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All questions of CDS Previous Year Question Paper Tests (2016 - 19) for CDS Exam
Who was the founder of Mahakali Pathshala in Calcutta?- a)Her Holiness Mataji Maharani Tapaswini
- b)Sister Nivedita
- c)Madamee Blavatsky
- d)Sarojini Naidu
Correct answer is option 'A'. Can you explain this answer?
Who was the founder of Mahakali Pathshala in Calcutta?
a)
Her Holiness Mataji Maharani Tapaswini
b)
Sister Nivedita
c)
Madamee Blavatsky
d)
Sarojini Naidu
|
Advait Singh answered |
Mataji Maharani Tapaswini was one of the strongest proponents of female education in India. Her greatest contribution came in the form of the Mahakali Pathshala which she set up in Kolkata in 1893.
The school was a completely indigenous affair which did not rely on either foreign aid or assistance. The education of girls was carried out on a strictly national basis in the hopes that they would be able to revive and regenerate Hindu society.
The school was a completely indigenous affair which did not rely on either foreign aid or assistance. The education of girls was carried out on a strictly national basis in the hopes that they would be able to revive and regenerate Hindu society.
Ice-cream, completely filled in a cylinder of diameter 35 cm and height 32 cm, is to be served by completely filling identical disposable cones of diameter 4 cm and height 7 cm. The maximum number of persons that can be served in this way is - a)950
- b)1000
- c)1050
- d)1100
Correct answer is option 'C'. Can you explain this answer?
Ice-cream, completely filled in a cylinder of diameter 35 cm and height 32 cm, is to be served by completely filling identical disposable cones of diameter 4 cm and height 7 cm. The maximum number of persons that can be served in this way is
a)
950
b)
1000
c)
1050
d)
1100
|
Notes Wala answered |
Let n persons can be served;
∴ Volume of the cylinder = n × (Volume of a disposable cone)
⇒ π × (35/2) × (35/2) × 32 = n × π/3 × 4 × 7
⇒ n = 350 × 3 = 1050
∴ 1050 persons can be served.
∴ Volume of the cylinder = n × (Volume of a disposable cone)
⇒ π × (35/2) × (35/2) × 32 = n × π/3 × 4 × 7
⇒ n = 350 × 3 = 1050
∴ 1050 persons can be served.
The following question consists of six sentences of a passage. The first and the sixth sentences are given in the beginning as S1 and S6. The middle four sentences in each have been jumbled up and labelled P, Q, R and S. You are required to find the proper sequence of the four sentences and mark your response accordingly.SI: History shows that the growth of civilization depends upon the gifts of nature, particularly the wealth yielded by the soil.
S6: In fact, most of the wars at the beginning of humanity’s history were fought for the gain of territory.
P: The more land they had, the more they were satisfied.
Q: The nature and the quality of the land they possessed were of great importance to them.
R: All ancient communities worked hard to produce food.
S: There was also a great desire among them to possess as much land as possible. The proper sequence should be- a)R Q S P
- b)Q R S P
- c)S Q R P
- d)P R Q S
Correct answer is option 'B'. Can you explain this answer?
The following question consists of six sentences of a passage. The first and the sixth sentences are given in the beginning as S1 and S6. The middle four sentences in each have been jumbled up and labelled P, Q, R and S. You are required to find the proper sequence of the four sentences and mark your response accordingly.
SI: History shows that the growth of civilization depends upon the gifts of nature, particularly the wealth yielded by the soil.
S6: In fact, most of the wars at the beginning of humanity’s history were fought for the gain of territory.
P: The more land they had, the more they were satisfied.
Q: The nature and the quality of the land they possessed were of great importance to them.
R: All ancient communities worked hard to produce food.
S: There was also a great desire among them to possess as much land as possible. The proper sequence should be
S6: In fact, most of the wars at the beginning of humanity’s history were fought for the gain of territory.
P: The more land they had, the more they were satisfied.
Q: The nature and the quality of the land they possessed were of great importance to them.
R: All ancient communities worked hard to produce food.
S: There was also a great desire among them to possess as much land as possible. The proper sequence should be
a)
R Q S P
b)
Q R S P
c)
S Q R P
d)
P R Q S
|
|
Advait Singh answered |
The correct sequence is 'QRSP'.
The first sentence S1 offers a historical perspective on the growth of civilization. It notes that land was essential for such growth.
The second sentence should be Q, which elaborates that the quality of the land was of great importance.
The third sentence should be R since none of the other options could serve as a viable follow-up the sentence and sentence R begins a new subject by pointing out that all communities worked hard to produce food.
The fourth sentence should be S as the ‘also’ shows a causal connection with the previous sentence. The fifth sentence should be P since S6 as a matter of justification draws upon the logic of the previous sentence before making a conclusion.
The sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is- a)17
- b)29
- c)43
- d)None of the above
Correct answer is option 'D'. Can you explain this answer?
The sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is
a)
17
b)
29
c)
43
d)
None of the above
|
|
Advait Singh answered |
Let the three prime numbers be x, y, y+36
x+y+y+36 = 100
x+2y = 64
2y is an even number always
We know that
Even + even = even or odd + odd = even
So x has to be even to satisfy x+2y = 64
The only even prime no is 2
Put x=2
2y = 62
Or y = 31
So the numbers are 2, 31, 67
Thus option D is the answer.
x+y+y+36 = 100
x+2y = 64
2y is an even number always
We know that
Even + even = even or odd + odd = even
So x has to be even to satisfy x+2y = 64
The only even prime no is 2
Put x=2
2y = 62
Or y = 31
So the numbers are 2, 31, 67
Thus option D is the answer.
If 3x = 4y = 12z, then z is equal to - a)xy
- b)x + y
- c)xy/x+y
- d)4x +3y
Correct answer is option 'C'. Can you explain this answer?
If 3x = 4y = 12z, then z is equal to
a)
xy
b)
x + y
c)
xy/x+y
d)
4x +3y
|
|
Advait Singh answered |
3x = 4y = 12z
Taking log of all 3 we get
xln3 = yln4 = zln12 = k
z = k/ln12 = k / ln(3*4) = k/ln3 + ln4 = k / (k/x +k/y) = xy / (x+y)
Taking log of all 3 we get
xln3 = yln4 = zln12 = k
z = k/ln12 = k / ln(3*4) = k/ln3 + ln4 = k / (k/x +k/y) = xy / (x+y)
The Most Favoured Nation (MFN) Clause under WTO regime is based on the principle of- a)Non-discrimination between nations
- b)Discrimination between nations
- c)Differential treatment between locals and foreigners
- d)Uniform tariff across commodities
Correct answer is option 'A'. Can you explain this answer?
The Most Favoured Nation (MFN) Clause under WTO regime is based on the principle of
a)
Non-discrimination between nations
b)
Discrimination between nations
c)
Differential treatment between locals and foreigners
d)
Uniform tariff across commodities
|
|
Simran Shah answered |
- Most-favoured-nation (MFN): treating other people equally without any discrimination under the WTO agreements.
- The MFN status under WTO implies that a country shall treat its all trading partners with parity and shall not make partial provisions.
- Hence, all the countries that are trading partners to a country shall enjoy the MFN status.
