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If A = 315^{∘} then find the value of 3(tan^{2} A + cotA − 3)^{2}?
⇒ 3 (tan^{2}A + cot A – 3)^{2} = 3 (tan^{2}(315°) + cot (315°) – 3)^{2}
⇒ 3(tan^{2}(315°) + cot (315°) – 3)^{2} = 3(tan^{2}(360°  45°) + cot (360°  45°) – 3)^{2}
We know that, tan (360°  θ) =  tan θ and cot (360°  θ) =  cot θ then,
⇒ 3(tan^{2}(315°) + cot (315°) – 3)^{2} = 3(tan^{2} 45°  cot 45°  3)^{2}
As we know that, tan 45° = 1 = cot 45°,
⇒ 3(tan^{2} A + cotA − 3)^{2} = 3 (9) = 27
Hence, the correct option is (D).
We know that,
tan (90^{0}  A) = cot A
= 0
Hence, the correct option is (D).
A matrix having m rows and n columns is called a matrix of order m×n or simply m×n matrix.
Given,
As we can see that the given matrix A has 3 rows and 2 columns.
∴ The order of the given matrix A is 3 × 2.
Hence, the correct option is (B).
Direction: Study the following graph carefully and answer the question that follows.
The number of students from four different schools who qualified in an exam in six different years from 2012 to 2017 is shown in the graph given below.
What was the total number of students who qualified in the exam from school A in 2016, from school B in 2015, from school C in 2014 and from school D in 2012?
= 2405
Hence, the correct option is (A).
Direction: Study the following graph carefully and answer the question that follows.
The number of students from four different schools who qualified in an exam in six different years from 2012 to 2017 is shown in the graph given below.
What was the average number of students who qualified in the exam from school C over all the years together?
= 800 + 845 + 710 + 900 + 1100 + 950 = 5305
Therefore, the required average
= 5305/6 = 884.17 ≈ 884
Hence, the correct option is (A).
Direction: Study the following graph carefully and answer the question that follows.
The number of students from four different schools who qualified in an exam in six different years from 2012 to 2017 is shown in the graph given below.
What was the difference between the total number of students who qualified in the exam from schools A and B together in the year 2017 and the total number of students who qualified in the exam from schools C and D together in the year 2015?
The total number of students who qualified in the exam from schools C and D together in the year 2015 = 900 + 400 = 1300
Therefore, required difference = 1300  1170 = 130
Hence, the correct option is (D).
If X={4^{n }− 3n − 1, n ∈ N} and Y = {9n − 9, n ∈ N}, then X ∪ Y is equal to:
Set theory:
A ∪ B means set of all the values in the set A and B.
A ∩ B is the set of common elements of A and B.
Binomial theorm:
(a+b)^{n} = ^{n}C_{0}a^{n}b^{0} +^{ n}C_{1}a^{n − 1}b^{1} + ^{n}C_{2}a^{n − 2}b^{2} +…+ ^{n}C_{n − 2}a^{2}b^{n − 2} + ^{n}C_{n−1}a^{1}b^{n−1} + ^{n}C_{n}a^{0}b^{n}
Calculation:
Given X = {4^{n }− 3n−1, n ∈ N} and Y = {9n−9, n ∈ N}
x = 4^{n }− 3n−1 = (3 + 1)n − 3n−1
(∵ ^{n}C_{n−1 }= n and ^{n}C_{n }= 1)
⇒ X = 3^{2}(^{n}C_{0}3^{n−2}+^{n}C_{1}3^{n−3}+^{n}C_{2}3^{n−4}+…+^{n}C_{n−2})
⇒ x = 9(^{n}C_{0}3^{n−2}+^{n}C_{1}3^{n−3}+^{n}C_{2}3^{n−4}+…+^{n}C_{n−2})
For n ≥ 2, X is some multiple of 9.
And Xn = 1 = 0
∴ X = {0, some multiples of 9 but not all} .....(i)
Y = 9n − 9 = 9(n − 1)
∴ Y = { All multiple of 9 starting from 0} .......(ii)
From (i) and (ii) we can say,
∴ X ∪ Y = Y
Hence, the correct option is (A).
If the sum of n numbers in the GP 4, 8, 16,… is 2044 then n is?
Here, a = 4, r = 2
Sum of n numbers = S_{n }= 2044
As we know that, Sum of n terms of GP
= S_{n }= a(r^{n }− 1)/r − 1
Where r > 1
∴S_{n }= 4(2^{n }− 1)/2 − 1
2044 = 4×(2^{n }− 1)
⇒ 511 = (2^{n }− 1)
⇒ 2^{n }= 512
⇒ 2^{n }= 29
∴ n = 9
Hence, the correct option is (D).
In a factory, the average salary of the employees is Rs. 1500. After the inclusion of 5 employees, the total salary increased by Rs. 3000 and the average salary was reduced by Rs. 100, then now the number of employees are:
Average salary of all employees = Rs. 1500
Total salary increased by Rs. (3000 after 5 new employees
Decrease in average after new employees induction = Rs. 100
Formula used:
Average of n numbers = sum of total numbers/n
Let the total number of employees before new employees induction = x
⇒ Total salary of the employees = 1500x
⇒ After new induction, total salary = 1500x + 3000
Then, according to the question:
1400 = ((1500x + 3000)/x) + 5
⇒ 1400x + 7000 = 1500x + 3000
⇒ x = 40
⇒ x + 5 = 45
∴ Now the number of employees = 45
Hence, the correct option is (D).
The average age of 3 sisters is 15. If the ages of 2 sisters are 12 years and 15 years, the age of the third sister is:
So,
(x + y + z/3) = 15
x + y + z = 45
Given that x, y = 12, 15
⇒ 12 + 15 + z = 45
⇒ z = 18
Therefore, age of third sister is 18 years.
Hence, the correct option is (C).
On selling an article for Rs. 265 a man loses 4%. In order to gain 12%, for how much he must sell the article?
Loss % = ((CP − SP)/CP) × 100
Let the Cost price of article be x
Loss =4%
Selling price of article = x − (4/100) × x = 0.96x
0.96x = 265 ⇒ x = Rs. 276
Now the article is sold at gain
Gain = 12%
Selling price of article = 276 + (12/100) × 276 = Rs. 308
Hence, the correct option is (B).
The divisor is 25 times the quotient and 5 times the remainder. If the quotient is 16, the dividend is:
Quotient is 16 and the divisor is 25 times the quotient.
⇒ Divisor = 25 × 16 = 400
Also, divisor is 5 times the remainder
⇒ Remainder = divisor/ 5
= 400/5 = 80
We know that,
Dividend = quotient × divisor + remainder
⇒ Dividend = 16 × 400 + 80
= 6480
Hence, the correct option is (B).
In a two digit number, the digit at the unit's place is 1 less than twice the digit at the ten's place. If the digits at unit's and ten's place are interchanged, the difference between the new and the original number is less than the original number by 20. The original number is:
Then,Unit digit be 2x  1
Original number:
= 10x + 2x  1
= 12x  1
New number:
= 10(2x  1) + x
= 20x  10 + x
= 21x  10
According to the question,
(21x  10)  (12x  1)
= (12x  1)  20
9x  9 = 12x  21
3x = 12
x = 4
Original number:
= 12x  1
= 12 × 4  1
= 47
Hence, the correct option is (D).
If 432P1 is completely divisible by 9, then what is the value of P?
Now 4 + 3 + 2 + P + 1 should be divisible by 9.
So, 10 + P should be divisible by 9.
Also P is a singledigit number.
The number after 10 which is divisible by 9 is 18.
So P = 18 − 10 = 8
Hence, the correct option is (B).
= 16/81
Hence, the correct option is (C).
A man completes a certain journey by a car. If he covered 30% of the distance at the speed of 20kmph, 60% of the distance at 40km/h and the remaining of the distance at 10 kmph, his average speed is:
Average speed
= 25 km/h
Hence, the correct option is (A).
Using number line rule:
1 ≤ x < />
⇒ x ∈ (2, 1) ∪ (1, 2)
Hence, the correct option is (C).
Shikha invested a total of Rs. 1500 in two different schemes offering simple interest of 6% and 4% respectively. In two years' time, the scheme offering higher interest rate gives Rs. 100 more interest than the scheme offering the lower rate. What was the ratio of amount invested at higher interest rate to the other amount?
So, Sum invested by Shikha in another scheme = (1500  x)
Thus,
= 100
= 100
On solving,
x = Rs. 1100
Another amount = 1500 − 1100
= Rs. 400
Thus, the required ratio = 11 : 4
Hence, the correct option is (B).
In how many ways can a team of 6 members be selected from 7 boys and 4 girls, consisting of equal number of boys and girls.
The number of ways to select r things out of n things is given by,^{ n}C_{r}
Calculation:
Here, we have 7 boys and 4 girls out of which we have to select an equal number of boys and girls to form a team of 6 (i.e., 3 boys and 3 girls)
∴ Required number of ways^{ 7}C_{3} x ^{4}C_{3}
= 35 x 4
= 140
Hence, the correct option is (D).
If x, y, z are three consecutive positive integers, then log (1 + xz) is
⇒ y = x + 1 and z = y + 1
⇒ z = x + 2
Consider, log (1 + xz)
= log [1 + x(x + 2)]
= log [1 + x^{2} + 2x]
= log (1 + x)^{2}
= 2 log (1 + x)
= 2 log y
So, If x, y, z are three consecutive positive integers, then log (1 + xz) is 2 log y.
Hence, the correct option is (D).
Equation of the circle having diameter 8 and diameters y + 2x  5 = 0 and 2y + 3x  8 = 0 is?
Diameter = 8
Radius = 4
Also diameters equations:
y + 2x − 5 = 0 ...(i)
2y + 3x − 8 = 0 ..(ii)
Subtracting 2× (i) from (ii)
−x + 2 = 0
x = 2
Putting back in (i):
y + 2 × 2 − 5 = 0
y = 1
So center is (2,1) and radius is 4.
