Calculate the percentage of people who remain infected but do not show symptoms:
To find the percentage, we divide the number of infected people who do not develop the disease by the total number of people and multiply by 100.
Therefore, the percentage is (35/100) * 100 = 35%.
Hence, the correct answer is option C) 35%.
Let's assume that 100 people are moving through the tuberculosis prone zone.
1. Calculate the number of people who become infected:
Out of the 100 people, there is a 50% probability of becoming infected. So, 50 people become infected.
2. Calculate the number of infected people who develop the disease:
Out of the 50 infected people, only 30% develop the disease. So, 30% of 50 is (30/100) * 50 = 15 people develop the disease.
3. Calculate the number of infected people who do not develop the disease:
The remaining infected people who do not develop the disease can be calculated by subtracting the number of people who develop the disease from the total number of infected people.
So, the number of infected people who do not develop the disease is 50 - 15 = 35 people.
4. Calculate the percentage of people who remain infected but do not show symptoms:
To find the percentage, we divide the number of infected people who do not develop the disease by the total number of people and multiply by 100.
Therefore, the percentage is (35/100) * 100 = 35%.
Hence, the correct answer is option C) 35%.
Choose the most appropriate phrase from the options given below to complete the following sentence.The aircraft_______ take off as soon as its flight plan was filed.- a)is allowed to
- b)will be allowed to
- c)was allowed to
- d)has been allowed to
Correct answer is option 'C'. Can you explain this answer?
Choose the most appropriate phrase from the options given below to complete the following sentence.The aircraft_______ take off as soon as its flight plan was filed.
a)
is allowed to
b)
will be allowed to
c)
was allowed to
d)
has been allowed to
|
|
Anjana Deshpande answered |
The most appropriate phrase to complete the given sentence is "was allowed to". Here is the detailed explanation:
Understanding the sentence:
The sentence is talking about an aircraft and its takeoff. It states that the aircraft took off as soon as its flight plan was filed. We need to choose the correct phrase to complete the sentence.
Options:
a) is allowed to
b) will be allowed to
c) was allowed to
d) has been allowed to
Explanation:
To determine the correct phrase, let's analyze each option:
a) is allowed to: This phrase indicates a present state of permission. However, the sentence is in the past tense, so this option is not suitable.
b) will be allowed to: This phrase indicates future permission. Again, the sentence is in the past tense, so this option is not appropriate.
c) was allowed to: This phrase indicates that the aircraft had permission to take off in the past. Since the sentence is in the past tense, this option fits perfectly. It shows that the aircraft had the necessary authorization to take off after its flight plan was filed.
d) has been allowed to: This phrase indicates a past action with present relevance. However, the sentence does not require present relevance, as it simply talks about a past event. Therefore, this option is not the most appropriate.
Conclusion:
The correct phrase to complete the sentence is "was allowed to". It accurately conveys that the aircraft had permission to take off in the past after its flight plan was filed.
Understanding the sentence:
The sentence is talking about an aircraft and its takeoff. It states that the aircraft took off as soon as its flight plan was filed. We need to choose the correct phrase to complete the sentence.
Options:
a) is allowed to
b) will be allowed to
c) was allowed to
d) has been allowed to
Explanation:
To determine the correct phrase, let's analyze each option:
a) is allowed to: This phrase indicates a present state of permission. However, the sentence is in the past tense, so this option is not suitable.
b) will be allowed to: This phrase indicates future permission. Again, the sentence is in the past tense, so this option is not appropriate.
c) was allowed to: This phrase indicates that the aircraft had permission to take off in the past. Since the sentence is in the past tense, this option fits perfectly. It shows that the aircraft had the necessary authorization to take off after its flight plan was filed.
d) has been allowed to: This phrase indicates a past action with present relevance. However, the sentence does not require present relevance, as it simply talks about a past event. Therefore, this option is not the most appropriate.
Conclusion:
The correct phrase to complete the sentence is "was allowed to". It accurately conveys that the aircraft had permission to take off in the past after its flight plan was filed.
Which one of the statements is logically valid and can be inferred from the sentence given below?One inter-continental flight causes more pollution than twelve months of car travel. Consider Carbon dioxide as the major emission in the pollution.- a)Carbon dioxide emissions are higher from cars than flights.
- b)Carbon dioxide emissions are higher from flights than cars.
- c)Flights are a major contributor to global warming.
- d)None of the above.
Correct answer is option 'B'. Can you explain this answer?
Which one of the statements is logically valid and can be inferred from the sentence given below?
One inter-continental flight causes more pollution than twelve months of car travel. Consider Carbon dioxide as the major emission in the pollution.
a)
Carbon dioxide emissions are higher from cars than flights.
b)
Carbon dioxide emissions are higher from flights than cars.
c)
Flights are a major contributor to global warming.
d)
None of the above.
|
|
Naina Tiwari answered |
Statement: One inter-continental flight causes more pollution than twelve months of car travel. Consider Carbon dioxide as the major emission in the pollution.
Inference: Carbon dioxide emissions are higher from flights than cars.
Explanation:
1. Understanding the given statement:
The given statement tells us that one inter-continental flight causes more pollution than twelve months of car travel. It specifically mentions carbon dioxide as the major emission in the pollution.
2. Comparison between inter-continental flights and car travel:
To determine which mode of transportation emits more carbon dioxide, we need to compare the carbon dioxide emissions from inter-continental flights and cars.
3. Carbon dioxide emissions from one inter-continental flight:
According to the given statement, one inter-continental flight causes more pollution than twelve months of car travel. This implies that the carbon dioxide emissions from one inter-continental flight are higher than the carbon dioxide emissions from twelve months of car travel.
4. Reasoning behind the inference:
Since the given statement states that one inter-continental flight causes more pollution than twelve months of car travel, and carbon dioxide is considered the major emission, it can be inferred that the carbon dioxide emissions from flights are higher than the carbon dioxide emissions from cars.
5. Inference:
Based on the above reasoning, the logically valid inference from the given statement is that carbon dioxide emissions are higher from flights than cars.
Therefore, the correct answer is option 'B' - Carbon dioxide emissions are higher from flights than cars.
Inference: Carbon dioxide emissions are higher from flights than cars.
