Q. The concept of 'Swaraj' as articulated by Mahatma Gandhi primarily refers to which of the following? (1920)
A.
Self-rule and self-governance
B.
Economic independence
C.
Cultural revival
D.
Political alliances
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Solution
Swaraj, as articulated by Gandhi, refers to self-rule and self-governance, emphasizing the need for Indians to govern themselves.
Correct Answer:
A
— Self-rule and self-governance
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Q. The concept of 'Swaraj' was popularized by which of the following leaders? (1920)
A.
Mahatma Gandhi
B.
Jawaharlal Nehru
C.
Subhas Chandra Bose
D.
B.R. Ambedkar
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Solution
'Swaraj', meaning self-rule, was popularized by Mahatma Gandhi as a central theme of the Indian independence movement.
Correct Answer:
A
— Mahatma Gandhi
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Q. The concept of 'Swaraj' was significantly influenced by which of the following movements in neighboring countries? (1916)
A.
Chinese Nationalist Movement
B.
Irish Home Rule Movement
C.
Egyptian Nationalist Movement
D.
Vietnamese Independence Movement
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Solution
The Irish Home Rule Movement had a profound influence on the Indian National Congress and the concept of 'Swaraj', as Indian leaders drew parallels between their struggle for self-governance and that of the Irish.
Correct Answer:
B
— Irish Home Rule Movement
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Q. The concept of 'total war' was most prominently utilized during which conflict?
A.
World War I
B.
World War II
C.
The Vietnam War
D.
The Korean War
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Solution
Total war during World War II involved the complete mobilization of resources and people, blurring the lines between civilian and military targets.
Correct Answer:
B
— World War II
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Q. The concept of 'Welfare State' in the context of Indian history is closely associated with which of the following? (1950)
A.
Colonial policies
B.
Constitution of India
C.
Economic liberalization
D.
Socialism
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Solution
The Constitution of India enshrines the principles of a Welfare State, aiming for inclusive growth through social justice and equality.
Correct Answer:
B
— Constitution of India
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Q. The concept of absolute zero is defined as the temperature at which: (2020)
A.
Molecular motion ceases
B.
Pressure is zero
C.
Volume is zero
D.
Density is maximum
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Solution
Absolute zero is defined as the temperature at which molecular motion ceases, corresponding to 0 Kelvin.
Correct Answer:
A
— Molecular motion ceases
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Q. The concept of absolute zero refers to: (2020)
A.
The lowest possible temperature
B.
The temperature at which gas molecules stop moving
C.
Both A and B
D.
The temperature at which gas has maximum volume
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Solution
Absolute zero refers to the lowest possible temperature, at which gas molecules theoretically stop moving, making both A and B correct.
Correct Answer:
C
— Both A and B
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Q. The concept of an ideal gas is based on which of the following assumptions?
A.
Molecules have no volume
B.
Molecules do not attract or repel each other
C.
Collisions are perfectly elastic
D.
All of the above
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Solution
The concept of an ideal gas is based on the assumptions that molecules have no volume, do not attract or repel each other, and that collisions are perfectly elastic.
Correct Answer:
D
— All of the above
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Q. The concept of mean free path is associated with which of the following?
A.
Distance traveled by a gas molecule between collisions
B.
Average speed of gas molecules
C.
Pressure of the gas
D.
Volume of the gas
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Solution
Mean free path is defined as the average distance traveled by a gas molecule between successive collisions.
Correct Answer:
A
— Distance traveled by a gas molecule between collisions
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Q. The condition for the lines represented by ax^2 + 2hxy + by^2 = 0 to be parallel is:
A.
h^2 = ab
B.
h^2 > ab
C.
h^2 < ab
D.
a + b = 0
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Solution
The lines are parallel if h^2 = ab.
Correct Answer:
A
— h^2 = ab
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Q. The condition for the lines represented by the equation x^2 + 2xy + y^2 = 0 to be coincident is:
A.
Discriminant > 0
B.
Discriminant = 0
C.
Discriminant < 0
D.
None of the above
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Solution
For the lines to be coincident, the discriminant must be equal to zero.
Correct Answer:
B
— Discriminant = 0
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Q. The condition for the lines represented by the equation x^2 + y^2 + 2xy = 0 to be coincident is:
A.