The equation of circle:
(x − 2)^{2 }+ (y − 1)^{2} = 42
x^{2} + 4 − 4x + y^{2} + 1 − 2y = 16
x^{2} + y^{2} − 4x − 2y − 11 = 0
Hence, the correct option is (B).
A man completes a journey in 10 hours. He travels the first half of the journey at the rate of 21 km/hr and the second half at the rate of 24 km/hr. Find the total journey in km.
Total time = 10 hours
Half journey at the rate of speed = 21 km/hr
and
Half journey at the rate of speed = 24 km/hr
We know that,
Time = Distance/Speed
Let distance = x
Hence, the correct option is (B).
When a number n is divided by 5, the remainder is 2. When n^{2} is divided by 5, the remainder will be:
Dividend = Divisor × Quotient + Remainder
Let the quotient be =b
n = 5 × b + 2
n^{2 }= (5b + 2)^{2}
⇒ n^{2 }= 25b^{2 }+ 4 + 2 × 5b × 2
⇒ n^{2 }= 25b^{2 }+ 4 + 20b
⇒ n^{2 }= 5(5b^{2 }+ 4b) + 4
∴ When n2 is divided by 5, the remainder will be 4.
Hence, the correct option is (C).
log_{6}√2 + log_{6}√3
= log_{6}(√2 × √3) (∵ logm + logn = logmn)
= log_{6}(√6)
= log_{6}6^{1/2}
=(½)log_{6}6 (∵ logm^{n }= nlogm)
As we know,
log_{m}m = (log_{a}m/log_{a}m) = 1
∴ log_{6}√2 + log_{6}√3 = ( ½)log_{6}6
= (½) ×1 = 1/2
Hence, the correct option is (A).
Direction: Study the following graph carefully and answer the question that follows.
The number of students from four different schools who qualified in an exam in six different years from 2012 to 2017 is shown in the graph given below.
What was the ratio of the number of students who qualified in the exam from school C in the year 2014 to the number of students who qualified in the exam from school D in the year 2017?
Number of students who qualified in the exam from school D in the year 2017 = 600
Required ratio = 710 : 600
= 71 : 60
Hence, the correct option is (B).
Direction: Study the following graph carefully and answer the question that follows.
The number of students from four different schools who qualified in an exam in six different years from 2012 to 2017 is shown in the graph given below.
What was the approximate percentage increase in the number of students who qualified in the exam from school A in the year 2013 as compared to that in the previous year?
The number of students who qualified in the exam from school A in the year 2012 = 450
Increase = 625  450 = 175
Therefore, required percentage
= (175/450) × 100 = (350/9) = 38.88% ≈ 39%
Hence, the correct option is (A).
If A = [2, 3] then cardinality of A × A × A is:
A = [2, 3]
Then,
A × A = [2, 3] × [2, 3]
= [(2, 2), (2, 3), (3, 2), (3, 3)]
Therefore,
A × A × A = [2, 3] × [2, 3] × [2, 3]
= [(2, 2), (2, 3), (3, 2), (3, 3)] × [2, 3]
= [(2, 2, 2), (2, 2, 3), (2, 3, 2), (2, 3, 3), (3, 2, 2), (3, 2, 3), (3, 3, 2), (3, 3, 3)]
So, n(A × A × A) = 8
Therefore, cardinality = 8
Hence, the correct option is (C).
Find the equation of the tangent to the ellipse x^{2 }+ 2y^{2} = 4 at the point where ordinate is 1 such that point lies in the first quadrant?
Equation of ellipse is x^{2} + 2y^{2} = 4
Here, we have to find the equation of the tangent to the given ellipse at the point where ordinate is 1 such that the point lies in the first quadrant.
Let the point be P = (c, 1)
Now this point P lies on the ellipse. So, x = c and y = 1 will satisfy the equation x^{2} + 2y^{2} = 4
c/2 + 2 = 4
c = ± √2
So, the point P is (√2, 1) because the point P lies in the first quadrant.
The given equation of ellipse we can be rewritten as: (x^{2}/4) + (y^{2}/2) = 1
As we know that, the equation of the tangent to the horizontal ellipse x^{2}/a^{2 }+ y^{2}/b^{2} = 1 where 0 < b="" />< a="" at="" the="" point="" />_{1}, y_{1}) is given by:
So, the required equation of tangent is √2x + 2y  4 = 0
Hence, the correct option is (D).
Now, we can get transpose of AB by switching its rows with its columns.
Hence, the correct option is (B).
The total surface area of a cube is 108 cm^{2}. Find the volume of the cube?
Total surface area of cube = 108 cm^{2}
Formula used:
TSA of cube = 6a^{2}
Volume of cube = a^{3}
Let, the side of the cube be a.
∵ TSA of cube = 6a^{2}
⇒ 108 cm^{2 }= 6a^{2}
⇒ a^{2 }= 108/6
⇒ a^{2 }= 18 cm^{2}
⇒ a = √18 = 3√2 cm
∴ Volume of cube = a^{3}
= (3√2)^{3}
= 54√2 cm^{3}
Hence, the correct option is (B).
= 1
Hence, the correct option is (C).
Let f: R → R be defined as f(x) = x^{4}. Choose the correct answer.
Let x, y ∈ R such that:
f(x) = f(y)
Then,
x^{4} = y^{4}
x = ±y
∴ f(x_{1}) = f(x_{2}) does not imply that x_{1 }= x_{2}
For instance f(1) = f(−1) = 1
∴ f is not oneone.
Consider an element −2 in codomain R.
It is clear that, there does not exist any x in domain R such that:
f(x)=−2
∴ f is not onto.
Therefore, function f is neither oneone nor onto.
Hence, the correct option is (D).
As we know,
If two matrices and are said to be equal, then
Order of matrix A = Order of matrix B
Corresponding element of matrix A= Corresponding element of B
So,
x − y = 2...(1)
x + y = 16...(2)
On adding equation (1) and (2) we get,
2x = 18
⇒ x = 9
Substituting x = 9 in equation (2) we get
9 + y = 16
⇒ y = 16 − 9
⇒ y = 7
So, the value of x = 9 and y = 7
Hence, the correct option is (B).
A train crossed a 110 m long platform in 13.5 seconds and a 205 m long platform in 18.25 seconds. What was the speed of the train?
⇒ Speed of train = (length of platform + length of train)/time
According to question,
⇒ 401.5 + 3.65x = 553.5 + 2.7x
⇒ 0.95x = 152
⇒ x = 160
⇒ Speed of train
= (110 + 160)/13.5
= 20 m/sec
= 20 × (18/5) = 72 km/hr
Hence, the correct option is (A).
^{n}P_{r}= (n!/(n−r)!) = n×(n−1)×….×(n−r+1)
Here, ^{10}P_{r }= 5040
⇒ ^{10}P_{r }= 10 × 504
⇒ ^{10}P_{r }= 10 × 9 × 56
= 10 × 9 × 8 × 7
= 10 × (10 − 1) × (10 − 2) × (10 − 4 + 1)
On comparing with,
^{n}P_{r }= n × (n−1)×……(n−r+1),
We get,
R = 4
Hence, the correct option is (C).
A problem is given to three persons and their chances of solving it are 1/3,1/4,1/5 respectively. This probability that none will solve it is:
Probability of Solving the problem by first person = 1/3
Probability of Solving the problem by second person = 1/4
Probability of Solving the problem by third person = 1/5
We know that,
Probability of occurrence of an event =1− Probability of not happening of the same event
Then,
Probability of Not Solving the problem by first person
= 1 − (1/3)
= 2/3
Probability of not Solving the problem by second person
= 1 − (1/4)
= 3/4
Probability of not Solving the problem by third person
= 1 − (1/5)
= 4/5
So,
The probability of none solving the problem
= (⅔) × (¾) × (4/5)
= 2/5
Hence, the correct option is (B).
If the distance between point A(5,a) and B(17,12) is 13 units, then find the value of a:
Point A = (5, a) and Point B = (17, 12)
The distance between the two points is 13 units.
Formula Used:
Distance between two points
Point A = (5, a)
⇒ x_{1} = 5 and y_{1} = a
Point B = (17, 12)
⇒ x_{2 }= 17 and y_{2 }= 12
Using the formula,
⇒ 132 = (12)^{2 }+ (12 − a)^{2}
⇒ 169 = 144 + (12 − a)^{2}
⇒ (12 − a)^{2 }= 169 − 144
⇒ (12 − a)^{2 }= 25
⇒ 12 − a = √25
⇒ 12 − a = 5
⇒ a = 12 − 5
⇒ a = 7
∴ The value of a is 7 units.
Hence, the correct option is (A).
In an examination, 20% of the total number of students failed in English, 15% of the total number of students failed in Maths, and 5% of the total number of students failed in both. What is the percentage of students who passed in both the subjects?
Total number of students failed in English (x) = 20%
Total number of students failed in Maths (y) = 15%
Total number of students failed in both (z) = 5%
Formula Used:
Percentage of students passed in both = [100 − (x + y − z)]
= [100 − (20 + 15 − 5)]
= [100 − 30]
= 70%
∴ 70% students passed in both subjects.
Hence, the correct option is (A).
If A = {2, 3}, B = {4, 5}, C = {5, 6}, then what is the number of elements in A x (B ∩ C)?
If A and B be any two sets, then:
(A ∩ B) = {x, x ∈ A and x ∈ B}
A × B = {(x, y), x ∈ A and y ∈ B}
Given that,
A = {2, 3}, B = {4, 5}, C = {5, 6}
Then,
(B ∩ C) = {5}
A × (B ∩ C) = {(2, 5), (3, 5)}
Therefore, the number of elements in A × (B ∩ C) = 2
Hence, the correct option is (A).