Explanation:
1. Understanding the given statement:
The given statement tells us that one inter-continental flight causes more pollution than twelve months of car travel. It specifically mentions carbon dioxide as the major emission in the pollution.
2. Comparison between inter-continental flights and car travel:
To determine which mode of transportation emits more carbon dioxide, we need to compare the carbon dioxide emissions from inter-continental flights and cars.
3. Carbon dioxide emissions from one inter-continental flight:
According to the given statement, one inter-continental flight causes more pollution than twelve months of car travel. This implies that the carbon dioxide emissions from one inter-continental flight are higher than the carbon dioxide emissions from twelve months of car travel.
4. Reasoning behind the inference:
Since the given statement states that one inter-continental flight causes more pollution than twelve months of car travel, and carbon dioxide is considered the major emission, it can be inferred that the carbon dioxide emissions from flights are higher than the carbon dioxide emissions from cars.
5. Inference:
Based on the above reasoning, the logically valid inference from the given statement is that carbon dioxide emissions are higher from flights than cars.
Therefore, the correct answer is option 'B' - Carbon dioxide emissions are higher from flights than cars.
He is known for his unscrupulous ways. He always sheds ____ tears to deceive people.- a)fox's
- b)crocodile's
- c)crocodile
- d)fox
Correct answer is option 'C'. Can you explain this answer?
He is known for his unscrupulous ways. He always sheds ____ tears to deceive people.
a)
fox's
b)
crocodile's
c)
crocodile
d)
fox
|
|
Sudhir Patel answered |
The correct answer is Option C i.e. Crocodile
"Crocodile tears" is a phrase that means - to put on an insincere show of sorrow. When someone feigns sadness they 'cry crocodile tears' a phrase that comes from an old myth that the animals cry while eating.
Complete sentence: He is known for his unscrupulous ways. He always sheds Crocodile tears to deceive people.
Given (9 inches)1/2 = (0.25 yards) 1/2, which one of the following statements is TRUE?- a)3 inches = 0.5 yards
- b)9 inches = 1.5 yards
- c)9 inches = 0.25 yards
- d)81 inches = 0.0625 yards
Correct answer is option 'C'. Can you explain this answer?
Given (9 inches)1/2 = (0.25 yards) 1/2, which one of the following statements is TRUE?
a)
3 inches = 0.5 yards
b)
9 inches = 1.5 yards
c)
9 inches = 0.25 yards
d)
81 inches = 0.0625 yards
|
Sahana Chavan answered |
Understanding the Given Equation
The equation (9 inches)^(1/2) = (0.25 yards)^(1/2) indicates that the square roots of both sides are equivalent. To analyze this, we can simplify both sides.
Evaluating Each Side
- The square root of 9 inches is 3 inches.
- The square root of 0.25 yards is 0.5 yards (since 0.25 is the same as 1/4).
So, we have:
- 3 inches = 0.5 yards
Verifying the Options
Now, let’s assess each option:
- a) 3 inches = 0.5 yards
This statement is true, as derived from the equation.
- b) 9 inches = 1.5 yards
To check this, convert 9 inches to yards:
9 inches ÷ 36 = 0.25 yards.
This is false.
- c) 9 inches = 0.25 yards
As calculated above, this is true.
- d) 81 inches = 0.0625 yards
Converting 81 inches to yards:
81 inches ÷ 36 = 2.25 yards.
This is false.
Conclusion
The correct statement, based on the calculations and conversions, confirms that option 'C' is indeed true:
9 inches = 0.25 yards
The equation (9 inches)^(1/2) = (0.25 yards)^(1/2) indicates that the square roots of both sides are equivalent. To analyze this, we can simplify both sides.
Evaluating Each Side
- The square root of 9 inches is 3 inches.
- The square root of 0.25 yards is 0.5 yards (since 0.25 is the same as 1/4).
So, we have:
- 3 inches = 0.5 yards
Verifying the Options
Now, let’s assess each option:
- a) 3 inches = 0.5 yards
This statement is true, as derived from the equation.
- b) 9 inches = 1.5 yards
To check this, convert 9 inches to yards:
9 inches ÷ 36 = 0.25 yards.
This is false.
- c) 9 inches = 0.25 yards
As calculated above, this is true.
- d) 81 inches = 0.0625 yards
Converting 81 inches to yards:
81 inches ÷ 36 = 2.25 yards.
This is false.
Conclusion
The correct statement, based on the calculations and conversions, confirms that option 'C' is indeed true:
9 inches = 0.25 yards
Choose the statement(s) where the underlined word is used correctly:(i) A prone is a dried plum.(ii) He was lying prone on the floor.(iii) People who eat a lot of fat are prone to heart disease.- a)(i) and (iii) only
- b)(iii) only
- c)(i) and (ii) only
- d)(ii) and (iii) only
Correct answer is option 'D'. Can you explain this answer?
Choose the statement(s) where the underlined word is used correctly:
(i) A prone is a dried plum.
(ii) He was lying prone on the floor.
(iii) People who eat a lot of fat are prone to heart disease.
a)
(i) and (iii) only
b)
(iii) only
c)
(i) and (ii) only
d)
(ii) and (iii) only
|
|
Sudhir Patel answered |
The word ‘prone’ means to be susceptible to something or lying flat. Thus, the correct sentence in which it has been used is (II) and (III).
In the first sentence, the word to be used is ‘prune’. A prune is a dried plum of any cultivar.
A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs. The probability that the current batch is accepted is _________- a)0.6145
- b)0.7145
- c)0.8145
- d)0.9145
Correct answer is option 'C'. Can you explain this answer?
A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs. The probability that the current batch is accepted is _________
a)
0.6145
b)
0.7145
c)
0.8145
d)
0.9145
|
|
Sudhir Patel answered |
Probability for one bulb to be non defective is 
∴ Probabilities that none of the bulbs is defectives
Binomial Problem with n = 4 and p(not defective) = 0.95
P(x = 4 non defective) = 0.95 x 4 = 0.8145
∴ Probabilities that none of the bulbs is defectives
Binomial Problem with n = 4 and p(not defective) = 0.95
P(x = 4 non defective) = 0.95 x 4 = 0.8145
Crowd funding deals with mobilisation of funds for a project from a large number of people, who would be willing to invest smaller amounts through web-based platforms in the project.