A plane is going in circles around an airport. The plane takes 3 minutes to complete one round. The angle of elevation of the plane from a point P on the ground at time t seconds is equal to that at time (t + 30) seconds. At time (t + x) seconds, the plane flies vertically above the point P. What is x equal to?- a)75 seconds
- b)90 seconds
- c)105 seconds
- d)135 seconds
Correct answer is option 'C'. Can you explain this answer?
A plane is going in circles around an airport. The plane takes 3 minutes to complete one round. The angle of elevation of the plane from a point P on the ground at time t seconds is equal to that at time (t + 30) seconds. At time (t + x) seconds, the plane flies vertically above the point P. What is x equal to?
a)
75 seconds
b)
90 seconds
c)
105 seconds
d)
135 seconds
|
|
Notes Wala answered |
Let the plane be at point A at t seconds and at point B after t + 30 seconds
Since the motion is uniform, we can say that at time t+15 seconds, the plane is above the point is diametrically opposite to the point P from where the angle is same.
Now since the time taken to cover the full circle is 3 minutes (180 seconds), the time taken by the plane to reach the diametrically opposite point will be 90 seconds.
So the time after which the plane reaches the point P will be = t+ 15 + 90 seconds = (t + 105 )seconds
Which of the following substances cause temporary hardness in water?
1. Mg (HC03)2
2. Ca (HC03)2
3. CaCl2
4. MgS04Select the correct answer using the code given below.- a)3 and 4
- b)2 and 3
- c)1 and 4
- d)1 and 2
Correct answer is option 'D'. Can you explain this answer?
Which of the following substances cause temporary hardness in water?
1. Mg (HC03)2
2. Ca (HC03)2
3. CaCl2
4. MgS04
1. Mg (HC03)2
2. Ca (HC03)2
3. CaCl2
4. MgS04
Select the correct answer using the code given below.
a)
3 and 4
b)
2 and 3
c)
1 and 4
d)
1 and 2
|
|
Advait Singh answered |
- Mg (HCO3)2 Magnesium Hydrogen Carbonate and Ca (HCO3)2 Calcium bicarbonate cause temporary hardness in water.
- Hard water is water that contains cations with a charge of +2, especially Ca2+ and Mg2+ Hence, both the salts mentioned above impart hardness to water. Hardness of water can be removed by boiling water, ion exchange process, Calgon process, by adding washing soda etc.
A gentleman left a sum of Rs. 39000 to be distributed among his widow, 5 sons and 4 daughters. If each son receives three times as much as a daughter receives, and each daughter receives twice as much as their mother receives, then what is the widow’s share?- a)Rs. 1000
- b)Rs. 1200
- c)Rs. 1500
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
A gentleman left a sum of Rs. 39000 to be distributed among his widow, 5 sons and 4 daughters. If each son receives three times as much as a daughter receives, and each daughter receives twice as much as their mother receives, then what is the widow’s share?
a)
Rs. 1000
b)
Rs. 1200
c)
Rs. 1500
d)
None of the above
|
|
Advait Singh answered |
Let the amount received by the widow = Rs x
∴ Amount received by daughter = 2 × x = 2x
Amount received by son = 3 × 2x = 6x
∴ Amount received by daughter = 2 × x = 2x
Amount received by son = 3 × 2x = 6x
Total amount = Amount received by widow + 5 × Amount received by sons + 4 × Amount received by daughter
39000 = x + 5 × 6x + 4 × 2x
39000 = x + 30x + 8x
39000 = 39x
∴ x = 1000
Widow receives Rs. 1000
39000 = x + 30x + 8x
39000 = 39x
∴ x = 1000
Widow receives Rs. 1000
Which one of the following statements regarding freedom to manage religious affairs as per the Constitution of India is not correct?- a)Every religious denomination shall have the right to manage its own affairs in matters of religion except some minor communities.
- b)Every religion or any section thereof shall have the right to own and acquire movable and immovable property.
- c)Every religious community has the right to establish and maintain institutions for religious and charitable purposes.
- d)Every community has the right to manage its own affairs in matters of religion.
Correct answer is option 'A'. Can you explain this answer?
Which one of the following statements regarding freedom to manage religious affairs as per the Constitution of India is not correct?
a)
Every religious denomination shall have the right to manage its own affairs in matters of religion except some minor communities.
b)
Every religion or any section thereof shall have the right to own and acquire movable and immovable property.
c)
Every religious community has the right to establish and maintain institutions for religious and charitable purposes.
d)
Every community has the right to manage its own affairs in matters of religion.
|
|
Advait Singh answered |
According to Article 26, every religious denomination or any of its section shall have the following rights:
(a) Right to establish and maintain institutions for religious and charitable Purposes;(No exception for some minor communities)
(b) Right to manage its own affairs in matters of religion
(c) Right to own and acquire movable and immovable property
(d) Right to administer such property in accordance with law.
Consider the following statements:
(1) The point of intersection of the perpendicular bisectors of the sides of a triangle may lie outside the triangle.
(2) The point of intersection of the perpendicular drawn from the vertices to the opposite side of a triangle may lie on two sides.Q. Which of the above statements is/are correct?- a)1 only
- b)2 only
- c)Both 1 and 2
- d)Neither 1 and 2
Correct answer is option 'C'. Can you explain this answer?
Consider the following statements:
(1) The point of intersection of the perpendicular bisectors of the sides of a triangle may lie outside the triangle.
(2) The point of intersection of the perpendicular drawn from the vertices to the opposite side of a triangle may lie on two sides.
(1) The point of intersection of the perpendicular bisectors of the sides of a triangle may lie outside the triangle.
(2) The point of intersection of the perpendicular drawn from the vertices to the opposite side of a triangle may lie on two sides.
Q. Which of the above statements is/are correct?
a)
1 only
b)
2 only
c)
Both 1 and 2
d)
Neither 1 and 2
|
|
Advait Singh answered |
Point of intersection of the perpendicular bisector is the circumcenter of the triangle.
It is possible for three chords to form a triangle but do not include the center when it is an obtuse angled triangle
∴ Statement 1 is possible
In a right triangle the perpendicular drawn from two vertices of the hypotenuse are the sides themselves. They meet on the vertex and lie on the side
∴ Statement 2 is possible
∴ Both 1 and 2 true
∴ Both 1 and 2 true
4 goats or 6 sheep can graze a field in 50 days. 2 goats and 3 sheep will graze it in- a)200 days
- b)150 days
- c)100 days
- d)50 days
Correct answer is option 'D'. Can you explain this answer?
4 goats or 6 sheep can graze a field in 50 days. 2 goats and 3 sheep will graze it in
a)
200 days
b)
150 days
c)
100 days
d)
50 days
|
Akshita Kulkarni answered |
6 sheep are equal to 4 goats
⇒ 3 sheep are equivalent to 4/2 = 2 goats
⇒ 2 goats and 3 sheep are equivalent to = 2 + 2 = 4 goats
∴ 4 goats can graze the field in 50 days [Given]
⇒ 3 sheep are equivalent to 4/2 = 2 goats
⇒ 2 goats and 3 sheep are equivalent to = 2 + 2 = 4 goats
∴ 4 goats can graze the field in 50 days [Given]
The following question consists of six sentences of a passage. The first and the sixth sentences are given in the beginning as S1 and S6. The middle four sentences in each have been jumbled up and labelled P, Q, R and S. You are required to find the proper sequence of the four sentences and mark your response accordingly.S1: It would be possible to adduce many examples showing what could be done with the limited means' at our ancestor’s disposal in the way of making life comfortable.