Prem buys a table for Rs. 450 and spends Rs. 30 on its transportation. If he sells the table for Rs. 600 what will be his gain percent?
Purchased price of a table = Rs. 450
Transportation charges = Rs. 30
Total cost price of a table
= 450 + 30 = 480
Cost price of a table = Rs. 480
Selling price of a table = Rs. 600
Profit percentage
= 25
∴ Profit percentage is 25%
Hence, the correct option is (B).
Direction: Rearrange the following five sentences/ group of sentences A, B, C, D and E in the proper sequence to form a meaningful paragraph; then answer the questions given below them.
Which of the following should be the FIRST sentence after rearrangement?
Sentence A and E which describes the various components of the building complex should come in next. Sentence A should be the third sentence as it states what is in the front of the monument and sentence E follows as it describes what is inside the monument. Sentence D is the last sentence of the passage. The correct order is BCAED.
Hence, the correct answer is B.
Direction: Rearrange the following five sentences/ group of sentences A, B, C, D and E in the proper sequence to form a meaningful paragraph; then answer the questions given below them.
Which of the following should be the LAST sentence after rearrangement?
Sentence A and E which describes the various components of the building complex should come in next. Sentence A should be the third sentence as it states what is in the front of the monument and sentence E follows as it describes what is inside the monument. Sentence D is the last sentence of the passage. The correct order is BCAED.
Hence, the correct answer is D.
Direction: In this question, a part of the sentence is made bold. Below are given alternatives to the bold part at (A), (B), and (C) which may improve the sentence. Choose the correct alternative. In case no correction is needed, mark (D) as your answer.
Students from around the world have increasing started opting to online education.
Reason: As we can observe that the sentence is made in Present Perfect Tense (Have + V3), usage of ‘increasing’ is ungrammatical in the sentence. Instead of it, the adverb ‘increasingly’ should be used here.
Besides, the verb ‘opt’ always takes preposition ‘for’ after it. Therefore, ‘to’ must be replaced by ‘for’ to make it a grammatically correct sentence.
Clearly, among the given choices option (C) replaces the bold part most appropriately.
The sentence after replacement becomes:
Students from around the world have increasingly started opting for online education.
Hence, the correct option is (C).
Direction: In this question, a part of the sentence is made bold. Below are given alternatives to the bold part at (A), (B), and (C) which may improve the sentence. Choose the correct alternative. In case no correction is needed, mark (D) as your answer.
Getting to hire as the assistant to a pastry chef seemed like a dream come true.
Reason: The sentence is starting with a gerund and implying as the narrator is feeling happy to have got the job of the assistant to a pastry chef. Therefore, instead of ‘to hire’, the past participle ‘hired’ must be used to make the sentence meaningful.
Ex. Getting married was the best decision of my life. (Correct)
Ex. Getting to marry was the best decision of my life. (Incorrect)
Clearly, among the given choices option (C) replaces the bold part most appropriately.
The sentence after replacement becomes:
Getting hired as the assistant to a pastry chef seemed like a dream come true.
Hence, the correct option is (C).
Direction: In this question, a part of the sentence is made bold. Below are given alternatives to the bold part at (A), (B), and (C) which may improve the sentence. Choose the correct alternative. In case no correction is needed, mark (D) as your answer.
A federal government climatechange report released last year shows the Pacific Northwest is already seeing damage from rising temperatures.
Hence, the correct option is (D).
Direction: In each question a sentence is given followed by a blank. You are provided with three fragments I, II and III. You have to identify which statement/statements can carry forward the given sentence in the most logical way so as to make the sentence coherent and contextually correct.
On one hand, the government is providing ___________.
I. power to industrialists of Vidarbha and Marathwada at concessional rates but on the other, the State Discom MSEDCL is providing free electricity to them.
II. cheap food to people and on the other, it is increasing fuel prices.
III. water and power supply in some colonies but on the other side, government has lifted the ban on their development.
Whenever we have the expression ‘on one hand..on the other hand..’, we have two contradicting statements for each. Here, both statements agree with each other and hence, the sentence is not logical.
II. On one hand, the government is providing cheap food to people and on the other, it is increasing fuel prices. This is correct.
III. On one hand, the government is providing water and power supply in some colonies but on the other side, government has lifted the ban on their development.
Here too, we have two statements agreeing with one another and hence illogical.
Hence, the correct option is (A).
Direction: In each question a sentence is given followed by a blank. You are provided with three fragments I, II and III. You have to identify which statement/statements can carry forward the given sentence in the most logical way so as to make the sentence coherent and contextually correct.
No matter how much we ____________.
I. mitigate, there prevails some information asymmetry which makes some amount of climate change unavoidable.
II. understand him, we will fully grasp the myriad ways in which he has made the sport better.
III. care for her, it will not be in vain.
Statement I: No matter how much we mitigate, some amount of climate change is unavoidable.
This is correct.
Statement II: No matter how much we understand him, we will fully grasp the myriad ways in which he has made the sport better.
This is incorrect as both statements are in agreement with each other.
Statement III: No matter how much we care for her, it will not be in vain.
Again, these statements are not in contradiction and hence incorrect.
Hence, the correct option is (A).
Direction: In each question a sentence is given followed by a blank. You are provided with three fragments I, II and III. You have to identify which statement/statements can carry forward the given sentence in the most logical way so as to make the sentence coherent and contextually correct.
From its establishment many decades back, _________.
I. the value of the CanadaU.S. surface trade has increased by 76% in the present day, while that of the U.S.Mexico surface trade has increased by 372%.
II. Magnet has invested till date, over €120m in developing its own advanced telecoms network.
III. much of Germany’s political class has worried that the 92 MPs entering the Bundestag could throw a spanner in the works of German democracy.
This is correct.
From its establishment many decades back, Magnet has invested till date, over €120m in developing its own advanced telecoms network.
This is correct.
From its establishment many decades back, much of Germany’s political class has worried that the 92 MPs entering the Bundestag could throw a spanner in the works of German democracy.
This does not make sense either grammatically or contextually and is wrong.
Hence, the correct option is (C).
Directions: The following question has two blanks, each blank indicating that something has been omitted. Choose the set of words for each blank that best fits in the context of the sentence.
Central banks across the globe are preparing to loosen monetary policies, to _______ their respective economies and it is expected that gold will continue the ongoing ________.
The word “ongoing” before the second blank, implies that a force has already been set in motion and would be continued. In other words, the “momentum” would be continued. This eliminated options (B) and (D).
Hence, the correct option is (A).
Directions: The following question has two blanks, each blank indicating that something has been omitted. Choose the set of words for each blank that best fits in the context of the sentence.
Investors can think of putting in at least 10 percent of their savings in gold as it has the _____ to be an ______ for the portfolio in a fragile trade environment.
Investors can think of putting in at least 10 percent of their savings in gold as it has the potential to be an insurance for the portfolio in a fragile trade environment.
Hence, the correct option is (C).
Direction: Complete the paragraph given below.
Vinyasa, as commonly understood, consists of moving from one asana or body position to another, combining breathing with the movement. The concept is to take orderly steps, each step placed correctly while considering the person and goal so that progress is consistent and steady. The order in which the poses are done in an asana practice is not an arbitrary matter. _____________ . When strung together without purpose they form nonsense, but when properly ordered they create words, sentences, and wondrous literature.
Option (A) and (B) are clearly not relevant to the primary idea. Option (D) goes against the central idea of 'orderly steps'. Thus, option (C) brings out a metaphor (that of alphabet's orderly nature) to stress the central idea of the passage and continues into a valid conclusion.
The correct paragraph Vinyasa, as commonly understood, consists of moving from one asana or body position to another, combining breathing with the movement. The concept is to take orderly steps, each step placed correctly while considering the person and goal so that progress is consistent and steady. The order in which the poses are done in an asana practice is not an arbitrary matter. It is as if the asanas were letters of the alphabet. When strung together without purpose they form nonsense, but when properly ordered they create words, sentences and wondrous literature.
Hence, the correct option is (C).
Direction: Read the passage given below and answer the questions that follow by selecting the correct most appropriate options.
1. Each drop represents a little bit of creation and of life itself. When the monsoon brings to northern India the first rains of summer, the parched earth opens its pores and quenches its thirst with a hiss of ecstasy. After baking in the sun for the last few months, the land looks cracked, dusty and tired. Now, almost overnight, new grass springs up, there is renewal everywhere, and the damp earth releases a fragrance sweeter than any devised by man.
2. Water brings joy to earth, grass, leaf bud, blossom, insect, bird, animal and the pounding heart of man. Small children run out of their homes to romp naked in the rain. Buffaloes, which have spent the summer listlessly around lakes gone dry, now plunge into heaven of muddy water. Soon the lakes and rivers will overflow with the monsoon’s generosity, Trekking in the Himalayan foothills, I recently walked for kilometres without encountering habitation. I was just scolding myself for not having brought along a water bottle when I came across a patch of green on a rock face. I parted a curtain of tender maidenhair fern and discovered a tiny spring issuing from the rocknectar for the thirsty traveller.
3. I stayed there for hours, watching the water descend, drop by drop, into a tiny casement in the rocks. Each drop reflected creation. That same spring, I later discovered, joined other springs to form a. swift, tumbling. stream, which went cascading down the hill into other streams until, in the plains, it became part of a river. And that river flowed into another mightier river that kilometres later emptied into the ocean. Be like water, taught Laotzu, philosopher ‘and founder of Taoism. Soft and limpid, it finds its way through, over or under any obstacle. It does not quarrel; it simply moves on.
Which of the following words is most similar in meaning to the word ‘pounding’ as used in para 2 of the passage?
Pounding means the sound, feeling, or action of something beating repeatedly.
Palpitating means (of the heart) beating rapidly and strongly.
Benumbing means to make numb, especially by cold.
Sinking means to go below the surface of water or another liquid.