Based on the above paragraph, which of the following is correct about crowd funding?- a)Funds raised through unwilling contributions on web-based platforms.
- b)Funds raised through large contributions on web-based platforms.
- c)Funds raised through coerced contributions on web-based platforms.
- d)Funds raised through voluntary contributions on web-based platforms
Correct answer is option 'D'. Can you explain this answer?
Crowd funding deals with mobilisation of funds for a project from a large number of people, who would be willing to invest smaller amounts through web-based platforms in the project.
Based on the above paragraph, which of the following is correct about crowd funding?
Based on the above paragraph, which of the following is correct about crowd funding?
a)
Funds raised through unwilling contributions on web-based platforms.
b)
Funds raised through large contributions on web-based platforms.
c)
Funds raised through coerced contributions on web-based platforms.
d)
Funds raised through voluntary contributions on web-based platforms
|
|
Sudhir Patel answered |
The correct answer is Option D i.e. Funds raised through voluntary contributions on web-based platforms.
After reading the above paragraph one can easily comprehend that a large number of people voluntarily (proceeding from the will or from one's own choice or consent) invested in small amounts for the crowd-funding, now let's go through each option one by one.
- Option A states that- "Funds raised through unwilling contributions on web-based platforms.", this option is incorrect because the contribution was made willingly in small amounts by a large number of peoples.
- Option B states that- "Funds raised through large contributions on web-based platforms.", this option is incorrect, it has been clearly mentioned in the passage that a large number of people invest small amounts. (Large contributions are mentioned nowhere in the paragraph)
- Option C states that- "Funds raised through coerced contributions on web-based platforms.", Coerced means to compel to an act or choice or to achieve by force or threat, people were not forced to make a contribution in this crowd-funding they willingly invested small amounts. Hence, this option is incorrect as well.
A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.- a)1 : 4
- b)1 : 3
- c)1 : 2
- d)2 : 3
Correct answer is option 'C'. Can you explain this answer?
A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.
a)
1 : 4
b)
1 : 3
c)
1 : 2
d)
2 : 3
|
|
Nayanika Sengupta answered |
Understanding the Problem
To solve this problem, we first need to visualize the setup. A cube with a side length of 3 units consists of smaller cubes, each with a side length of 1 unit.
Calculating the Number of Smaller Cubes
- The total number of smaller cubes in the larger cube is:
- Volume of larger cube = 3^3 = 27
- Therefore, there are 27 smaller cubes (1 unit each).
Faces of Smaller Cubes
- Each smaller cube has 6 faces.
- Total faces of all smaller cubes = 27 * 6 = 162 faces.
Visible Faces Calculation
- To determine the number of visible faces, we need to analyze the arrangement of the smaller cubes in the larger cube.
- The cubes on the surface of the larger cube are the ones whose faces are visible.
Identifying Visible Faces
- The cubes on the corners contribute 3 visible faces each (8 corners).
- The cubes on the edges contribute 2 visible faces each (12 edges, 1 cube per edge).
- The cubes on the faces contribute 1 visible face each (6 faces, 1 cube per face).
- By careful counting:
- Corner cubes = 8 cubes * 3 faces = 24 visible faces
- Edge cubes = 12 cubes * 2 faces = 24 visible faces
- Face cubes = 6 cubes * 1 face = 6 visible faces
- Total visible faces = 24 + 24 + 6 = 54 faces.
Calculating Non-visible Faces
- Total faces = 162 (calculated previously).
- Non-visible faces = Total faces - Visible faces = 162 - 54 = 108 faces.
Finding the Proportion
- Proportion of visible to non-visible faces = 54 : 108 = 1 : 2.
Thus, the correct answer is option 'C': 1 : 2.
To solve this problem, we first need to visualize the setup. A cube with a side length of 3 units consists of smaller cubes, each with a side length of 1 unit.
Calculating the Number of Smaller Cubes
- The total number of smaller cubes in the larger cube is:
- Volume of larger cube = 3^3 = 27
- Therefore, there are 27 smaller cubes (1 unit each).
Faces of Smaller Cubes
- Each smaller cube has 6 faces.
- Total faces of all smaller cubes = 27 * 6 = 162 faces.
Visible Faces Calculation
- To determine the number of visible faces, we need to analyze the arrangement of the smaller cubes in the larger cube.
- The cubes on the surface of the larger cube are the ones whose faces are visible.
Identifying Visible Faces
- The cubes on the corners contribute 3 visible faces each (8 corners).
- The cubes on the edges contribute 2 visible faces each (12 edges, 1 cube per edge).
- The cubes on the faces contribute 1 visible face each (6 faces, 1 cube per face).
- By careful counting:
- Corner cubes = 8 cubes * 3 faces = 24 visible faces
- Edge cubes = 12 cubes * 2 faces = 24 visible faces
- Face cubes = 6 cubes * 1 face = 6 visible faces
- Total visible faces = 24 + 24 + 6 = 54 faces.
Calculating Non-visible Faces
- Total faces = 162 (calculated previously).
- Non-visible faces = Total faces - Visible faces = 162 - 54 = 108 faces.
Finding the Proportion
- Proportion of visible to non-visible faces = 54 : 108 = 1 : 2.
Thus, the correct answer is option 'C': 1 : 2.
The student _____the teacher on teachers' day for twenty years of dedicated teaching.
- a)facilitated
- b)felicitated
- c)fantasized
- d)Fabricated
Correct answer is option 'B'. Can you explain this answer?
The student _____the teacher on teachers' day for twenty years of dedicated teaching.
a)
facilitated
b)
felicitated
c)
fantasized
d)
Fabricated
|
|
Sudhir Patel answered |
(i) Facilitated: to make easier or less difficult; help forward (an action, a process, etc.)
(ii) Felicitated: to compliment upon a happy event; congratulate.
(iii) Fantasized: to create in one's fancy, daydreams, or the like; imagine
(iv) Facillitated: incorrect word
The student’s felicitated the teacher on teachers' day for twenty years of dedicated teaching
(ii) Felicitated: to compliment upon a happy event; congratulate.