S6: I hope, in this essay, to make that connection manifest.
P: What have comfort and cleanliness to do with politics, morals, and religion?
Q: But look more closely and you will discover that there exists the closest connection between the recent growth of comfort and the recent history of ideas.
R: They show that if they lived in filth and discomfort, it was because filth and discomfort fitted in with their principles, political, moral and religious.
S: At a first glance one would say that there could be no causal connection between arm chairs and democracies, sofas and the family system, hot baths and religious orthodoxy.
The correct sequence should be- a)P R Q S
- b)R P S Q
- c)Q S R P
- d)Q S P R
Correct answer is option 'A'. Can you explain this answer?
The following question consists of six sentences of a passage. The first and the sixth sentences are given in the beginning as S1 and S6. The middle four sentences in each have been jumbled up and labelled P, Q, R and S. You are required to find the proper sequence of the four sentences and mark your response accordingly.
S1: It would be possible to adduce many examples showing what could be done with the limited means' at our ancestor’s disposal in the way of making life comfortable.
S6: I hope, in this essay, to make that connection manifest.
P: What have comfort and cleanliness to do with politics, morals, and religion?
Q: But look more closely and you will discover that there exists the closest connection between the recent growth of comfort and the recent history of ideas.
R: They show that if they lived in filth and discomfort, it was because filth and discomfort fitted in with their principles, political, moral and religious.
S: At a first glance one would say that there could be no causal connection between arm chairs and democracies, sofas and the family system, hot baths and religious orthodoxy.
The correct sequence should be
S6: I hope, in this essay, to make that connection manifest.
P: What have comfort and cleanliness to do with politics, morals, and religion?
Q: But look more closely and you will discover that there exists the closest connection between the recent growth of comfort and the recent history of ideas.
R: They show that if they lived in filth and discomfort, it was because filth and discomfort fitted in with their principles, political, moral and religious.
S: At a first glance one would say that there could be no causal connection between arm chairs and democracies, sofas and the family system, hot baths and religious orthodoxy.
The correct sequence should be
a)
P R Q S
b)
R P S Q
c)
Q S R P
d)
Q S P R
|
|
Advait Singh answered |
S1 is followed by P as the questions asked in S1 are further asked in P.
PR as a pair is correct since it analyses comfort and cleanliness. The word 'they' in R denotes a connection with P.
But later, the speaker is asking us to be a keen observer that is pointing to Q. Then the topic of connection between growth and ideas is carried forward in S and ending it with S6. The correct sequence is PRQS.
If a + b = 5 and ab = 6, then what is the value of a3 + b3?- a)35
- b)40
- c)90
- d)125
Correct answer is option 'A'. Can you explain this answer?
If a + b = 5 and ab = 6, then what is the value of a3 + b3?
a)
35
b)
40
c)
90
d)
125
|
|
Advait Singh answered |
We know the formula∶
(a3 + b3) = (a + b) (a2 + b2 – ab)
That can be written as∶
(a3 + b3) = (a + b) ((a + b)2 – 3ab)
Putting the given values;
(a3 + b3) = 5 × (25 – 18) = 35
(a3 + b3) = (a + b) (a2 + b2 – ab)
That can be written as∶
(a3 + b3) = (a + b) ((a + b)2 – 3ab)
Putting the given values;
(a3 + b3) = 5 × (25 – 18) = 35
Sound waves cannot travel through a _________.- a)Copper wire placed in air
- b)Silver slab placed in air
- c)Glass prism placed in water
- d)Wooden hollow pipe placed in vacuum.
Correct answer is option 'D'. Can you explain this answer?
Sound waves cannot travel through a _________.
a)
Copper wire placed in air
b)
Silver slab placed in air
c)
Glass prism placed in water
d)
Wooden hollow pipe placed in vacuum.
|
|
Advait Singh answered |
Sound wave cannot travel through a wooden hollow pipe placed in vacuum.
Sound energy transfer in form of vibrations, these vibrations need matter to travel, absence of matter in vacuum makes these waves impossible to travel.
Sound energy transfer in form of vibrations, these vibrations need matter to travel, absence of matter in vacuum makes these waves impossible to travel.
Which of the following statements relating to the Scheduled Tribes and Other Traditional Forest Dwellers (Recognition of Forest Rights) Act, 2006 are correct?
1. The Act recognizes forest rights of forest dwelling Scheduled Tribes who have been occupying the forest land before October 25, 1980.
2. The onus of implementation of the Act lies at the level of the State / UT Governments.
3. The Act seeks to recognize and vest certain forest rights in the forest dwelling Scheduled Tribes and other traditional forest dwellers.Select the correct answer using the code given below :- a)1 and 2 only
- b)2 and 3 only
- c)1 and 3 only
- d)1, 2 and 3
Correct answer is option 'D'. Can you explain this answer?
Which of the following statements relating to the Scheduled Tribes and Other Traditional Forest Dwellers (Recognition of Forest Rights) Act, 2006 are correct?
1. The Act recognizes forest rights of forest dwelling Scheduled Tribes who have been occupying the forest land before October 25, 1980.
2. The onus of implementation of the Act lies at the level of the State / UT Governments.
3. The Act seeks to recognize and vest certain forest rights in the forest dwelling Scheduled Tribes and other traditional forest dwellers.
1. The Act recognizes forest rights of forest dwelling Scheduled Tribes who have been occupying the forest land before October 25, 1980.
2. The onus of implementation of the Act lies at the level of the State / UT Governments.
3. The Act seeks to recognize and vest certain forest rights in the forest dwelling Scheduled Tribes and other traditional forest dwellers.
Select the correct answer using the code given below :
a)
1 and 2 only
b)
2 and 3 only
c)
1 and 3 only
d)
1, 2 and 3
|
|
Advait Singh answered |
- Scheduled Tribes and Other Traditional Forest Dwellers (Recognition of Forest Rights) Act, 2006, has been enacted to recognize and vest the forest rights and occupation of forest land in forest dwelling Scheduled Tribes and other traditional forest dwellers, who have been residing in such forests for generations, but whose rights could not be recorded.
- It is recognized to those who have been occupying the land before October 25, 1980.
- The onus of implementation of the Act lies at the level of the State / UT Governments.
A ladder is resting against a vertical wall and its bottom is 2.5 m away from the wall. If it slips 0.8 m down the wall, then its bottom will move away from the wall by 1.4 m. What is the length of the ladder?- a)6.2 m
- b)6.5 m
- c)6.8 m
- d)7.5 m
Correct answer is option 'B'. Can you explain this answer?
A ladder is resting against a vertical wall and its bottom is 2.5 m away from the wall. If it slips 0.8 m down the wall, then its bottom will move away from the wall by 1.4 m. What is the length of the ladder?
a)
6.2 m
b)
6.5 m
c)
6.8 m
d)
7.5 m
|
|
Notes Wala answered |
AB = CD = x = Length of ladder
Let OC = y m
y2 + 3.92 = x2
(y+0.8)2 + 2.52 = x2
So y2 + 3.92 = (y+0.8)2 + 2.52
y = 5.2m
x= √(5.22+3.92)
x= 6.5m
What would be the maximum value of Q in the equation 5P9 + 3R7 + 2Q8 = 1114?- a)9
- b)8
- c)5
- d)4
Correct answer is option 'A'. Can you explain this answer?