Shaking means to move backwards and forwards or up and down in quick, short movements, or to make something or someone do this.
Thus, palpitating and pounding are similar in meaning.
Hence, the correct option is (C).
Direction: Read the passage given below and answer the questions that follow by selecting the correct most appropriate options.
1. Each drop represents a little bit of creation and of life itself. When the monsoon brings to northern India the first rains of summer, the parched earth opens its pores and quenches its thirst with a hiss of ecstasy. After baking in the sun for the last few months, the land looks cracked, dusty and tired. Now, almost overnight, new grass springs up, there is renewal everywhere, and the damp earth releases a fragrance sweeter than any devised by man.
2. Water brings joy to earth, grass, leaf bud, blossom, insect, bird, animal and the pounding heart of man. Small children run out of their homes to romp naked in the rain. Buffaloes, which have spent the summer listlessly around lakes gone dry, now plunge into heaven of muddy water. Soon the lakes and rivers will overflow with the monsoon’s generosity, Trekking in the Himalayan foothills, I recently walked for kilometres without encountering habitation. I was just scolding myself for not having brought along a water bottle when I came across a patch of green on a rock face. I parted a curtain of tender maidenhair fern and discovered a tiny spring issuing from the rocknectar for the thirsty traveller.
3. I stayed there for hours, watching the water descend, drop by drop, into a tiny casement in the rocks. Each drop reflected creation. That same spring, I later discovered, joined other springs to form a. swift, tumbling. stream, which went cascading down the hill into other streams until, in the plains, it became part of a river. And that river flowed into another mightier river that kilometres later emptied into the ocean. Be like water, taught Laotzu, philosopher ‘and founder of Taoism. Soft and limpid, it finds its way through, over or under any obstacle. It does not quarrel; it simply moves on.
Which one of the following words is most opposite in meaning to the word ‘descend’ (para 3) as used in the passage?
Descend means move or fall downwards.
Ascend means go up or climb.
Hover means remain in one place in the air.
Zoom means move or travel very quickly.
Flow means the action or fact of moving along in a steady, continuous stream.
Thus, ascend and descend are opposite in meaning.
Hence, the correct option is (B).
Direction: Read the passage given below and answer the questions that follow by selecting the correct most appropriate options.
1. Each drop represents a little bit of creation and of life itself. When the monsoon brings to northern India the first rains of summer, the parched earth opens its pores and quenches its thirst with a hiss of ecstasy. After baking in the sun for the last few months, the land looks cracked, dusty and tired. Now, almost overnight, new grass springs up, there is renewal everywhere, and the damp earth releases a fragrance sweeter than any devised by man.
2. Water brings joy to earth, grass, leaf bud, blossom, insect, bird, animal and the pounding heart of man. Small children run out of their homes to romp naked in the rain. Buffaloes, which have spent the summer listlessly around lakes gone dry, now plunge into heaven of muddy water. Soon the lakes and rivers will overflow with the monsoon’s generosity, Trekking in the Himalayan foothills, I recently walked for kilometres without encountering habitation. I was just scolding myself for not having brought along a water bottle when I came across a patch of green on a rock face. I parted a curtain of tender maidenhair fern and discovered a tiny spring issuing from the rocknectar for the thirsty traveller.
3. I stayed there for hours, watching the water descend, drop by drop, into a tiny casement in the rocks. Each drop reflected creation. That same spring, I later discovered, joined other springs to form a. swift, tumbling. stream, which went cascading down the hill into other streams until, in the plains, it became part of a river. And that river flowed into another mightier river that kilometres later emptied into the ocean. Be like water, taught Laotzu, philosopher ‘and founder of Taoism. Soft and limpid, it finds its way through, over or under any obstacle. It does not quarrel; it simply moves on.
Which part of speech is the underlined word in the following sentence?
Almost overnight new grass spring up.
An adverb is a word that is used to change, modify or qualify several types of words including an adjective, a verb, a clause, another adverb, or any other type of word or phrase, with the exception of determiners and adjectives, that directly modify nouns.
Hence, the correct option is (D).
Direction: In the following question, the given sentence has four parts marked (P), (Q), (R) and (S). Choose the part of the sentence with the error and mark it as your answer. If there is no error, mark 'No error (S)' as your answer.
Can you tell me (P) / the name of the person (Q) / whom wrote the book? (R) / No error (S)
We need to replace 'whom' with 'who' to correct the sentence.
We use Who as a relative pronoun to introduce a relative clause about people. Ex: The police officer who came was a friend of my father’s.
Whom is the object form of 'who'. We use whom to refer to people in formal styles or in writing when the person is the object of the verb. Ex: Whom did he marry?
Hence, the correct option is (C).
Direction: In the following question, the given sentence has four parts marked (P), (Q), (R) and (S). Choose the part of the sentence with the error and mark it as your answer. If there is no error, mark 'No error (S)' as your answer.
Men who has risen (P) / by their own exertions (Q) / are always respected. (R) / No error (S)
Replace has with have in part P.
Subjects and verbs must agree with one another in number (singular or plural). Thus, if a subject is singular, its verb must also be singular; if the subject is a plural, its verb must also be plural.
Here, Men is the plural subject so we need a plural helping verb(have).
Hence, the correct option is (A).
Direction: Read the passage given below and answer the questions that follow by selecting the correct most appropriate options.
1. Each drop represents a little bit of creation and of life itself. When the monsoon brings to northern India the first rains of summer, the parched earth opens its pores and quenches its thirst with a hiss of ecstasy. After baking in the sun for the last few months, the land looks cracked, dusty and tired. Now, almost overnight, new grass springs up, there is renewal everywhere, and the damp earth releases a fragrance sweeter than any devised by man.
2. Water brings joy to earth, grass, leaf bud, blossom, insect, bird, animal and the pounding heart of man. Small children run out of their homes to romp naked in the rain. Buffaloes, which have spent the summer listlessly around lakes gone dry, now plunge into heaven of muddy water. Soon the lakes and rivers will overflow with the monsoon’s generosity, Trekking in the Himalayan foothills, I recently walked for kilometres without encountering habitation. I was just scolding myself for not having brought along a water bottle when I came across a patch of green on a rock face. I parted a curtain of tender maidenhair fern and discovered a tiny spring issuing from the rocknectar for the thirsty traveller.
3. I stayed there for hours, watching the water descend, drop by drop, into a tiny casement in the rocks. Each drop reflected creation. That same spring, I later discovered, joined other springs to form a. swift, tumbling. stream, which went cascading down the hill into other streams until, in the plains, it became part of a river. And that river flowed into another mightier river that kilometres later emptied into the ocean. Be like water, taught Laotzu, philosopher ‘and founder of Taoism. Soft and limpid, it finds its way through, over or under any obstacle. It does not quarrel; it simply moves on.
Children respond to the first rains of summer by:
According to the passage, 'Small children run out of their homes to romp naked in the rain.'
Romp means to play in a rough, excited, and noisy way. It can be concluded that the children played excitedly in the rain.
Hence, the correct option is (C).
Directions: Read the passage carefully and answer the questions given below.
As NASA works toward its longterm goal of establishing a human settlement on Mars, SpaceX is fleshing out its plans to help NASA make that dream a reality.
The private spaceflight company, which regularly launches cargo to the International Space Station with the Falcon 9 rocket and will soon launch astronauts up there, is currently building an interplanetary spacecraft for Mars. Known as Starship, the rocketspacecraft combo will be able to launch 100 passengers and large amounts of cargo to and from the Red Planet.
Before Starship can launch to Mars, it will start off launching commercial satellites as early as 2021, followed by a manned flight around the moon in 2023. Although SpaceX has not given a timeline for its first missions to Mars, SpaceX founder Elon Musk has said that the first Mars base could be up and running in 2028. And while Musk shared some eyecatching artist illustrations depicting what he called "Mars Base Alpha" as an intricate network of buildings and infrastructure, SpaceX's plans for the Red Planet are not quite that extensive.
"SpaceX very much is a transportation company," Paul Wooster, the principal Mars development engineer at SpaceX, said during a speech at the Humans to Mars Summit in Washington in May. He explained that SpaceX plans to build whatever infrastructure is necessary to support the company's Starship flights to and from Mars; that could include landing pads and refueling stations for the reusable rockets.
For its very first Mars missions, SpaceX will land at least two unmanned cargo ships on the Red Planet before sending any humans there, Wooster said. Those cargo missions would bring supplies, such as life support systems and power generators that the first astronauts on Mars will need when they set up camp.
The first unmanned Mars missions will also be tasked with confirming the presence of natural resources that can provide fuel for future twoway missions to the Red Planet, Wooster said. SpaceX wants to use water ice from the planet's surface and carbon dioxide from the Martian atmosphere to refuel Starships on Mars, enabling the rockets to return to Earth.
After those first two cargo missions, SpaceX will launch two manned missions alongside two additional cargoonly flights to begin setting up a propellant production plant. At that plant, water and carbon dioxide will be converted into liquid methane and liquid oxygen, which fuel the rocket's engines.
So, while SpaceX intends to set up a transportation system for humans and cargo traveling to the Red Planet, the company won't be building an entire Mars base on its own. Musk has laid out his vision to create a millionperson colony on Mars, but to establish that colony SpaceX will have to work together with NASA and the agency's international partners and other commercial space companies. Several companies have already begun designing concepts for Mars habitats and have proposed orbital outposts similar to NASA's Lunar Gateway, which could serve as a waypoint for Starship and reduce the amount of fuel needed for return trips to Earth.
What is the name of the spacecraft that SpaceX is building that will carry passengerFalcon 9and cargo to mars?
Hence, the correct option is (B).
Directions: Read the passage carefully and answer the questions given below.
As NASA works toward its longterm goal of establishing a human settlement on Mars, SpaceX is fleshing out its plans to help NASA make that dream a reality.