(iii) Fantasized: to create in one's fancy, daydreams, or the like; imagine
(iv) Facillitated: incorrect word
The student’s felicitated the teacher on teachers' day for twenty years of dedicated teaching
After India's cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket till then, decided to concentrate only on cricket. And the rest is history.
What does the underlined phrase mean in this context?- a)History will rest in peace
- b)rest is recorded in history books
- c)Rest is well known
- d)rest is archaic
Correct answer is option 'C'. Can you explain this answer?
After India's cricket world cup victory in 1985, Shrotria who was playing both tennis and cricket till then, decided to concentrate only on cricket. And the rest is history.
What does the underlined phrase mean in this context?
What does the underlined phrase mean in this context?
a)
History will rest in peace
b)
rest is recorded in history books
c)
Rest is well known
d)
rest is archaic
|
|
Sudhir Patel answered |
The phrasal verb "rest is history" means that the later part of the story is well known
An electric bus has onboard instruments that report the total electricity consumed since the start of the trip as well as the total distance covered. During a single day of operation, the bust travels on stretches M, N, O and P, in that order. The cumulative distances traveled and the corresponding electricity consumption are shown in the Table below:
Q. The stretch where the electricity consumption per km is minimum is- a)M
- b)N
- c)O
- d)P
Correct answer is option 'D'. Can you explain this answer?
An electric bus has onboard instruments that report the total electricity consumed since the start of the trip as well as the total distance covered. During a single day of operation, the bust travels on stretches M, N, O and P, in that order. The cumulative distances traveled and the corresponding electricity consumption are shown in the Table below:
Q. The stretch where the electricity consumption per km is minimum is
Q. The stretch where the electricity consumption per km is minimum is
a)
M
b)
N
c)
O
d)
P
|
Khushi Chaurasiya answered |
Correct answer -(D)
The sum of eight consecutive odd numbers is 656. The average of four consecutive even numbers is 87. What is the sum of the smallest odd number and second largest even number?- a)125
- b)144
- c)158
- d)163
Correct answer is option 'D'. Can you explain this answer?
The sum of eight consecutive odd numbers is 656. The average of four consecutive even numbers is 87. What is the sum of the smallest odd number and second largest even number?
a)
125
b)
144
c)
158
d)
163
|
|
Sudhir Patel answered |
The sum of 8 consecutive odd numbers is 656
⇒ Average of the 8 odd numbers = 656/8 = 82
the odd numbers immediately preceding and succeeding 82 are 81 are 83 respectively and these will be the middle numbers.
Therefore, we see that 4th and 5th odd numbers are 81 and 83 respectively.
Thus we can easily obtain the odd numbers as 75, 77, 79, 81, 83, 85, 87, 89 and smallest odd number as 75
the average of four consecutive even numbers is 87
As seen earlier, 86 and 88 will be 2nd and 3rd even numbers.
i.e., 84, 86, 88 and 90 will be the even numbers and the second largest even number is 88
Therefore required sum is 75 + 88 = 163
⇒ Average of the 8 odd numbers = 656/8 = 82
the odd numbers immediately preceding and succeeding 82 are 81 are 83 respectively and these will be the middle numbers.
Therefore, we see that 4th and 5th odd numbers are 81 and 83 respectively.
Thus we can easily obtain the odd numbers as 75, 77, 79, 81, 83, 85, 87, 89 and smallest odd number as 75
the average of four consecutive even numbers is 87
As seen earlier, 86 and 88 will be 2nd and 3rd even numbers.
i.e., 84, 86, 88 and 90 will be the even numbers and the second largest even number is 88
Therefore required sum is 75 + 88 = 163
The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 is- a)781
- b)791
- c)881
- d)891
Correct answer is option 'C'. Can you explain this answer?
The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 is
a)
781
b)
791
c)
881
d)
891
|
Kirti Iyer answered |
Problem:
Find the number of 3-digit numbers such that the digit 1 is never to the immediate right of 2.
Solution:
To solve this problem, we can consider the possible positions of the digits in a 3-digit number and count the number of valid arrangements.
Case 1: 1 is in the first position:
If 1 is in the first position, the second and third digits can be any digit from 0 to 9 except 2. Thus, there are 9 choices for the second digit and 10 choices for the third digit. So, the total number of valid arrangements in this case is 9 * 10 = 90.
Case 2: 1 is in the second position:
If 1 is in the second position, the first digit can be any digit from 1 to 9 except 2. The third digit can be any digit from 0 to 9 except 1. Thus, there are 8 choices for the first digit and 9 choices for the third digit. So, the total number of valid arrangements in this case is 8 * 9 = 72.
Case 3: 1 is in the third position:
If 1 is in the third position, the first and second digits can be any digit from 1 to 9 except 2. Thus, there are 8 choices for the first digit and 9 choices for the second digit. So, the total number of valid arrangements in this case is 8 * 9 = 72.
Total number of valid arrangements:
To find the total number of valid arrangements, we sum up the number of valid arrangements from each case:
Total = 90 + 72 + 72 = 234
However, we need to exclude the numbers with leading zeroes, as they are not 3-digit numbers.
There are 9 choices for the first digit (excluding 0) and 9 choices for the second digit (excluding 1). The third digit can be any digit from 0 to 9 except 1. Thus, there are 9 * 9 * 9 = 729 valid 3-digit numbers.
Final answer:
The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 is 729.
Explanation:
The correct answer is option 'C' (881) because it represents the total count of valid 3-digit numbers.
Find the number of 3-digit numbers such that the digit 1 is never to the immediate right of 2.
Solution:
To solve this problem, we can consider the possible positions of the digits in a 3-digit number and count the number of valid arrangements.
Case 1: 1 is in the first position:
If 1 is in the first position, the second and third digits can be any digit from 0 to 9 except 2. Thus, there are 9 choices for the second digit and 10 choices for the third digit. So, the total number of valid arrangements in this case is 9 * 10 = 90.
Case 2: 1 is in the second position:
If 1 is in the second position, the first digit can be any digit from 1 to 9 except 2. The third digit can be any digit from 0 to 9 except 1. Thus, there are 8 choices for the first digit and 9 choices for the third digit. So, the total number of valid arrangements in this case is 8 * 9 = 72.