What would be the maximum value of Q in the equation 5P9 + 3R7 + 2Q8 = 1114?
a)
9
b)
8
c)
5
d)
4
|
Dishani Iyer answered |
5P9 + 3R7 + 2Q8 = 1114
We can see that, the sum of last digits i.e. (5 + 3 + 2) = 10 and 1 is added as carry
And 2 is added as carry in the sum of middle digits of the numbers (P + Q + R)
⇒ (P + Q + R + 2) will be 11 only.
⇒ P + Q + R = 9
⇒ P + Q + R = 9
For maximum value of Q, values of P and R should be minimum
If P = R = 0 then Q = 9
∴ Maximum value of Q = 9
If P = R = 0 then Q = 9
∴ Maximum value of Q = 9
A student secure 40% of the marks to pass an examination. He gets only 45 marks and fails by 5 marks. The maximum marks are- a)120
- b)125
- c)130
- d)150
Correct answer is option 'B'. Can you explain this answer?
A student secure 40% of the marks to pass an examination. He gets only 45 marks and fails by 5 marks. The maximum marks are
a)
120
b)
125
c)
130
d)
150
|
Defence Exams answered |
Total marks required for passing = 45 + 5 = 50 marks
50 marks is 40% of the maximum marks
⇒ 50 = 40/100 × Maximum marks
∴ Maximum mark = 50 × 100/40 = 125 marks
50 marks is 40% of the maximum marks
⇒ 50 = 40/100 × Maximum marks
∴ Maximum mark = 50 × 100/40 = 125 marks
Which of the following statements about the olive ridley turtles is/are correct?
1. They are the smallest and most abundant of all sea turtles found in the world.
2. They live in warm waters of Pacific, Atlantic and Indian Oceans.
3. The Coromandel Coast in India is the largest mass nesting site for the olive ridley turtles.Select the correct Answer using the code given below.- a)1, 2 and 3
- b)1 and 2 only
- c)2 and 3 only
- d)1 only
Correct answer is option 'B'. Can you explain this answer?
Which of the following statements about the olive ridley turtles is/are correct?
1. They are the smallest and most abundant of all sea turtles found in the world.
2. They live in warm waters of Pacific, Atlantic and Indian Oceans.
3. The Coromandel Coast in India is the largest mass nesting site for the olive ridley turtles.
1. They are the smallest and most abundant of all sea turtles found in the world.
2. They live in warm waters of Pacific, Atlantic and Indian Oceans.
3. The Coromandel Coast in India is the largest mass nesting site for the olive ridley turtles.
Select the correct Answer using the code given below.
a)
1, 2 and 3
b)
1 and 2 only
c)
2 and 3 only
d)
1 only
|
V.v.ramana So answered |
B
In the figure given below, p and q are parallel lines. What are the values of the angles x, y and z?
- a)x = 80°, y = 40°, z = 100°
- b)x = 80°, y = 50°, z = 105°
- c)x = 70°, y = 40°, z = 110°
- d)x = 60°, y = 20°, z = 120°
Correct answer is option 'D'. Can you explain this answer?
In the figure given below, p and q are parallel lines. What are the values of the angles x, y and z?
a)
x = 80°, y = 40°, z = 100°
b)
x = 80°, y = 50°, z = 105°
c)
x = 70°, y = 40°, z = 110°
d)
x = 60°, y = 20°, z = 120°
|
|
Advait Singh answered |
x/3 = y [∵ Alternate interior angles are equal]
x + z = 180° [∵ Co-interior angles are supplementary]
z + 40 + x/3 = 180° [∵ Angle in a straight line is 180°]
⇒ 180 – x + 40 + x/3 = 180
⇒ 40 – 2x/3 = 0
⇒ x = 60°
∴ x = 60°, y = x/3 = 20° and z = 180 – x = 120°
⇒ 180 – x + 40 + x/3 = 180
⇒ 40 – 2x/3 = 0
⇒ x = 60°
∴ x = 60°, y = x/3 = 20° and z = 180 – x = 120°
The mean marks obtained by 300 students in a subject are 60. The mean of top 100 students was found to be 80 and the mean of last 100 students was found to be 50. The mean marks of the remaining 100 students are- a)70
- b)65
- c)60
- d)50
Correct answer is option 'D'. Can you explain this answer?
The mean marks obtained by 300 students in a subject are 60. The mean of top 100 students was found to be 80 and the mean of last 100 students was found to be 50. The mean marks of the remaining 100 students are
a)
70
b)
65
c)
60
d)
50
|
|
Defence Exams answered |
Since the mean marks obtained by 300 students in a subject are 60;
∴ Sum of marks of 300 students = 300 × 60 = 18000
Mean of top 100 students was found to be 80;
∴ Sum of marks of top 100 students = 100 × 80 = 8000
Mean of last 100 students was found to be 50;
∴ Sum of marks of last 100 students = 100 × 50 = 5000
∴ Sum of marks of remaining 100 students = 18000 - 5000 - 8000 = 5000
∴ Mean of remaining 100 students = 5000/100 = 50
If (4a +7b) (4c-7d) = (4a -7b) (4c +7d, then which one of the following is correct?
- a)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
If (4a +7b) (4c-7d) = (4a -7b) (4c +7d, then which one of the following is correct?
a)
b)
c)
d)
|
|
Defence Exams answered |
(4a+7b)(4c-7d) = (4a-7b)(4c+7d)
(4a+7b)/(4a-7b) = (4c+7d)/(4c-7d)
Using componendo and dividendo
(4a+7b)+(4a-7b) / (4a+7b)-(4a-7b) = (4c+7d)+(4c-7d) / (4c+7d)-(4c-7d)
Or 8a/14b = 8c/14d
Or a/b = c/d
(4a+7b)/(4a-7b) = (4c+7d)/(4c-7d)
Using componendo and dividendo
(4a+7b)+(4a-7b) / (4a+7b)-(4a-7b) = (4c+7d)+(4c-7d) / (4c+7d)-(4c-7d)
Or 8a/14b = 8c/14d
Or a/b = c/d
Each of the following items in this section consists of a sentence the parts of which have been jumbled. These parts have been labelled P, Q, R and S. Given below each sentence are four sequences namely (a), (b), (c) and (d). You are required to re-arrange the jumbled parts of the sentence and mark your response accordingly.While some live (P) to eat and drink (Q) many do not have enough (R) in luxury (S)The proper sequence should be- a)P S R Q
- b)P R S Q
- c)S P Q R
- d)R Q S P
Correct answer is option 'A'. Can you explain this answer?
Each of the following items in this section consists of a sentence the parts of which have been jumbled. These parts have been labelled P, Q, R and S. Given below each sentence are four sequences namely (a), (b), (c) and (d). You are required to re-arrange the jumbled parts of the sentence and mark your response accordingly.