The private spaceflight company, which regularly launches cargo to the International Space Station with the Falcon 9 rocket and will soon launch astronauts up there, is currently building an interplanetary spacecraft for Mars. Known as Starship, the rocketspacecraft combo will be able to launch 100 passengers and large amounts of cargo to and from the Red Planet.
Before Starship can launch to Mars, it will start off launching commercial satellites as early as 2021, followed by a manned flight around the moon in 2023. Although SpaceX has not given a timeline for its first missions to Mars, SpaceX founder Elon Musk has said that the first Mars base could be up and running in 2028. And while Musk shared some eyecatching artist illustrations depicting what he called "Mars Base Alpha" as an intricate network of buildings and infrastructure, SpaceX's plans for the Red Planet are not quite that extensive.
"SpaceX very much is a transportation company," Paul Wooster, the principal Mars development engineer at SpaceX, said during a speech at the Humans to Mars Summit in Washington in May. He explained that SpaceX plans to build whatever infrastructure is necessary to support the company's Starship flights to and from Mars; that could include landing pads and refueling stations for the reusable rockets.
For its very first Mars missions, SpaceX will land at least two unmanned cargo ships on the Red Planet before sending any humans there, Wooster said. Those cargo missions would bring supplies, such as life support systems and power generators that the first astronauts on Mars will need when they set up camp.
The first unmanned Mars missions will also be tasked with confirming the presence of natural resources that can provide fuel for future twoway missions to the Red Planet, Wooster said. SpaceX wants to use water ice from the planet's surface and carbon dioxide from the Martian atmosphere to refuel Starships on Mars, enabling the rockets to return to Earth.
After those first two cargo missions, SpaceX will launch two manned missions alongside two additional cargoonly flights to begin setting up a propellant production plant. At that plant, water and carbon dioxide will be converted into liquid methane and liquid oxygen, which fuel the rocket's engines.
So, while SpaceX intends to set up a transportation system for humans and cargo traveling to the Red Planet, the company won't be building an entire Mars base on its own. Musk has laid out his vision to create a millionperson colony on Mars, but to establish that colony SpaceX will have to work together with NASA and the agency's international partners and other commercial space companies. Several companies have already begun designing concepts for Mars habitats and have proposed orbital outposts similar to NASA's Lunar Gateway, which could serve as a waypoint for Starship and reduce the amount of fuel needed for return trips to Earth.
What is the name of the proposed Mars base as put forward by SpaceX?
Hence, the correct option is (A).
Directions: Read the passage carefully and answer the questions given below.
As NASA works toward its longterm goal of establishing a human settlement on Mars, SpaceX is fleshing out its plans to help NASA make that dream a reality.
The private spaceflight company, which regularly launches cargo to the International Space Station with the Falcon 9 rocket and will soon launch astronauts up there, is currently building an interplanetary spacecraft for Mars. Known as Starship, the rocketspacecraft combo will be able to launch 100 passengers and large amounts of cargo to and from the Red Planet.
Before Starship can launch to Mars, it will start off launching commercial satellites as early as 2021, followed by a manned flight around the moon in 2023. Although SpaceX has not given a timeline for its first missions to Mars, SpaceX founder Elon Musk has said that the first Mars base could be up and running in 2028. And while Musk shared some eyecatching artist illustrations depicting what he called "Mars Base Alpha" as an intricate network of buildings and infrastructure, SpaceX's plans for the Red Planet are not quite that extensive.
"SpaceX very much is a transportation company," Paul Wooster, the principal Mars development engineer at SpaceX, said during a speech at the Humans to Mars Summit in Washington in May. He explained that SpaceX plans to build whatever infrastructure is necessary to support the company's Starship flights to and from Mars; that could include landing pads and refueling stations for the reusable rockets.
For its very first Mars missions, SpaceX will land at least two unmanned cargo ships on the Red Planet before sending any humans there, Wooster said. Those cargo missions would bring supplies, such as life support systems and power generators that the first astronauts on Mars will need when they set up camp.
The first unmanned Mars missions will also be tasked with confirming the presence of natural resources that can provide fuel for future twoway missions to the Red Planet, Wooster said. SpaceX wants to use water ice from the planet's surface and carbon dioxide from the Martian atmosphere to refuel Starships on Mars, enabling the rockets to return to Earth.
After those first two cargo missions, SpaceX will launch two manned missions alongside two additional cargoonly flights to begin setting up a propellant production plant. At that plant, water and carbon dioxide will be converted into liquid methane and liquid oxygen, which fuel the rocket's engines.
So, while SpaceX intends to set up a transportation system for humans and cargo traveling to the Red Planet, the company won't be building an entire Mars base on its own. Musk has laid out his vision to create a millionperson colony on Mars, but to establish that colony SpaceX will have to work together with NASA and the agency's international partners and other commercial space companies. Several companies have already begun designing concepts for Mars habitats and have proposed orbital outposts similar to NASA's Lunar Gateway, which could serve as a waypoint for Starship and reduce the amount of fuel needed for return trips to Earth.
As per the passage, what fuel will be used to power the Starship rocket while returning from Mars?
Hence, the correct option is (D).
Direction: Rearrange the following five sentences/ group of sentences A, B, C, D and E in the proper sequence to form a meaningful paragraph; then answer the questions given below them.
Which of the following should be the SECOND sentence after rearrangement?
Sentence A and E which describes the various components of the building complex should come in next. Sentence A should be the third sentence as it states what is in the front of the monument and sentence E follows as it describes what is inside the monument. Sentence D is the last sentence of the passage. The correct order is BCAED.
Hence, the correct answer is C.
Direction: In this question, a part of the sentence is made bold. Below are given alternatives to the bold part at (A), (B), and (C) which may improve the sentence. Choose the correct alternative. In case no correction is needed, mark (D) as your answer.
Bhavana is the only student by Kerala to rank among the 13 national toppers who secured 499 marks.
Here relation between student and his/her native place is described, thus the only preposition which describes belongingness is "from".
Correct sentence: Bhavana is the only student from Kerala to rank among the 13 national toppers who secured 499 marks.
Hence, the correct option is (B).
Direction: In this question, a part of the sentence is made bold. Below are given alternatives to the bold part at (A), (B), and (C) which may improve the sentence. Choose the correct alternative. In case no correction is needed, mark (D) as your answer.
The article explores the problem and the consequences damage arises out of dumping about 5 to 13 million tonnes of plastic into the ocean each year.
Reason: The given part is grammatically as well as contextually incorrect as two nouns ‘consequences’ and ‘damage’ are coming together and making no sense. Instead of ‘consequences’ the adjective ‘consequential’ would make sense in the given context of the sentence.
Besides, usage of the second verb ‘arises’ is also ungrammatical here.
Ex. My mother is next to the lady wears the red hat. (Incorrect)
Ex. My mother is next to the lady wearing the red hat. (Correct)
Instead of ‘arises’, present participle ‘arising’ should be used here.
Clearly, among the given choices option (C) replaces the bold part most appropriately.
The sentence after replacement becomes:
The article explores the problem and the consequential damage arising out of dumping about 5 to 13 million tonnes of plastic into the ocean each year.
Hence, the correct option is (C).
Direction: In this question, a part of the sentence is made bold. Below are given alternatives to the bold part at (A), (B), and (C) which may improve the sentence. Choose the correct alternative. In case no correction is needed, mark (D) as your answer.
A comedian analyzes the mundane from a variety of angles and find the thread among two points.
Reason: The verb ‘find’ is not in agreement with the subject ‘A comedian’ which is singular in number. Besides, ‘for two points’ usage of ‘among’ is erroneous. Instead of ‘among’ ‘between’ must be used to make the sentence grammatically correct.
Clearly, among the given choices option (B) replaces the bold part most appropriately.
The sentence after replacement becomes:
A comedian analyzes the mundane from a variety of angles and finds the thread between two points.
Hence, the correct option is (B).
Direction: In each question a sentence is given followed by a blank. You are provided with three fragments I, II and III. You have to identify which statement/statements can carry forward the given sentence in the most logical way so as to make the sentence coherent and contextually correct.
________ shifting further attention to security, rather than the economy.
I. Cyber security has become an increasingly large problem for major financial institutions, prompting major investments and has led to shifting further attention to security, rather than the economy.
II. One indication that the nation is worried about its relationship with USA is the increasing militarization which has led to shifting attention to security, rather than economy.
III. Recent racial tensions and conflict in Rakhine as well as international pressure on human rights are shifting further attention to security, rather than the economy.
This is grammatically correct but does not really make sense. Cyber security is an issue for financial Institutions but saying their attention has shifted away from economy sounds illogical.
So, this is incorrect.
II. One indication that the nation is worried about its relationship with USA is the increasing militarization which has led to shifting attention to security, rather than economy.
This is correct.
III. Recent racial tensions and conflict in Rakhine as well as international pressure on human rights are shifting further attention to security, rather than the economy.
This is correct.
Hence, the correct option is (D).
Direction: In each question a sentence is given followed by a blank. You are provided with three fragments I, II and III. You have to identify which statement/statements can carry forward the given sentence in the most logical way so as to make the sentence coherent and contextually correct.
___________ the monsoon never recovered from the stuttered start which saw progress stall for over 10 days off the western coast.
I. Although rainfall over the entire country falls under the normal category,
II. Just as the distribution of rain has been in sync with IMD scientists' forecast,
III. There is an increasing trend in monsoon rainfall and decrease in postmonsoon rainfall incidentally due to the fact that
This is correct contextually and grammatically.
Statements II: Just as the distribution of rain has been in sync with IMD scientists' forecast, the monsoon never recovered from the stuttered start which saw progress stall for over 10 days off the western coast.
This has no meaning.
Statements III: There is an increasing trend in monsoon rainfall and decrease in postmonsoon rainfall incidentally due to the fact that the monsoon never recovered from the stuttered start which saw progress stall for over 10 days off the western coast.