Case 3: 1 is in the third position:
If 1 is in the third position, the first and second digits can be any digit from 1 to 9 except 2. Thus, there are 8 choices for the first digit and 9 choices for the second digit. So, the total number of valid arrangements in this case is 8 * 9 = 72.
Total number of valid arrangements:
To find the total number of valid arrangements, we sum up the number of valid arrangements from each case:
Total = 90 + 72 + 72 = 234
However, we need to exclude the numbers with leading zeroes, as they are not 3-digit numbers.
There are 9 choices for the first digit (excluding 0) and 9 choices for the second digit (excluding 1). The third digit can be any digit from 0 to 9 except 1. Thus, there are 9 * 9 * 9 = 729 valid 3-digit numbers.
Final answer:
The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 is 729.
Explanation:
The correct answer is option 'C' (881) because it represents the total count of valid 3-digit numbers.
Find the odd one from the following group:
W, E, K, O, I Q, W, A F, N, T, X N, V, B, D- a)W, E, K, O
- b)I, Q, W, A
- c)F, N, T, X
- d)N, V, B, D
Correct answer is option 'D'. Can you explain this answer?
Find the odd one from the following group:
W, E, K, O, I Q, W, A F, N, T, X N, V, B, D
W, E, K, O, I Q, W, A F, N, T, X N, V, B, D
a)
W, E, K, O
b)
I, Q, W, A
c)
F, N, T, X
d)
N, V, B, D
|
|
Nitya Ahuja answered |
Odd One Out: N, V, B, D
Explanation:
The given group consists of four sets of letters. Each set contains four letters. We need to identify the odd one out from these sets.
Let's analyze each set one by one:
Set 1: W, E, K, O
- These letters are in alphabetical order.
- There is no irregularity or odd one out in this set.
Set 2: I, Q, W, A
- These letters are not in alphabetical order.
- The odd one out in this set is "A" as it does not follow the alphabetical sequence.
Set 3: F, N, T, X
- These letters are not in alphabetical order.
- The odd one out in this set is "F" as it does not follow the alphabetical sequence.
Set 4: N, V, B, D
- These letters are not in alphabetical order.
- The odd one out in this set is "D" as it does not follow the alphabetical sequence.
Therefore, the odd one out from the given group is "N, V, B, D" (Set 4).
In summary, the odd one out is "N, V, B, D" because it is the only set of letters that does not follow the alphabetical sequence.
Explanation:
The given group consists of four sets of letters. Each set contains four letters. We need to identify the odd one out from these sets.
Let's analyze each set one by one:
Set 1: W, E, K, O
- These letters are in alphabetical order.
- There is no irregularity or odd one out in this set.
Set 2: I, Q, W, A
- These letters are not in alphabetical order.
- The odd one out in this set is "A" as it does not follow the alphabetical sequence.
Set 3: F, N, T, X
- These letters are not in alphabetical order.
- The odd one out in this set is "F" as it does not follow the alphabetical sequence.
Set 4: N, V, B, D
- These letters are not in alphabetical order.
- The odd one out in this set is "D" as it does not follow the alphabetical sequence.
Therefore, the odd one out from the given group is "N, V, B, D" (Set 4).
In summary, the odd one out is "N, V, B, D" because it is the only set of letters that does not follow the alphabetical sequence.
Operators □ , ◊ and → are defined by: 
Find the value (66 □ 6) → (66◊6).- a)-2
- b)-1
- c)1
- d)2
Correct answer is option 'C'. Can you explain this answer?
Operators □ , ◊ and → are defined by: Find the value (66 □ 6) → (66◊6).
Find the value (66 □ 6) → (66◊6).a)
-2
b)
-1
c)
1
d)
2
|
|
Pooja Patel answered |
Correct answer is option C) 1
M and N had four children P, Q, R and S. Of them, only P and R were married. They had children X and Y respectively. If Y is a legitimate child of W, which one of the following statements is necessarily FALSE?- a)M is the grandmother of Y
- b)R is the father of Y
- c)W is the wife of R
- d) W is the wife of P
Correct answer is option 'D'. Can you explain this answer?
M and N had four children P, Q, R and S. Of them, only P and R were married. They had children X and Y respectively. If Y is a legitimate child of W, which one of the following statements is necessarily FALSE?
a)
M is the grandmother of Y
b)
R is the father of Y
c)
W is the wife of R
d)
W is the wife of P
|
|
Isha Menon answered |
Given Information:
- M and N have four children: P, Q, R, and S.
- P and R are married.
- P has a child named X.
- R has a child named Y.
- Y is a legitimate child of W.
Analysis:
Let's analyze the given options one by one to determine which one is necessarily false.
a) M is the grandmother of Y:
- Since P is married and has a child named X, M can be the grandmother of X.
- Since R is married and has a child named Y, M can also be the grandmother of Y.
- Therefore, option a) is true.
b) R is the father of Y:
- Given that R has a child named Y, it is true that R is the father of Y.
- Therefore, option b) is true.
c) W is the wife of R:
- The given information states that Y is a legitimate child of W, which means that W is either the mother or the father of Y.
- If W is the mother of Y, then W is the wife of R.
- Therefore, option c) can be true.
d) W is the wife of P:
- The given information states that Y is a legitimate child of W, which means that W is either the mother or the father of Y.
- If W is the mother of Y, then W is the wife of R, not P.
- Therefore, option d) is necessarily false.
Conclusion:
The statement "W is the wife of P" (option d) is necessarily false.
- M and N have four children: P, Q, R, and S.
- P and R are married.
- P has a child named X.
- R has a child named Y.
- Y is a legitimate child of W.
Analysis:
Let's analyze the given options one by one to determine which one is necessarily false.
a) M is the grandmother of Y:
- Since P is married and has a child named X, M can be the grandmother of X.
- Since R is married and has a child named Y, M can also be the grandmother of Y.
- Therefore, option a) is true.
b) R is the father of Y:
- Given that R has a child named Y, it is true that R is the father of Y.
- Therefore, option b) is true.
c) W is the wife of R:
- The given information states that Y is a legitimate child of W, which means that W is either the mother or the father of Y.
- If W is the mother of Y, then W is the wife of R.