While some live (P) to eat and drink (Q) many do not have enough (R) in luxury (S)
The proper sequence should be
a)
P S R Q
b)
P R S Q
c)
S P Q R
d)
R Q S P
|
|
Advait Singh answered |
Option A forms a correct sentence of the order PSRQ – “While some live in luxury many do not have enough to eat and drink".
Since option A is appropriate therefore, all other options rule out.
If x = a cosθ + b sinθ and y = a sinθ - b cosθ, then what is (x2 + y2) equal to?- a)2ab
- b)a + b
- c)a2 + b2
- d)a2 - b2
Correct answer is option 'C'. Can you explain this answer?
If x = a cosθ + b sinθ and y = a sinθ - b cosθ, then what is (x2 + y2) equal to?
a)
2ab
b)
a + b
c)
a2 + b2
d)
a2 - b2
|
|
Advait Singh answered |
Given x = a cosθ + b sinθ and y = a sinθ - b cosθ;
(x2 + y2) = (a cosθ + b sinθ)2 + (a sinθ - b cosθ)2
⇒ a2cos2θ + b2sin2θ + 2sinθ cosθ + a2cos2θ + b2sin2θ - 2sinθ cosθ
⇒ a2(cos2θ + sin2θ) + b2(cos2θ + sin2θ)
⇒ a2 + b2
⇒ a2 + b2
In a circle of radius 8 cm, AB and AC are two chords such that AB = AC = 12 cm. What is the length of chord BC?- a)
- b)
- c)
- d)
Correct answer is option 'D'. Can you explain this answer?
In a circle of radius 8 cm, AB and AC are two chords such that AB = AC = 12 cm. What is the length of chord BC?
a)
b)
c)
d)
|
|
Defence Exams answered |
O is the center of circle
Here ABC forms an isosceles triangle as AB=AC=12cm
So AE (a perpendicular bisector) passes through O as OE also bisects chord BC at right angle
AD = DB = 6
In triangle ADO
AO2 = AD2 + DO2
OD = √64 – 36 = √28
Now using similarity AEB~ADO
AB/AO = EB/DO
12/8 = (BC/2)/ √28
BC=6√7
It is given that log10 2= 0.301 and log10 3 = 0.477. How many digits are there in (108)10?- a)19
- b)20
- c)21
- d)22
Correct answer is option 'C'. Can you explain this answer?
It is given that log10 2= 0.301 and log10 3 = 0.477. How many digits are there in (108)10?
a)
19
b)
20
c)
21
d)
22
|
|
Advait Singh answered |
No of digits in (108)10
We have to find the log of the given number with base 10 and add one to its integral part to find the no of digits
log (108)10 = 10 log 108 = 10 log(22 * 33) = 10[2log2 + 3log3]
= 10[2*0.301 + 3*0.477] = 20.33
Integral part = 20
No of digits = 20+1 = 21
We have to find the log of the given number with base 10 and add one to its integral part to find the no of digits
log (108)10 = 10 log 108 = 10 log(22 * 33) = 10[2log2 + 3log3]
= 10[2*0.301 + 3*0.477] = 20.33
Integral part = 20
No of digits = 20+1 = 21
The vertical angle of a right circular cone is π/2 and the slant height is √2r cm. What is the volume of the cone in cubic cm?- a)πr3
- b)9π3
- c)πr3/3
- d)3πr3
Correct answer is option 'C'. Can you explain this answer?
The vertical angle of a right circular cone is π/2 and the slant height is √2r cm. What is the volume of the cone in cubic cm?
a)
πr3
b)
9π3
c)
πr3/3
d)
3πr3
|
|
Advait Singh answered |
Semi - vertical angle, α = ½ × π/2 = π/4 = 45°
Slant height, l × sinα = radius
⇒ √2r × sin 45° = √2r × 1/√2 = r = radius
⇒ Height = rtanα = rtan45° = r
∴ Volume of the cone = 1/3πr2H = πr3/3
Slant height, l × sinα = radius
⇒ √2r × sin 45° = √2r × 1/√2 = r = radius
⇒ Height = rtanα = rtan45° = r
∴ Volume of the cone = 1/3πr2H = πr3/3
The Twelfth Five-Year Plan focussed on inclusive growth. Which of the following were considered as challenges for inclusiveness?
1. Poverty
2. Group inequality
3. Regional imbalance
4. UnemploymentSelect the correct answer using the code given below.- a)1, 3 and 4 only
- b)1, 2, 3 and 4
- c)1, 2 and 4 only
- d)2 and 3 only
Correct answer is option 'B'. Can you explain this answer?
The Twelfth Five-Year Plan focussed on inclusive growth. Which of the following were considered as challenges for inclusiveness?
1. Poverty
2. Group inequality
3. Regional imbalance
4. Unemployment
1. Poverty
2. Group inequality
3. Regional imbalance
4. Unemployment
Select the correct answer using the code given below.
a)
1, 3 and 4 only
b)
1, 2, 3 and 4
c)
1, 2 and 4 only
d)
2 and 3 only
|
|
Advait Singh answered |
- All the above mentioned options were considered as challenges for inclusiveness.
- Inclusiveness - the quality of including many different types of people and treating them all fairly and equally.
How many numbers between 500 and 1000 are divisible by 13?- a)36
- b)37
- c)38
- d)39
Correct answer is option 'C'. Can you explain this answer?
How many numbers between 500 and 1000 are divisible by 13?
a)
36
b)
37
c)
38
d)
39
|
|
Advait Singh answered |
500 = 13 × 38 + 6 [∵ 13 × 38 = 494]
⇒ First number divisible by 13 = 13 × 39 = 507
1000 = 76 × 13 + 12 [∵ 76 × 13 = 988]
⇒ Last number divisible by 13 in the given interval = 13 × 76
⇒ Number of multiples = 76 – 39 + 1 = 38 [1 is added ∵ 507 is also included]
∴ There are 38 numbers between 500 and 1000 that are divisible by 13
1000 = 76 × 13 + 12 [∵ 76 × 13 = 988]
⇒ Last number divisible by 13 in the given interval = 13 × 76
⇒ Number of multiples = 76 – 39 + 1 = 38 [1 is added ∵ 507 is also included]
∴ There are 38 numbers between 500 and 1000 that are divisible by 13
Which of the following are the powers of the Supreme Court of India?
1. Original jurisdiction in a dispute between the Government of India and one or more States
2. The power to hear appeals from the High Courts
3 Passing decrees and orders for doing justice in any matter before it
4. Render advice to the President of India in matters of lawSelect the correct answer using the code given below.- a)1, 2, 3 and 4
- b)1, 2 and 3 only
- c)1 and 2 only
- d)3 and 4 only
Correct answer is option 'A'. Can you explain this answer?
Which of the following are the powers of the Supreme Court of India?
1. Original jurisdiction in a dispute between the Government of India and one or more States
2. The power to hear appeals from the High Courts
3 Passing decrees and orders for doing justice in any matter before it
4. Render advice to the President of India in matters of law
1. Original jurisdiction in a dispute between the Government of India and one or more States
2. The power to hear appeals from the High Courts
3 Passing decrees and orders for doing justice in any matter before it
4. Render advice to the President of India in matters of law
Select the correct answer using the code given below.
a)
1, 2, 3 and 4
b)
1, 2 and 3 only
c)
1 and 2 only
d)
3 and 4 only
|
|
Advait Singh answered |
Which one of the following is not correct?The proportion of various items in a pie diagram is proportional to the - a)Area of slices
- b)Angles of slices
- c)Lengths of the curved surface arcs of slices
- d)Perimeters of the slices
Correct answer is option 'D'. Can you explain this answer?