This has no meaning.
Only statement I is correct.
Hence, the correct option is (B).
Direction: In each question a sentence is given followed by a blank. You are provided with three fragments I, II and III. You have to identify which statement/statements can carry forward the given sentence in the most logical way so as to make the sentence coherent and contextually correct.
Although annual inflation rate has hovered on the lower side of 6%, _______.
I. it has steadily been trending upwards since 2015.
II. the Central Bank considers those readings to be consistent with its goal of 57%.
III.growth forecast has been reduced to 6% from 6.3%.
Statement I: Although annual inflation rate has hovered on the lower side of 6%, it has steadily been trending upwards since 2015.
The first statement says inflation has been rising since 2015. This means that although the annual inflation is lower this year yet, as compared to the years since 2015, it has risen. This makes sense and is correct.
Statement II: Although annual inflation rate has hovered on the lower side of 6%, the Central Bank considers those readings to be consistent with its goal of 57%.
Statement II says the Central Bank considers those readings to be consistent with its goal of 57%.This also looks consistent with the context.
Statement III: Although annual inflation rate has hovered on the lower side of 6%, growth forecast has been reduced to 6% from 6.3%.
The last statement, however, does not match with the original statement. When inflation is low, growth slows down. So both the statements are in agreement with each other rather than contradiction.
Hence, the correct option is (C).
Directions: The following question has two blanks, each blank indicating that something has been omitted. Choose the set of words for each blank that best fits in the context of the sentence.
Basic principles of credit _____________ and monitoring are obviated in PSBs and must be sharpened to _____________ defects of capital, business purpose and character.
In order to eliminate the “defects of capital”, the shortcomings must first be identified and analyzed. The only word that aptly conveys this meaning is “diagnose”. "Emphasize" or "clarify" defects does not indicate this meaning and this eliminates options (B) and (C) as well.
Hence, the correct option is (D).
Directions: The following question has two blanks, each blank indicating that something has been omitted. Choose the set of words for each blank that best fits in the context of the sentence.
Promoters of MSMEs must have _____________ in the game to ensure that funds — venture capital, as well as bank loans made liberal by fiat — are not _____________ off.
Skin in the game (Idiom)
Meaning: to be at risk financially because you have invested in something that you want to happen
E.g.: You take more ownership of something when you have some skin in the game.
Siphoned off (Phrasal verb)
Meaning: to gradually steal money or goods, usually from a business or government
E.g.: Over the years, she siphoned off hundreds of thousands of dollars from various accounts.
Hence, the correct option is (C).
Directions: The following question has two blanks, each blank indicating that something has been omitted. Choose the set of words for each blank that best fits in the context of the sentence.
Buildings must ______ be examined and certified for safety, and those that fail to _____ to the NBC must be demolished.
Buildings must periodically be examined and certified for safety, and those that fail to conform to the NBC must be demolished.
Hence, the correct option is (D).
Direction: Find out which part has an error and mark it as your answer. If there is no error, mark ‘No error’ as your answer.
Everybody understands that (A)/ Australian continent is reeling under the worst B)/ forest fires of its history, don't they? C)/ No error D).
There are some nouns that are singular in a sense but take plural question tag, e.g: Everyone, each, every, nobody, none, everybody, no one, etc.
The pattern of a question tag is:
I. Auxiliary (e.g. do, did, is etc.) + not + subject (if the statement is affirmative)
II. Auxiliary (e.g. do, did, is, etc.) + subject (if the statement is negative)
Hence, the correct option is (D).
Direction: Read the passage given below and answer the questions that follow by selecting the correct most appropriate options.
1. Each drop represents a little bit of creation and of life itself. When the monsoon brings to northern India the first rains of summer, the parched earth opens its pores and quenches its thirst with a hiss of ecstasy. After baking in the sun for the last few months, the land looks cracked, dusty and tired. Now, almost overnight, new grass springs up, there is renewal everywhere, and the damp earth releases a fragrance sweeter than any devised by man.
2. Water brings joy to earth, grass, leaf bud, blossom, insect, bird, animal and the pounding heart of man. Small children run out of their homes to romp naked in the rain. Buffaloes, which have spent the summer listlessly around lakes gone dry, now plunge into heaven of muddy water. Soon the lakes and rivers will overflow with the monsoon’s generosity, Trekking in the Himalayan foothills, I recently walked for kilometres without encountering habitation. I was just scolding myself for not having brought along a water bottle when I came across a patch of green on a rock face. I parted a curtain of tender maidenhair fern and discovered a tiny spring issuing from the rocknectar for the thirsty traveller.
3. I stayed there for hours, watching the water descend, drop by drop, into a tiny casement in the rocks. Each drop reflected creation. That same spring, I later discovered, joined other springs to form a. swift, tumbling. stream, which went cascading down the hill into other streams until, in the plains, it became part of a river. And that river flowed into another mightier river that kilometres later emptied into the ocean. Be like water, taught Laotzu, philosopher ‘and founder of Taoism. Soft and limpid, it finds its way through, over or under any obstacle. It does not quarrel; it simply moves on.
To become part of a river, a tiny drop has to:
From the lines, it is evident that every drop of rain has its own identity which it represents and to become a part of the river it has to merge its identity.
Hence, the correct option is (D).
Direction: Read the passage given below and answer the questions that follow by selecting the correct most appropriate options.
1. Each drop represents a little bit of creation and of life itself. When the monsoon brings to northern India the first rains of summer, the parched earth opens its pores and quenches its thirst with a hiss of ecstasy. After baking in the sun for the last few months, the land looks cracked, dusty and tired. Now, almost overnight, new grass springs up, there is renewal everywhere, and the damp earth releases a fragrance sweeter than any devised by man.
2. Water brings joy to earth, grass, leaf bud, blossom, insect, bird, animal and the pounding heart of man. Small children run out of their homes to romp naked in the rain. Buffaloes, which have spent the summer listlessly around lakes gone dry, now plunge into heaven of muddy water. Soon the lakes and rivers will overflow with the monsoon’s generosity, Trekking in the Himalayan foothills, I recently walked for kilometres without encountering habitation. I was just scolding myself for not having brought along a water bottle when I came across a patch of green on a rock face. I parted a curtain of tender maidenhair fern and discovered a tiny spring issuing from the rocknectar for the thirsty traveller.
3. I stayed there for hours, watching the water descend, drop by drop, into a tiny casement in the rocks. Each drop reflected creation. That same spring, I later discovered, joined other springs to form a. swift, tumbling. stream, which went cascading down the hill into other streams until, in the plains, it became part of a river. And that river flowed into another mightier river that kilometres later emptied into the ocean. Be like water, taught Laotzu, philosopher ‘and founder of Taoism. Soft and limpid, it finds its way through, over or under any obstacle. It does not quarrel; it simply moves on.
The tiny spring issuing from the rock is hidden by:
Upon the perusal of the above statement, it can be concluded that the tiny spring issuing from the rock is hidden by maidenhair fern.
Hence, the correct option is (B).
Direction: Complete the paragraph given below.
Malaria is a lifethreatening mosquitoborne blood disease caused by a Plasmodium parasite. It is transmitted to humans through the bite of the Anopheles mosquito. Once an infected mosquito bites a human, the parasites multiply in the host's liver before infecting and destroying red blood cells. ______. However, some countries lack the resources to do this treatment effectively.
The complete paragraph Malaria is a lifethreatening mosquitoborne blood disease caused by a Plasmodium parasite. It is transmitted to humans through the bite of the Anopheles mosquito. Once an infected mosquito bites a human, the parasites multiply in the host's liver before infecting and destroying red blood cells. In some places, malaria can be treated and controlled with early diagnosis. However, some countries lack the resources to do this treatment effectively.
Hence, the correct option is (B).
Direction: In the following question, the given sentence has four parts marked (P), (Q), (R) and (S). Choose the part of the sentence with the error and mark it as your answer. If there is no error, mark 'No error (S)' as your answer.
If you describe someone as a maverick, (P) / you mean that he is unconventional and independent (Q) / and does not think or behave in the same way as other people. (R) / No error (S)
Replace 'as' with 'that in' part R.
We often use that after the demonstrative pronoun the same. Ex: This is the same man that deceived me.
Hence, the correct option is (C).
Direction: In the following question, the given sentence has four parts marked (P), (Q), (R) and (S). Choose the part of the sentence with the error and mark it as your answer. If there is no error, mark 'No error (S)' as your answer.
The consequence of (P) / his carelessness was (Q) / that the game was lost. (R) / No error (S)
Here, was is correct in both of the clauses.
Hence, the correct option is (D).
Directions: Read the passage carefully and answer the questions given below.
As NASA works toward its longterm goal of establishing a human settlement on Mars, SpaceX is fleshing out its plans to help NASA make that dream a reality.
The private spaceflight company, which regularly launches cargo to the International Space Station with the Falcon 9 rocket and will soon launch astronauts up there, is currently building an interplanetary spacecraft for Mars. Known as Starship, the rocketspacecraft combo will be able to launch 100 passengers and large amounts of cargo to and from the Red Planet.
Before Starship can launch to Mars, it will start off launching commercial satellites as early as 2021, followed by a manned flight around the moon in 2023. Although SpaceX has not given a timeline for its first missions to Mars, SpaceX founder Elon Musk has said that the first Mars base could be up and running in 2028. And while Musk shared some eyecatching artist illustrations depicting what he called "Mars Base Alpha" as an intricate network of buildings and infrastructure, SpaceX's plans for the Red Planet are not quite that extensive.
"SpaceX very much is a transportation company," Paul Wooster, the principal Mars development engineer at SpaceX, said during a speech at the Humans to Mars Summit in Washington in May. He explained that SpaceX plans to build whatever infrastructure is necessary to support the company's Starship flights to and from Mars; that could include landing pads and refueling stations for the reusable rockets.