- Therefore, option c) can be true.
d) W is the wife of P:
- The given information states that Y is a legitimate child of W, which means that W is either the mother or the father of Y.
- If W is the mother of Y, then W is the wife of R, not P.
- Therefore, option d) is necessarily false.
Conclusion:
The statement "W is the wife of P" (option d) is necessarily false.
A tiger is 50 leaps of its own behind a deer. The tiger takes 5 leaps per minute to the deer’s 4. If the tiger and the deer cover 8 meters and 5 meters per leap respectively. What distance in metres will be tiger have to run before it catches the deer?- a)568
- b)800
- c)400
- d)200
Correct answer is option 'B'. Can you explain this answer?
A tiger is 50 leaps of its own behind a deer. The tiger takes 5 leaps per minute to the deer’s 4. If the tiger and the deer cover 8 meters and 5 meters per leap respectively. What distance in metres will be tiger have to run before it catches the deer?
a)
568
b)
800
c)
400
d)
200
|
Raghav Saha answered |
If the tiger takes 5 leaps per minute towards the deer, it will take 50/5 = <50 =10="">>10 minutes for the tiger to catch up to the deer.
Choose the most appropriate word from the options given below to complete the following sentence.
Q. Communication and interpersonal skills are_____ important in their own ways.- a)each
- b)both
- c)all
- d)either
Correct answer is option 'B'. Can you explain this answer?
Choose the most appropriate word from the options given below to complete the following sentence.
Q. Communication and interpersonal skills are_____ important in their own ways.
Q. Communication and interpersonal skills are_____ important in their own ways.
a)
each
b)
both
c)
all
d)
either
|
|
Sudhir Patel answered |
Interpersonal skills are the skills we use every day when we communicate and interact with other people, both individually and in groups. They include a wide range of skills, but particularly communication skills such as listening and effective speaking. They also include the ability to control and manage your emotions.
A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third quarter. The average speed of the car in km per hour over the entire journey is- a)30
- b)36
- c)40
- d)24
Correct answer is option 'C'. Can you explain this answer?
A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third quarter. The average speed of the car in km per hour over the entire journey is
a)
30
b)
36
c)
40
d)
24
|
|
Ankit Dasgupta answered |
Calculation of Average Speed:
- To calculate the average speed of the car over the entire journey, we need to first determine the total distance covered by the car and the total time taken.
Total Distance Covered:
- The car travels 8 km in the first quarter, 6 km in the second quarter, and 16 km in the third quarter.
- Therefore, the total distance covered is 8 km + 6 km + 16 km = 30 km.
Total Time Taken:
- The car travels 8 km in the first quarter of an hour, 6 km in the second quarter, and 16 km in the third quarter.
- Therefore, the total time taken is 1/4 hour + 1/4 hour + 1/4 hour = 3/4 hour.
Calculation of Average Speed:
- Average speed = Total distance / Total time
- Average speed = 30 km / (3/4) hour
- Average speed = 30 km / 0.75 hour
- Average speed = 40 km/hour
Therefore, the average speed of the car over the entire journey is 40 km/hour. Hence, the correct answer is option 'C'.
- To calculate the average speed of the car over the entire journey, we need to first determine the total distance covered by the car and the total time taken.
Total Distance Covered:
- The car travels 8 km in the first quarter, 6 km in the second quarter, and 16 km in the third quarter.
- Therefore, the total distance covered is 8 km + 6 km + 16 km = 30 km.
Total Time Taken:
- The car travels 8 km in the first quarter of an hour, 6 km in the second quarter, and 16 km in the third quarter.
- Therefore, the total time taken is 1/4 hour + 1/4 hour + 1/4 hour = 3/4 hour.
Calculation of Average Speed:
- Average speed = Total distance / Total time
- Average speed = 30 km / (3/4) hour
- Average speed = 30 km / 0.75 hour
- Average speed = 40 km/hour
Therefore, the average speed of the car over the entire journey is 40 km/hour. Hence, the correct answer is option 'C'.
A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?- a)30
- b)40
- c)120
- d)180
Correct answer is option 'B'. Can you explain this answer?
A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?
a)
30
b)
40
c)
120
d)
180
|
|
Gopal Gupta answered |
To solve this problem, we need to find the length of the side of the square that will minimize the combined area of the square and the rectangle.
Let's assume the length of the side of the square is x mm. Since the sides of the rectangle are in the ratio of 1:2, the length of the rectangle will be 2x mm.
We know that the sum of the lengths of the two parts is equal to the total length of the wire, which is 340 mm. Therefore, we can write the equation:
x + 2x = 340
Simplifying this equation, we get:
3x = 340
Dividing both sides by 3, we find:
x = 113.33 mm
However, we can't have a fractional length for the side of the square, so we need to round it to the nearest whole number. In this case, x ≈ 113 mm.
Now, let's calculate the areas of the square and the rectangle.
Area of the square = x^2
Area of the rectangle = x * 2x = 2x^2
The combined area of the square and the rectangle is given by:
Total area = Area of the square + Area of the rectangle
Total area = x^2 + 2x^2
Total area = 3x^2
To minimize the total area, we need to find the minimum value of 3x^2. Since x is positive, the minimum value of x^2 will occur when x is at its minimum. Therefore, we need to choose the smallest possible value for x, which is 113 mm.
Let's calculate the total area using this value:
Total area = 3 * 113^2
Total area ≈ 38271 mm^2
Now, let's try to find the total area using a different value for x, such as 114 mm:
Total area = 3 * 114^2
Total area ≈ 38988 mm^2
Comparing the two values, we can see that the total area is smaller when x = 113 mm. Therefore, the length of the side of the square that will minimize the combined area is 113 mm.
So, the correct answer is option B) 40 mm.
Let's assume the length of the side of the square is x mm. Since the sides of the rectangle are in the ratio of 1:2, the length of the rectangle will be 2x mm.
We know that the sum of the lengths of the two parts is equal to the total length of the wire, which is 340 mm. Therefore, we can write the equation:
x + 2x = 340
Simplifying this equation, we get:
3x = 340
Dividing both sides by 3, we find:
x = 113.33 mm
However, we can't have a fractional length for the side of the square, so we need to round it to the nearest whole number. In this case, x ≈ 113 mm.