Which one of the following is not correct?
The proportion of various items in a pie diagram is proportional to the
a)
Area of slices
b)
Angles of slices
c)
Lengths of the curved surface arcs of slices
d)
Perimeters of the slices
|
|
Advait Singh answered |
Data in a pie chart ∝ Area
Area = θ/360 × πr2
∴ Area ∝ θ
∴ Data ∝ θ, where θ is the angle of slice
Length of the curved surface = θ/360 × 2πr
∴ Length of curved surface of arc ∝ θ
∴ Data ∝ Length of the curved surface
Perimeter of slices = θ/360 × 2πr + 2r
∴ Perimeter of slices is not proportional to the data
Area = θ/360 × πr2
∴ Area ∝ θ
∴ Data ∝ θ, where θ is the angle of slice
Length of the curved surface = θ/360 × 2πr
∴ Length of curved surface of arc ∝ θ
∴ Data ∝ Length of the curved surface
Perimeter of slices = θ/360 × 2πr + 2r
∴ Perimeter of slices is not proportional to the data
Two equal circular region of greatest possible area are cut off from a given circular sheet of area A. What is the remaining area of the sheet?- a)A/2
- b)A/3
- c)3A/5
- d)2A/5
Correct answer is option 'A'. Can you explain this answer?
Two equal circular region of greatest possible area are cut off from a given circular sheet of area A. What is the remaining area of the sheet?
a)
A/2
b)
A/3
c)
3A/5
d)
2A/5
|
|
Advait Singh answered |
The greatest possible area is cut off,
∴ Both the circles touch each other and extend to the two ends of the diameter of the main circle
Sum of diameters of the circle = Diameter of the larger circle
2 × diameter of the small circle = Diameter of the larger circle
The radius of the small circle = ½ × Radius of the larger circle
Area ∝ Radius2
Area of small circle/Area of large circle = (Radius of small circle/Radius of a large circle)2
?/A = (½)2
∴ Area of small circle = A/4
Remaining area = Area of the large circle – 2 × Area of the small circle
⇒ A – 2 × A/4 = A/2
If the surface area of a sphere is reduced to one-ninth of the area, its radius reduces to - a)One-fourth
- b)One-third
- c)One-fifth
- d)One-ninth
Correct answer is option 'B'. Can you explain this answer?
If the surface area of a sphere is reduced to one-ninth of the area, its radius reduces to
a)
One-fourth
b)
One-third
c)
One-fifth
d)
One-ninth
|
|
Advait Singh answered |
Surface area of a sphere = 4πr2
∴ Surface area of a sphere ∝∝ (Square of radius)
∴ Surface area of a sphere ∝∝ (Square of radius)
Since the surface area of a sphere is reduced to one-ninth, radius will reduce to One-third.
Consider the following frequency distribution:
What is the median for the distribution?- a)6
- b)7
- c)8
- d)9
Correct answer is option 'C'. Can you explain this answer?
Consider the following frequency distribution:
What is the median for the distribution?
What is the median for the distribution?
a)
6
b)
7
c)
8
d)
9
|
|
Advait Singh answered |
Summation of frequencies = 6+4+5+8+9+6+4 = 42
Median = mid value = average of 21st and 22nd value
Arranging data in increasing order we get
So mid value i.e 21st and 22nd value = 8
Median = mid value = average of 21st and 22nd value
Arranging data in increasing order we get
So mid value i.e 21st and 22nd value = 8
The ratio of two numbers is 1 ∶ 5 and their product is 320. What is the difference between the squares of these two numbers?- a)1024
- b)1256
- c)1536
- d)1640
Correct answer is option 'C'. Can you explain this answer?
The ratio of two numbers is 1 ∶ 5 and their product is 320. What is the difference between the squares of these two numbers?
a)
1024
b)
1256
c)
1536
d)
1640
|
|
Advait Singh answered |
The ratio of two numbers is 1 ∶ 5 and their product is 320;
Suppose the numbers are x and 5x;
∴ x × 5x = 320
⇒ 5x2 = 320
⇒ x2 = 64
⇒ x = 8
∴ The numbers are 8 and 40;
∴ Difference between the squares of these two numbers = 1600 – 64 = 1536
Suppose the numbers are x and 5x;
∴ x × 5x = 320
⇒ 5x2 = 320
⇒ x2 = 64
⇒ x = 8
∴ The numbers are 8 and 40;
∴ Difference between the squares of these two numbers = 1600 – 64 = 1536
Which one of the following is the maximum age of joining National Pension System (NPS) under the NPS-Private Sector?- a)55 years
- b)60 years
- c)65 years
- d)70 years
Correct answer is option 'C'. Can you explain this answer?
Which one of the following is the maximum age of joining National Pension System (NPS) under the NPS-Private Sector?
a)
55 years
b)
60 years
c)
65 years
d)
70 years
|
|
Advait Singh answered |
- The age of joining National Pension Scheme (NPS) under the NPS-Private sector is 18-65 years.
- National Pension Scheme was launched on 1 May 2009. Its aim is to provide social security after retirement.
- All the new entrants of Central Government service after 1 Jan 2004 will compulsorily join this scheme.
- All citizens of India can voluntary join this scheme with a minimum contribution Rs. 6000 per year.
The following question consists of six sentences of a passage. The first and the sixth sentences are given in the beginning as S1 and S6. The middle four sentences in each have been jumbled up and labelled P, Q, R and S. You are required to find the proper sequence of the four sentences and mark your response accordingly.S1: Chandran was terribly angry.
S6: Saro ran screaming.
P: His pen was in her hand and Chandran rushed at her.
Q: Just then his sister, Saro, appeared at the door-step.
R: His pen was missing from the place where he had left it.
S: He thought it was lost.The proper sequence should be- a)PRSQ
- b)RSQP
- c)PSQR
- d)SQPR
Correct answer is option 'B'. Can you explain this answer?
The following question consists of six sentences of a passage. The first and the sixth sentences are given in the beginning as S1 and S6. The middle four sentences in each have been jumbled up and labelled P, Q, R and S. You are required to find the proper sequence of the four sentences and mark your response accordingly.
S1: Chandran was terribly angry.
S6: Saro ran screaming.
P: His pen was in her hand and Chandran rushed at her.
Q: Just then his sister, Saro, appeared at the door-step.
R: His pen was missing from the place where he had left it.
S: He thought it was lost.
S6: Saro ran screaming.
P: His pen was in her hand and Chandran rushed at her.
Q: Just then his sister, Saro, appeared at the door-step.
R: His pen was missing from the place where he had left it.
S: He thought it was lost.
The proper sequence should be
a)
PRSQ
b)
RSQP
c)
PSQR
d)
SQPR
|
|
Advait Singh answered |
The correct option is option 2.