For its very first Mars missions, SpaceX will land at least two unmanned cargo ships on the Red Planet before sending any humans there, Wooster said. Those cargo missions would bring supplies, such as life support systems and power generators that the first astronauts on Mars will need when they set up camp.
The first unmanned Mars missions will also be tasked with confirming the presence of natural resources that can provide fuel for future twoway missions to the Red Planet, Wooster said. SpaceX wants to use water ice from the planet's surface and carbon dioxide from the Martian atmosphere to refuel Starships on Mars, enabling the rockets to return to Earth.
After those first two cargo missions, SpaceX will launch two manned missions alongside two additional cargoonly flights to begin setting up a propellant production plant. At that plant, water and carbon dioxide will be converted into liquid methane and liquid oxygen, which fuel the rocket's engines.
So, while SpaceX intends to set up a transportation system for humans and cargo traveling to the Red Planet, the company won't be building an entire Mars base on its own. Musk has laid out his vision to create a millionperson colony on Mars, but to establish that colony SpaceX will have to work together with NASA and the agency's international partners and other commercial space companies. Several companies have already begun designing concepts for Mars habitats and have proposed orbital outposts similar to NASA's Lunar Gateway, which could serve as a waypoint for Starship and reduce the amount of fuel needed for return trips to Earth.
According to Elon Musk, when could the first Mars base be operational?
Hence, the correct option is (C).
Directions: Read the passage carefully and answer the questions given below.
As NASA works toward its longterm goal of establishing a human settlement on Mars, SpaceX is fleshing out its plans to help NASA make that dream a reality.
The private spaceflight company, which regularly launches cargo to the International Space Station with the Falcon 9 rocket and will soon launch astronauts up there, is currently building an interplanetary spacecraft for Mars. Known as Starship, the rocketspacecraft combo will be able to launch 100 passengers and large amounts of cargo to and from the Red Planet.
Before Starship can launch to Mars, it will start off launching commercial satellites as early as 2021, followed by a manned flight around the moon in 2023. Although SpaceX has not given a timeline for its first missions to Mars, SpaceX founder Elon Musk has said that the first Mars base could be up and running in 2028. And while Musk shared some eyecatching artist illustrations depicting what he called "Mars Base Alpha" as an intricate network of buildings and infrastructure, SpaceX's plans for the Red Planet are not quite that extensive.
"SpaceX very much is a transportation company," Paul Wooster, the principal Mars development engineer at SpaceX, said during a speech at the Humans to Mars Summit in Washington in May. He explained that SpaceX plans to build whatever infrastructure is necessary to support the company's Starship flights to and from Mars; that could include landing pads and refueling stations for the reusable rockets.
For its very first Mars missions, SpaceX will land at least two unmanned cargo ships on the Red Planet before sending any humans there, Wooster said. Those cargo missions would bring supplies, such as life support systems and power generators that the first astronauts on Mars will need when they set up camp.
The first unmanned Mars missions will also be tasked with confirming the presence of natural resources that can provide fuel for future twoway missions to the Red Planet, Wooster said. SpaceX wants to use water ice from the planet's surface and carbon dioxide from the Martian atmosphere to refuel Starships on Mars, enabling the rockets to return to Earth.
After those first two cargo missions, SpaceX will launch two manned missions alongside two additional cargoonly flights to begin setting up a propellant production plant. At that plant, water and carbon dioxide will be converted into liquid methane and liquid oxygen, which fuel the rocket's engines.
So, while SpaceX intends to set up a transportation system for humans and cargo traveling to the Red Planet, the company won't be building an entire Mars base on its own. Musk has laid out his vision to create a millionperson colony on Mars, but to establish that colony SpaceX will have to work together with NASA and the agency's international partners and other commercial space companies. Several companies have already begun designing concepts for Mars habitats and have proposed orbital outposts similar to NASA's Lunar Gateway, which could serve as a waypoint for Starship and reduce the amount of fuel needed for return trips to Earth.
As per the passage, which rocket is used by SpaceX to send cargo to the International Space Station?
I. Falcon 9
II. Falcon Heavy
III. Starship
Hence, the correct option is (A).
Directions: Read the passage carefully and answer the questions given below.
As NASA works toward its longterm goal of establishing a human settlement on Mars, SpaceX is fleshing out its plans to help NASA make that dream a reality.
The private spaceflight company, which regularly launches cargo to the International Space Station with the Falcon 9 rocket and will soon launch astronauts up there, is currently building an interplanetary spacecraft for Mars. Known as Starship, the rocketspacecraft combo will be able to launch 100 passengers and large amounts of cargo to and from the Red Planet.
Before Starship can launch to Mars, it will start off launching commercial satellites as early as 2021, followed by a manned flight around the moon in 2023. Although SpaceX has not given a timeline for its first missions to Mars, SpaceX founder Elon Musk has said that the first Mars base could be up and running in 2028. And while Musk shared some eyecatching artist illustrations depicting what he called "Mars Base Alpha" as an intricate network of buildings and infrastructure, SpaceX's plans for the Red Planet are not quite that extensive.
"SpaceX very much is a transportation company," Paul Wooster, the principal Mars development engineer at SpaceX, said during a speech at the Humans to Mars Summit in Washington in May. He explained that SpaceX plans to build whatever infrastructure is necessary to support the company's Starship flights to and from Mars; that could include landing pads and refueling stations for the reusable rockets.
For its very first Mars missions, SpaceX will land at least two unmanned cargo ships on the Red Planet before sending any humans there, Wooster said. Those cargo missions would bring supplies, such as life support systems and power generators that the first astronauts on Mars will need when they set up camp.
The first unmanned Mars missions will also be tasked with confirming the presence of natural resources that can provide fuel for future twoway missions to the Red Planet, Wooster said. SpaceX wants to use water ice from the planet's surface and carbon dioxide from the Martian atmosphere to refuel Starships on Mars, enabling the rockets to return to Earth.
After those first two cargo missions, SpaceX will launch two manned missions alongside two additional cargoonly flights to begin setting up a propellant production plant. At that plant, water and carbon dioxide will be converted into liquid methane and liquid oxygen, which fuel the rocket's engines.
So, while SpaceX intends to set up a transportation system for humans and cargo traveling to the Red Planet, the company won't be building an entire Mars base on its own. Musk has laid out his vision to create a millionperson colony on Mars, but to establish that colony SpaceX will have to work together with NASA and the agency's international partners and other commercial space companies. Several companies have already begun designing concepts for Mars habitats and have proposed orbital outposts similar to NASA's Lunar Gateway, which could serve as a waypoint for Starship and reduce the amount of fuel needed for return trips to Earth.
Which of the following is/are not inferred by the term “Red Planet”?
The entire passage talks about Mars and journey to Mars. Nowhere is Venus or Jupiter mentioned. “Red Planet”, in this passage refers to Mars only.
Hence, the correct option is (D).
Direction: Complete the paragraph given below.
'How did you relax on Sunday?' 'What was your last holiday like?' Simple though these questions sound, your next job might depend on how you answer them. _______. Instead of the usual laborious online questionnaires or psychometric tests, some recruiters are asking job candidates to call a phone number, key in a personal pin code and respond to a string of questions posed by a computer.
The given passage talks about how some recruiters are exploring novel technological techniques to assess the suitability of candidates.
Option (C): i.e., 'And it won't be a human you're talking to, but a computer' is the correct answer because it adds the required meaning and completes the passage.
Option (A): i.e., 'How you answer is always more important than what your answer is' is not the answer even though it is mildly related to the passage because it draws the attention to the questions asked in the interview rather than the changing recruitment process itself.
Option (B): 'Computers are changing the world' do not contribute any meaning to the passage.
Option (D): i.e., 'It's how you say it' are both very vague sentences and do not contribute any meaning to the passage.
The complete paragraph 'How did you relax on Sunday?' 'What was your last holiday like?' Simple though these questions sound, your next job might depend on how you answer them. And it won't be a human you're talking to, but a computer. Instead of the usual laborious online questionnaires or psychometric tests, some recruiters are asking job candidates to call a phone number, key in a personal pin code and respond to a string of questions posed by a computer.
Hence, the correct option is (C).
Time taken by two trains running in opposite directions to cross a man standing near a pole is 48 seconds and 38 seconds respectively and it took 42 seconds for the trains to cross each other. What is the ratio of the speed of the trains?
Both trains cross the man in 48 seconds and 38 seconds
Speed = Distance/Time
Relative speed = when train in opposite direction = (x + y)m/s
Let the speed of trains be x m/s and y m/s respectively,
Length of the first train = speed × time = 48x
Length of the second train = speed × time = 38y
(48x + 38y)/(x + y) = 42
⇒ 48x + 38y = 42x + 42y
⇒ 6x = 4y
⇒ x/y = 2/3
∴ The ratio of the speed of the trains is 2 : 3
Hence, the correct answer is 2 : 3.
If a is a perfect square, what is the value of a, given that ax = 1/8 and x = 3/2[(log_{2} a)  3]?
⇒ a^{3/2[(log2 a)  3]} = ⅛
Applying log to base 2 in both sides, we get,
3/2[(log_{2} a)  3] log_{2} a = log_{2}(⅛)
⇒ 3/2[(log_{2} a)  3] log_{2} a = 3
Let log_{2} a = x
⇒ (x  3) x = 2
⇒ x^{2} 3x + 2 = 0
⇒ (x  1)(x  2) = 0
⇒ x = 1 or 2
⇒ log_{2 }a = 1 or log_{2} a = 2
⇒ a = 2 or a = 4
As given 'a' is a perfect square ⇒ a = 4
Hence, the correct answer is 4.
A, B, and C play cricket. If the ratio of the number of runs scored by A to that scored by B and the number of runs scored by B to that scored by C is 3:2. The total number of runs is 342. The number of runs scored by A was?