Now, let's calculate the areas of the square and the rectangle.
Area of the square = x^2
Area of the rectangle = x * 2x = 2x^2
The combined area of the square and the rectangle is given by:
Total area = Area of the square + Area of the rectangle
Total area = x^2 + 2x^2
Total area = 3x^2
To minimize the total area, we need to find the minimum value of 3x^2. Since x is positive, the minimum value of x^2 will occur when x is at its minimum. Therefore, we need to choose the smallest possible value for x, which is 113 mm.
Let's calculate the total area using this value:
Total area = 3 * 113^2
Total area ≈ 38271 mm^2
Now, let's try to find the total area using a different value for x, such as 114 mm:
Total area = 3 * 114^2
Total area ≈ 38988 mm^2
Comparing the two values, we can see that the total area is smaller when x = 113 mm. Therefore, the length of the side of the square that will minimize the combined area is 113 mm.
So, the correct answer is option B) 40 mm.
Choose the most suitable one word substitute for the following expression
Connotation of a road or way- a)Pertinacious
- b)Viaticum
- c)Clandestine
- d)Ravenous
Correct answer is option 'B'. Can you explain this answer?
Choose the most suitable one word substitute for the following expression
Connotation of a road or way
Connotation of a road or way
a)
Pertinacious
b)
Viaticum
c)
Clandestine
d)
Ravenous
|
|
Sudhir Patel answered |
Pertinacious : persistent
Viaticum : travel allowance for a journeyWord origin of 'viaticum': from Latin, from viāticus belonging to a journey, from viāre to travel, from via way
Clandestine : kept secret
Ravenous : extremely hungry
Denotation : defined meaning
Connotation : feelings associated or inner meaning
Viaticum is the most relevant word.
Viaticum : travel allowance for a journeyWord origin of 'viaticum': from Latin, from viāticus belonging to a journey, from viāre to travel, from via way
Clandestine : kept secret
Ravenous : extremely hungry
Denotation : defined meaning
Connotation : feelings associated or inner meaning
Viaticum is the most relevant word.
Two and a quarter hours back, when seen in a mirror, the reflection of a wall clock without number markings seemed to show 1:30. What is the actual current time shown by the clock?- a)8:15
- b)11:15
- c)12:15
- d)12:45
Correct answer is option 'D'. Can you explain this answer?
Two and a quarter hours back, when seen in a mirror, the reflection of a wall clock without number markings seemed to show 1:30. What is the actual current time shown by the clock?
a)
8:15
b)
11:15
c)
12:15
d)
12:45
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Sudhir Patel answered |
Present time is given by
= 10: 30 + 2 : 15
= 12 : 45
Fatima starts from point P, goes North for 3 km, and then East for 4km to reach point Q. She then turns to face point P and goes 15km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P?
- a)8km, East
- b)12 km, North
- c)6km, East
- d)10km, North
Correct answer is option 'A'. Can you explain this answer?
Fatima starts from point P, goes North for 3 km, and then East for 4km to reach point Q. She then turns to face point P and goes 15km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P?
a)
8km, East
b)
12 km, North
c)
6km, East
d)
10km, North
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Sudhir Patel answered |
It takes 30 minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it. What is the rate at which water has to be pumped in so that it gets fully filled in 10 minutes?- a)4 times the draining rate
- b)3 times the draining rate
- c)2.5 times the draining rate
- d)2 times the draining rate
Correct answer is option 'A'. Can you explain this answer?
It takes 30 minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it. What is the rate at which water has to be pumped in so that it gets fully filled in 10 minutes?
a)
4 times the draining rate
b)
3 times the draining rate
c)
2.5 times the draining rate
d)
2 times the draining rate
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Isha Menon answered |
To solve this problem, we need to determine the rate at which water needs to be pumped into the tank in order to fill it in 10 minutes while simultaneously draining it at a constant rate.
Let's assume the rate of draining the tank is D gallons per minute and the rate of pumping water into the tank is P gallons per minute.
1. Determine the rate of draining the tank:
Since it takes 30 minutes to empty a half-full tank, the rate of draining the tank is given by the formula:
D = (0.5 tank volume) / 30 = (0.5V) / 30
2. Determine the rate of filling the tank:
In 10 minutes, the tank needs to be completely filled. Therefore, the rate of filling the tank is given by the formula:
P = V / 10
3. Equate the rates of draining and filling:
Since the tank is being drained and filled simultaneously, the rate of pumping water in should be equal to the rate of draining.
Therefore, we have the equation:
P = D
4. Substitute the values of P and D:
From step 2, we know that P = V / 10
From step 1, we know that D = (0.5V) / 30
Substituting these values into the equation from step 3, we get:
V / 10 = (0.5V) / 30
5. Solve for V:
To solve this equation, we can cross-multiply and simplify:
30V = 10 * 0.5V
30V = 5V
V = 0.1667
6. Determine the rate of pumping in water:
Now that we know the volume of the tank (V), we can determine the rate at which water needs to be pumped in to fill it in 10 minutes.
P = V / 10 = 0.1667 / 10 = 0.0167
7. Compare the rate of pumping to the rate of draining:
Since the rate of pumping water in is given by P, and the rate of draining is given by D, we can compare these rates:
P / D = 0.0167 / [(0.5 * 0.1667) / 30] = 0.0167 / 0.00833 = 2
Conclusion:
The rate at which water needs to be pumped into the tank so that it gets fully filled in 10 minutes is 2 times the draining rate. Therefore, the correct answer is option 'D'.
Let's assume the rate of draining the tank is D gallons per minute and the rate of pumping water into the tank is P gallons per minute.
1. Determine the rate of draining the tank:
Since it takes 30 minutes to empty a half-full tank, the rate of draining the tank is given by the formula:
D = (0.5 tank volume) / 30 = (0.5V) / 30
2. Determine the rate of filling the tank:
In 10 minutes, the tank needs to be completely filled. Therefore, the rate of filling the tank is given by the formula:
P = V / 10
3. Equate the rates of draining and filling:
Since the tank is being drained and filled simultaneously, the rate of pumping water in should be equal to the rate of draining.