From S1 and S6, it is clear that the passage is about Chandan and Saro. The most appropriate order of sentences is RSQP. It would form a paragraph like this:
From S1 and S6, it is clear that the passage is about Chandan and Saro. The most appropriate order of sentences is RSQP. It would form a paragraph like this:
Chandran was terribly angry. His pen was missing from the place where he had left it. He thought it was lost. Just then his sister, Saro, appeared at the door-step. His pen was in her hand and Chandran rushed at her. Saro ran screaming.
If a point O in the interior of a rectangle ABCD is joined with each of vertices A, B, C and D, then OB2 + OD2 will be equal to- a)2 OC2 + OA2
- b)OC2 - OA2
- c)OC2 + OA2
- d)OC2 + 2OA2
Correct answer is option 'C'. Can you explain this answer?
If a point O in the interior of a rectangle ABCD is joined with each of vertices A, B, C and D, then OB2 + OD2 will be equal to
a)
2 OC2 + OA2
b)
OC2 - OA2
c)
OC2 + OA2
d)
OC2 + 2OA2
|
|
Advait Singh answered |
Solution can be easily obtained using coordinate geometry
Let the coordinates of O be (x, y)
⇒ Coordinates of A, B, C and D be (0, 0), (0, b), (l, b) and (l, 0) respectively where l and b are length and breadth of the rectangle
⇒ OB2 + OD2 = (x - 0)2 + (y - b)2 + (x - l)2 + (y - 0)2 [∵ Distance between two points O(x, y) and B(a, b) = √[(x - a)2 + (y - b)2]
⇒ OB2 + OD2 = (x - 0)2 + (y - 0)2 + (x - l)2 + (y - b)2
Similarly, Distance between points O(x, y) and A(0, 0) + Distance between the points O(x, y) and D(l, b)
⇒ OA2 + OC2
∴ OB2 + OD2 = OA2 + OC2
∴ OB2 + OD2 = OA2 + OC2
A 225 m long train is running at a speed of 30 km/hr. How much time does it take to cross a man running at 3 km/hr in the same direction? - a)40 seconds
- b)30 seconds
- c)25 seconds
- d)15 seconds
Correct answer is option 'B'. Can you explain this answer?
A 225 m long train is running at a speed of 30 km/hr. How much time does it take to cross a man running at 3 km/hr in the same direction?
a)
40 seconds
b)
30 seconds
c)
25 seconds
d)
15 seconds
|
Shubham Kumar answered |
Problem Statement:
A train of length 225 m is running at a speed of 30 km/hr. It has to cross a man running in the same direction at 3 km/hr. We need to find out how much time it will take for the train to cross the man.
Solution:
Given, length of the train = 225 m
Speed of the train = 30 km/hr = 30 x 5/18 m/s = 25/3 m/s
Speed of the man = 3 km/hr = 3 x 5/18 m/s = 5/6 m/s
When the train is crossing a man running in the same direction, the effective speed of the train with respect to the man will be the difference of their speeds.
Effective speed of train = (Speed of train - Speed of man) = (25/3 - 5/6) m/s = 65/6 m/s
Now, we can use the formula to find out the time taken by the train to cross the man.
Time taken = Distance / Speed
Distance = Length of the train = 225 m
Speed = Effective speed of train = 65/6 m/s
Time taken = 225 / (65/6) = 30 seconds
Therefore, the time taken by the train to cross the man running at a speed of 3 km/hr in the same direction is 30 seconds. Hence, option B is the correct answer.
A train of length 225 m is running at a speed of 30 km/hr. It has to cross a man running in the same direction at 3 km/hr. We need to find out how much time it will take for the train to cross the man.
Solution:
Given, length of the train = 225 m
Speed of the train = 30 km/hr = 30 x 5/18 m/s = 25/3 m/s
Speed of the man = 3 km/hr = 3 x 5/18 m/s = 5/6 m/s
When the train is crossing a man running in the same direction, the effective speed of the train with respect to the man will be the difference of their speeds.
Effective speed of train = (Speed of train - Speed of man) = (25/3 - 5/6) m/s = 65/6 m/s
Now, we can use the formula to find out the time taken by the train to cross the man.
Time taken = Distance / Speed
Distance = Length of the train = 225 m
Speed = Effective speed of train = 65/6 m/s
Time taken = 225 / (65/6) = 30 seconds
Therefore, the time taken by the train to cross the man running at a speed of 3 km/hr in the same direction is 30 seconds. Hence, option B is the correct answer.
Suppose 0 < θ < 90o, then for every θ 4 sin2 θ + 1 is greater than or equal to ?- a)2
- b)4 sin θ
- c)4 cos θ
- d)4 tan θ
Correct answer is option 'B'. Can you explain this answer?
Suppose 0 < θ < 90o, then for every θ 4 sin2 θ + 1 is greater than or equal to ?
a)
2
b)
4 sin θ
c)
4 cos θ
d)
4 tan θ
|
|
Advait Singh answered |
We know that,
Arithmetic mean ≥ Geometric mean
(4sin2 θ + 1)/2 ≥
4sin2 θ + 1 ≥ 2. 2 sin θ
4sin2 θ + 1 ≥ 4sin θ
Arithmetic mean ≥ Geometric mean
(4sin2 θ + 1)/2 ≥
4sin2 θ + 1 ≥ 2. 2 sin θ
4sin2 θ + 1 ≥ 4sin θ
In the following question, there is a sentence of which some parts have been jumbled up. You are required to rearrange these parts which are labelled P, Q, R and S to produce the correct sentence. Choose the proper sequence and mark the corresponding option. with an idea to reach the deprived child (P) by the United Nations Organization (Q) the year 1979 has been declared as (R) the International Year of the Child (S)The correct sequence should be- a)PQRS
- b)PSQR
- c)PRSQ
- d)RSPQ
Correct answer is option 'C'. Can you explain this answer?
In the following question, there is a sentence of which some parts have been jumbled up. You are required to rearrange these parts which are labelled P, Q, R and S to produce the correct sentence. Choose the proper sequence and mark the corresponding option.
with an idea to reach the deprived child (P) by the United Nations Organization (Q) the year 1979 has been declared as (R) the International Year of the Child (S)
The correct sequence should be
a)
PQRS
b)
PSQR
c)
PRSQ
d)
RSPQ
|
|
Advait Singh answered |
The correct option is option 3.
The correct rearrangement of the given parts to form a meaningful sentence is PRSQ.
The correct rearrangement of the given parts to form a meaningful sentence is PRSQ.
It would form a sentence like this:
With an idea to reach the deprived child, the year 1979 has been declared as the International Year of the Child by the United Nations Organization.
With an idea to reach the deprived child, the year 1979 has been declared as the International Year of the Child by the United Nations Organization.
Stalactites and stalagmites are features of:- a)Glacial topography
- b)Volcanic topography
- c)Karst topography
- d)Fluvial topography
Correct answer is option 'C'. Can you explain this answer?
Stalactites and stalagmites are features of:
a)
Glacial topography
b)
Volcanic topography
c)
Karst topography
d)
Fluvial topography
|
|
Advait Singh answered |
- Stalactites: It is a type of rock formation produced by the precipitation of minerals from water dripping through the cave ceiling. It hangs from the ceiling of a cave.
- Stalagmites: It is a type of rock formation that rises from the floor of a cave due to the accumulation of material deposited on the floor from ceiling drippings.