B : C :: 3 : 2
Let B = X
⇒A = 3X/2
and,
C = 2X/3
⇒ A + B + C = 342
⇒ 3X/2 + X + 2X/3 = 342
⇒ 9X + 6X + 4X = 342 × 6
⇐ 19X = 342 × 6
⇒ X = 108
⇒ Runs scored by A = (3(108))/2 = 162
Hence, the correct answer is 162.
If P and Q be two sets such that P ∪ Q = P, then P ∩ Q will be:
Let A and B be two sets. The intersection of A and B is the set of all those elements which are present in both sets A and B.
The intersection of A and B is denoted by A ∩ B
i.e., A ∩ B = {x : x ∈ A and x ∈ B}
The Venn diagram for intersection is as shown below:
Union:
Let A and B be two sets. The union of A and B is the set of all those elements which belong to either A or B or both A and B.
The union of A and B is denoted by A ∪ B.
i.e., A ∪ B = {x : x ∈ A or x ∈ B}
The Venn diagram for the union of any two sets is shown below:
A ∪ B = A + B  A ∩ B
As we know,
P ∪ Q = P + Q  P ∩ Q
Putting the values given in the question,
P = P + Q  P ∩ Q
P ∩ Q = Q
Hence, the correct answer is Q.
To find:
Using
= log_{n}(2017!)
= log_{n}(n) = 1
Hence, the correct answer is 1.
The areas of three adjacent faces of a cuboidal tank are 3 m^{2},12 m^{2} and 16 m^{2}. The capacity of the tank, in litres, is:
Areas of 3 adjacent faces of cuboidal tank = 3 m^{2},12 m^{2},16 m^{2}
As we know,
1 m^{3 }= 1000 Litres
If areas of 3 adjacent faces of a cuboid are x,y and z respectively, then
Volume of cuboid =
Areas of 3 adjacent faces of cuboidal tank = 3 m^{2}, 12 m^{2}, 16 m^{2}
Volume of cuboid =
Capacity of tank =
Capacity of tank = 24 m^{3}
1 m^{3}=1000 Litres
Capacity of tank = 24 × 1000 lites
Capacity of tank = 24000 litres
∴ The capacity of the tank, (in litres) is 24000 litres.
Hence, the correct answer is 24000.
If the number 2632A4878 is completely divisible by 9 . Find the possible value of ' A′?
Number 2632A4878 is divisible by 9.
The Sum of all digits should be divisible by 9.
The number is 2632 A4878.
= 2 + 6 + 3 + 2 + A + 4 + 8 + 7 + 8
= 40 + A
Put A = 5
= 40 + 5 = 45
⇒ 45 is divisible by 9.
The value of ' A′ is 5.
Hence, the correct answer is 5.
The range of the realvalued function f(x) = is:
Let, y^{2} = 9  x^{2}
⇒ x2 = 9  y2
x = ...(1)
We know that for any function f(x)= ,y ≥ 0…. (A)
From equation (1).
9 − y^{2 }≥ 0
y^{2 }− 9 ≤ 0
⇒ (y + 3)(y − 3) ≤ 0
⇒ −3 ≤ y ≤ 3
But from equation (A) y must be positive, then, y = [0, 3].
Range = the value of y = [0, 3]
Hence, the correct answer is [0, 3].
Point Q(b,−1) is the midpoint of segment EF. Coordinates of point E are (−4, a) and point F are (2,0). What is the value of a and b?
Point Q(b,−1) is the midpoint of segment with endpoints E(−4, a) and F(2, 0).
As we know,
The midpoint of a segment with endpoints (x_{1}, y_{1}) and (x_{2}, y_{2}) is given by,
On comparing, we get
b = −1, a = −2
Hence, the correct answer is a = 2, b = 1.
The coefficient of the term independent of x in the expansion of is
For term to be independent of x,
5  (5r/2) = 0
⇒ r = 2
Substituting the values in (1) we get:
T_{3 }= (−1)^{210}C2^{3−3}= 10(9)/2(27)
= 5/3
Hence, the correct answer is 5/3.
The sum of radii spheres A and B is 14 cm, the radius of A being larger than that of B. The difference between their surface areas is 112π. What is the ratio of the volumes of A and B?
The Difference between the surface area of the spheres is 112π
The sum of the radii of spheres of A and B is 14 cm
Radius of A is larger than the radius of B
As we know,
Area of a sphere =4πr^{2} (where ' r′ is the radius of the sphere)
Volume of a sphere
= (4/3)πr^{3}
Let the radius of the circle A be ′a′
Let the radius of the circle B be ' b '
Difference of the surface area of the circle is 112π
4πa^{2 }− 4πb^{2 }= 112π
(a + b)⋅(a − b) = 28
a − b = 2 [Given, (a + b) = 2]
a + b = 14… (i)
a − b = 2… (ii)
Solving equation (i) and (ii)
⇒ a = 8 and b = 6
So,
Volume of sphere with radius a cm : volume of sphere with radius b cm=4πa^{3}:4πb^{3}
= 8^{3}:6^{3}
= 512:216
= 64:27
∴ The ratio of the volume will be 64:27.
Hence, the correct answer is 64:27.
A train 1350 m long takes 135 seconds to cross a man running at a speed of 5kmph in a direction same to that of the train. What is the speed of the train?
Speed of men = 5 km/h
Time to cross the men = 135 seconds
Let the speed of the train be x km/h
Relative speed = (x − 5)km/h
⇒ (x − 5) = (1350 × 18)/(135 × 5)
⇒ x − 5 = 36
⇒ x = 36 + 5 = 41 km/h
So, 41 km/h is the speed of train
Hence, the correct answer is 41 km/h.
How many words can be formed with the letters of the word VOWELS that begin with O and end with E?
Number of arrangement of n different objects is given by n!
n! = n×(n−1)×…×1
The word VOWELS contains 6 letters, in which all the different letters occur only once.
Now, after fixing O in first place and E in the last place, we have only 4 letters.
∴ Number of words =4!=24.
Hence, the correct answer is 24.
If f(x) = tan^{−1}[sinx/1+cosx], then what is the first derivative of f(x)?
And, the first derivative of
Hence, the correct answer is 1/2.
It takes 10 hours for a person to travel a distance. If he reduces his speed by 20%, then what is the percentage increase in the time taken to cover the same distance?
Let, speed be x km/hour.
It takes 10 hours to travel the distance.
That means total distance = 10x km
Latter speed =
x(100 – 20)/100 = 4x/5 km/hour
Time taken to cover the whole distance at this speed is 10x/(4x/5) = 12.5 hour
Time increase = (12.5 – 10) hours = 2.5 hours
Percentage increase in time taken =
(2.5/10) × 100 = 25%
Hence, the correct answer is 25%.
In a football World Cup several teams participated. If the last place team in the point table receive $40,000 as a prize money and the award increases by $2500 for the successive finishing places. The champion team receives $65,000. Find how many teams participated in the world cup?
Last team received $40,000.
Champion team received $65,000.
Award increases by $2500 for the successive finishing places.
Prizes received by the teams in increasing order are, $40,000, $42500, $4500, $47500,
This is an A.P. with a = 40,000, d = 2500 and I = 65,000
Let the number of terms be n. Then,
a_{n} = 65000
a + (n − 1)d = 65000
⇒ 40000 + (n − 1) × 2500 = 65000
⇒ (n − 1) × 2500 = 65000 − 40000
⇒ (n − 1) = 25000/2500
⇒ n − 1 = 10
⇒ n = 10 + 1
n = 11
∴ 11 teams participated in Football World Cup.
Hence, the correct answer is 11.
^{n}P_{r }= n!/(n−r)! = n × (n − 1)×….×(n−r+1)
Given that:
^{10}P_{r }= 5040
⇒ 10Pr = 10 × 504
⇒ 10Pr = 10 × 9 × 56
⇒ 10Pr = 10 × 9 × 8 × 7
⇒ 10Pr = 10 × (10 − 1) × (10 − 2) × (10 − 4 + 1)
On comparing the above expression with ^{n}P_{r }= n × (n − 1)×……×(n − r + 1), we get:
r = 4
Hence, the correct answer is 4.
A person bought two bicycles for Rs. 1600 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the second at 10% profit, he would get 5 Rs. more. The difference in the cost price of the two bicycles was:
Case I, When he sells first at 10% profit and second at 20% profit:
∴ Profit on CP_{1 }= 10% on 600 = Rs. 60
Profit on CP_{2 }= 20% on 1000 = Rs. 200
Total Profit = ₹ 260 ...(i) Case II, When he sells first at 20% profit and second at 10% profit:
∴ Profit on CP_{1 }= 20% on 600 = Rs. 120
Profit on _{2 }= 10% on 1000 = Rs. 100
Total Profit = Rs. 220...(ii)
Difference in Profit [(i)−(ii)} = 260 − 220 Rs.
= Rs. 40
When difference in profit is Rs. 40, then difference in cost price would be Rs. (1000 − 600) = Rs. 400.
When difference in profit is Rs. 5, then difference in cost price would be:
Rs. =((400/40) × 5)
= Rs. 50.
Hence, the correct answer is 50.
A number when divided by 2567, gives a remainder of 147. If the same number is divided by 17, then what will be the remainder?
Dividend = (Quotient × Divisor) + Remainder
Let the quotient is k.
Dividend = 2567k + 147
When the number is divided by 17.
(2567k + 147/17) = 151k + (147/17)
While solving we get quotient as 8 and remainder = 11
∴ The required remainder is 11.
Hence, the correct answer is 11.
If f: R → R and g: R → R are two mappings defined as f(x) = 2x and g(x) = x^{2 }+ 2, then the value of (f + g)(2) is:
then, (f + g)(2) = f(2) + g(2)
= (2 × 2) + (22 + 2)
= 4 + 6
= 10
Hence, the correct answer is 10.
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