Therefore, we have the equation:
P = D
4. Substitute the values of P and D:
From step 2, we know that P = V / 10
From step 1, we know that D = (0.5V) / 30
Substituting these values into the equation from step 3, we get:
V / 10 = (0.5V) / 30
5. Solve for V:
To solve this equation, we can cross-multiply and simplify:
30V = 10 * 0.5V
30V = 5V
V = 0.1667
6. Determine the rate of pumping in water:
Now that we know the volume of the tank (V), we can determine the rate at which water needs to be pumped in to fill it in 10 minutes.
P = V / 10 = 0.1667 / 10 = 0.0167
7. Compare the rate of pumping to the rate of draining:
Since the rate of pumping water in is given by P, and the rate of draining is given by D, we can compare these rates:
P / D = 0.0167 / [(0.5 * 0.1667) / 30] = 0.0167 / 0.00833 = 2
Conclusion:
The rate at which water needs to be pumped into the tank so that it gets fully filled in 10 minutes is 2 times the draining rate. Therefore, the correct answer is option 'D'.
The number of Hens, Ducks, and Goats in farm P are 65, 91 and 169, respectively. The total number of Hens, Ducks and Goats in a nearby farm Q is 416. The ratio of hens : ducks : goats in farm Q is 5 : 14 : 13. All the hens, ducks and goats are sent from farm Q to farm P.The new ratio of hens : ducks : goats in farm P is ____________.- a)10 : 21 : 26
- b)21 : 10 : 26
- c)5 : 14 : 13
- d)5 : 7 : 13
Correct answer is option 'A'. Can you explain this answer?
The number of Hens, Ducks, and Goats in farm P are 65, 91 and 169, respectively. The total number of Hens, Ducks and Goats in a nearby farm Q is 416. The ratio of hens : ducks : goats in farm Q is 5 : 14 : 13. All the hens, ducks and goats are sent from farm Q to farm P.
The new ratio of hens : ducks : goats in farm P is ____________.
a)
10 : 21 : 26
b)
21 : 10 : 26
c)
5 : 14 : 13
d)
5 : 7 : 13
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Snehal Saha answered |
Given:
- Number of Hens, Ducks, and Goats in farm P are 65, 91 and 169, respectively.
- Total number of Hens, Ducks and Goats in a nearby farm Q is 416.
- Ratio of hens : ducks : goats in farm Q is 5 : 14 : 13.
To find: The new ratio of hens : ducks : goats in farm P after all the animals are sent from Q to P.
Solution:
1. Find the total number of animals in farm Q:
Total number of animals in farm Q = 5x + 14x + 13x = 416 (where x is the common factor)
32x = 416
x = 13
Therefore, the total number of animals in farm Q = 5x + 14x + 13x = 65 + 182 + 169 = 416
2. Find the number of each type of animal in farm Q:
Number of hens in farm Q = 5x = 5(13) = 65
Number of ducks in farm Q = 14x = 14(13) = 182
Number of goats in farm Q = 13x = 13(13) = 169
3. Find the number of each type of animal in farm P after all the animals are sent from Q to P:
Number of hens in farm P = 65 + (5/32) * 416 = 65 + 65 = 130
Number of ducks in farm P = 91 + (14/32) * 416 = 91 + 182 = 273
Number of goats in farm P = 169 + (13/32) * 416 = 169 + 169 = 338
4. Find the new ratio of hens : ducks : goats in farm P:
New ratio of hens : ducks : goats = 130 : 273 : 338
Divide each number by the greatest common factor to get the simplest ratio:
New ratio of hens : ducks : goats = 10 : 21 : 26
Therefore, the new ratio of hens : ducks : goats in farm P is 10 : 21 : 26.
- Number of Hens, Ducks, and Goats in farm P are 65, 91 and 169, respectively.
- Total number of Hens, Ducks and Goats in a nearby farm Q is 416.
- Ratio of hens : ducks : goats in farm Q is 5 : 14 : 13.
To find: The new ratio of hens : ducks : goats in farm P after all the animals are sent from Q to P.
Solution:
1. Find the total number of animals in farm Q:
Total number of animals in farm Q = 5x + 14x + 13x = 416 (where x is the common factor)
32x = 416
x = 13
Therefore, the total number of animals in farm Q = 5x + 14x + 13x = 65 + 182 + 169 = 416
2. Find the number of each type of animal in farm Q:
Number of hens in farm Q = 5x = 5(13) = 65
Number of ducks in farm Q = 14x = 14(13) = 182
Number of goats in farm Q = 13x = 13(13) = 169
3. Find the number of each type of animal in farm P after all the animals are sent from Q to P:
Number of hens in farm P = 65 + (5/32) * 416 = 65 + 65 = 130
Number of ducks in farm P = 91 + (14/32) * 416 = 91 + 182 = 273
Number of goats in farm P = 169 + (13/32) * 416 = 169 + 169 = 338
4. Find the new ratio of hens : ducks : goats in farm P:
New ratio of hens : ducks : goats = 130 : 273 : 338
Divide each number by the greatest common factor to get the simplest ratio:
New ratio of hens : ducks : goats = 10 : 21 : 26
Therefore, the new ratio of hens : ducks : goats in farm P is 10 : 21 : 26.
Choose the word most similar in meaning to the given word:
Awkward- a)Inept
- b)Graceful
- c)Suitable
- d)Dredfull
Correct answer is option 'A'. Can you explain this answer?
Choose the word most similar in meaning to the given word:
Awkward
Awkward
a)
Inept
b)
Graceful
c)
Suitable
d)
Dredfull
|
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Sudhir Patel answered |
Awkward means unsuitable and is a synonym for inept.
Dreadful is not suitable here as it means horrible and is more negative than "awkward".
Graceful and suitable are positive words and hence not applicable.
So,Among all the options Inept is the word whose meaning is similar to Awkward.
Dreadful is not suitable here as it means horrible and is more negative than "awkward".
Graceful and suitable are positive words and hence not applicable.
So,Among all the options Inept is the word whose meaning is similar to Awkward.
Chapter doubts & questions for Practice Tests for General Aptitude - General Aptitude for GATE 2025 is part of Mechanical Engineering exam preparation. The chapters have been prepared according to the Mechanical Engineering exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Mechanical Engineering 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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General Aptitude for GATE
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