The spring constant of a spring depends on its- a)length only
- b)material only
- c)length and its diameter
- d)thickness, its diameter, and its material
Correct answer is option 'D'. Can you explain this answer?
The spring constant of a spring depends on its
a)
length only
b)
material only
c)
length and its diameter
d)
thickness, its diameter, and its material
|
|
Advait Singh answered |
- The spring constant is the force applied if the displacement in the spring is unity.
- Hooke's law is a law of physics that states that the force needed to extend or compress a spring by some distance x scales linearly with respect to that distance. That is, where k is a constant factor characteristic of the spring: its stiffness. K is a spring constant.
- The spring constant will depend on the stiffness of the spring material, the thickness of the wire from which the spring is wound and, the diameter of the turns of the coil, the number of turns per unit length and the overall length of the spring.
Each question in this section has a sentence with three underlined parts labelled (a), (b) and (c). Read each sentence to find out whether there is any error in any underlined part and indicate your response. If you find no error, your response should be indicated as (d).Q. 
- a)a
- b)b
- c)c
- d)d
Correct answer is option 'A'. Can you explain this answer?
Each question in this section has a sentence with three underlined parts labelled (a), (b) and (c). Read each sentence to find out whether there is any error in any underlined part and indicate your response. If you find no error, your response should be indicated as (d).
Q.
a)
a
b)
b
c)
c
d)
d
|
|
Advait Singh answered |
There is an error in the first part of the sentence. Looked should not be followed by after in case of thief instead it should be replaced by looked for.
We looked for the thief but he was nowhere to be found.
The Hooke's law is valid for- a)only proportional region of the stress strain curve
- b)entire stress strain curve
- c)entire elastic region of the stress strain curve
- d)elastic as well as plastic region of the stress strain curve
Correct answer is option 'A'. Can you explain this answer?
The Hooke's law is valid for
a)
only proportional region of the stress strain curve
b)
entire stress strain curve
c)
entire elastic region of the stress strain curve
d)
elastic as well as plastic region of the stress strain curve
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Notes Wala answered |
Hooke's law states that within the elastic limit, stress developed is directly proportional to the strain produced in a body.
Hooke’s law is valid only in the linear part of the stress-strain curve. Hence, statement 1 is correct.
Hooke’s law is valid only in the linear part of the stress-strain curve. Hence, statement 1 is correct.
Consider the following statements:
1) The perimeter of a triangle is greater than the sum of its three medinas.
2) In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2AD.
Which of the above statements is/are correct?- a)1 only
- b)2 only
- c)Both 1 and 2
- d)Neither 1 nor 2
Correct answer is option 'C'. Can you explain this answer?
Consider the following statements:
1) The perimeter of a triangle is greater than the sum of its three medinas.
2) In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2AD.
Which of the above statements is/are correct?
1) The perimeter of a triangle is greater than the sum of its three medinas.
2) In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2AD.
Which of the above statements is/are correct?
a)
1 only
b)
2 only
c)
Both 1 and 2
d)
Neither 1 nor 2
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Notes Wala answered |
1. Perimeter of triangle is greater than the sum of 3 medians
Let ABC be the triangle and D. E and F are midpoints of BC, CA and AB respectively.
Recall that the sum of two sides of a triangle is greater than twice the median bisecting the third side,(Theorem to be remembered)
Hence in ΔABD, AD is a median
⇒ AB + AC > 2(AD)
Similarly, we get
BC + AC > 2CF
BC + AB > 2BE
On adding the above inequations, we get
(AB + AC) + (BC + AC) + (BC + AB )> 2AD + 2CD + 2BE
2(AB + BC + AC) > 2(AD + BE + CF)
∴ AB + BC + AC > AD + BE + CF
2.
To prove: AB + BC + CA > 2AD
Construction: AD is joined
Proof: In triangle ABD, AB + BD > AD [because, the sum of any two sides of a triangle is always greater than the third side] ---- 1
In triangle ADC, AC + DC > AD [because, the sum of any two sides of a triangle is always greater than the third side] ---- 2
Adding 1 and 2 we get,
AB + BD + AC + DC > AD + AD
=> AB + (BD + DC) + AC > 2AD
=> AB + BC + AC > 2AD
Hence proved
Let ABC be the triangle and D. E and F are midpoints of BC, CA and AB respectively.
Recall that the sum of two sides of a triangle is greater than twice the median bisecting the third side,(Theorem to be remembered)
Hence in ΔABD, AD is a median
⇒ AB + AC > 2(AD)
Similarly, we get
BC + AC > 2CF
BC + AB > 2BE
On adding the above inequations, we get
(AB + AC) + (BC + AC) + (BC + AB )> 2AD + 2CD + 2BE
2(AB + BC + AC) > 2(AD + BE + CF)
∴ AB + BC + AC > AD + BE + CF
2.
To prove: AB + BC + CA > 2AD
Construction: AD is joined
Proof: In triangle ABD, AB + BD > AD [because, the sum of any two sides of a triangle is always greater than the third side] ---- 1
In triangle ADC, AC + DC > AD [because, the sum of any two sides of a triangle is always greater than the third side] ---- 2
Adding 1 and 2 we get,
AB + BD + AC + DC > AD + AD
=> AB + (BD + DC) + AC > 2AD
=> AB + BC + AC > 2AD
Hence proved
What is the remainder when 135 + 145 + 155 + 165 is divided by 29?- a)8
- b)5
- c)3
- d)0
Correct answer is option 'D'. Can you explain this answer?
What is the remainder when 135 + 145 + 155 + 165 is divided by 29?
a)
8
b)
5
c)
3
d)
0
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Jithin Basu answered |
135 + 145 + 155 + 165
We know that (an + bn) is divisible by (a + b) if n is odd;
(135 + 165) + (145 + 155)
(135 + 165) will be divisible by (13 + 16) = 29 as n is 5 which is a odd number and,
(145 + 155) will be divisible by (14 + 15) = 29 as n is 5 which is a odd number.
∴ (135 + 145 + 155 + 165) will be completely divisible by 29
∴ The remainder will be 0.
We know that (an + bn) is divisible by (a + b) if n is odd;
(135 + 165) + (145 + 155)
(135 + 165) will be divisible by (13 + 16) = 29 as n is 5 which is a odd number and,
(145 + 155) will be divisible by (14 + 15) = 29 as n is 5 which is a odd number.
∴ (135 + 145 + 155 + 165) will be completely divisible by 29
∴ The remainder will be 0.
If the perimeter of a rectangle is 10 cm and the area is 4 cm2, then its length is- a)6 cm
- b)5 cm
- c)4.5 cm
- d)4 cm
Correct answer is option 'D'. Can you explain this answer?
If the perimeter of a rectangle is 10 cm and the area is 4 cm2, then its length is
a)
6 cm
b)
5 cm
c)
4.5 cm
d)
4 cm
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Advait Singh answered |
Let the length and breadth of the rectangle are l and b cm;
∴ 2(l + b) = 10 ⇒ (l + b) = 5
And lb = 4
From this;
⇒ l = 4 & b = 1 or l = 1 or b = 4
∴ Length = 4 cm
∴ 2(l + b) = 10 ⇒ (l + b) = 5
And lb = 4
From this;
⇒ l = 4 & b = 1 or l = 1 or b = 4
∴ Length = 4 cm
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