Discriminant = 0
B.
Discriminant > 0
C.
Discriminant < 0
D.
None of the above
Show solution
Solution
For the lines to be coincident, the discriminant of the quadratic must be zero.
Correct Answer:
A
— Discriminant = 0
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Q. The condition for the lines represented by the equation x^2 + y^2 - 4x - 6y + 9 = 0 to be coincident is:
A.
Discriminant = 0
B.
Discriminant > 0
C.
Discriminant < 0
D.
None of the above
Show solution
Solution
For the lines to be coincident, the discriminant of the quadratic must equal zero.
Correct Answer:
A
— Discriminant = 0
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Q. The Constitution of India was adopted on which date? (2021)
A.
26th January 1950
B.
15th August 1947
C.
26th November 1949
D.
1st January 1950
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Solution
The Constitution of India was adopted on 26th November 1949 and came into effect on 26th January 1950.
Correct Answer:
A
— 26th January 1950
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Q. The coordinates of the centroid of a triangle with vertices at (0, 0), (6, 0), and (3, 6) are:
A.
(3, 2)
B.
(3, 3)
C.
(2, 3)
D.
(0, 0)
Show solution
Solution
Centroid = ((x1+x2+x3)/3, (y1+y2+y3)/3) = (9/3, 6/3) = (3, 2).
Correct Answer:
B
— (3, 3)
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Q. The coordinates of the centroid of a triangle with vertices at (1, 2), (3, 4), and (5, 6) are:
A.
(3, 4)
B.
(2, 3)
C.
(4, 5)
D.
(3, 5)
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Solution
Centroid = ((1+3+5)/3, (2+4+6)/3) = (3, 4).
Correct Answer:
A
— (3, 4)
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Q. The coordinates of the centroid of a triangle with vertices at (2, 3), (4, 5), and (6, 1) are:
A.
(4, 3)
B.
(4, 4)
C.
(3, 3)
D.
(5, 3)
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Solution
Centroid = ((2+4+6)/3, (3+5+1)/3) = (4, 3).
Correct Answer:
A
— (4, 3)
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Q. The coordinates of the centroid of a triangle with vertices at (2, 3), (4, 5), and (6, 7) are:
A.
(4, 5)
B.
(3, 4)
C.
(5, 6)
D.
(6, 5)
Show solution
Solution
Centroid = ((2+4+6)/3, (3+5+7)/3) = (4, 5).
Correct Answer:
B
— (3, 4)
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Q. The coordinates of the centroid of the triangle with vertices (0, 0), (6, 0), and (3, 6) are:
A.
(3, 2)
B.
(2, 3)
C.
(3, 3)
D.
(0, 0)
Show solution
Solution
Centroid = ((0+6+3)/3, (0+0+6)/3) = (3, 2).
Correct Answer:
A
— (3, 2)
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Q. The coordinates of the centroid of the triangle with vertices (2, 3), (4, 5), and (6, 7) are:
A.
(4, 5)
B.
(3, 4)
C.
(5, 6)
D.
(6, 5)
Show solution
Solution
Centroid = ((2+4+6)/3, (3+5+7)/3) = (4, 5).
Correct Answer:
B
— (3, 4)
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Q. The coordinates of the foot of the perpendicular from the point (1, 2) to the line 2x + 3y = 6 are:
A.
(2, 0)
B.
(0, 2)
C.
(1, 1)
D.
(0, 0)
Show solution
Solution
Using the formula for foot of perpendicular, we find the coordinates to be (2, 0).
Correct Answer:
A
— (2, 0)
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Q. The coordinates of the foot of the perpendicular from the point (1, 2) to the line 3x + 4y = 12 are:
A.
(2, 1)
B.
(1, 2)
C.
(0, 3)
D.
(3, 0)
Show solution
Solution
Using the formula for foot of perpendicular, we find the coordinates to be (2, 1).
Correct Answer:
A
— (2, 1)
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Q. The coordinates of the foot of the perpendicular from the point (3, 4) to the line 2x + 3y - 6 = 0 are:
A.
(2, 0)
B.
(0, 2)
C.
(1, 1)
D.
(2, 2)
Show solution
Solution
Using the formula for foot of perpendicular, we find the coordinates to be (2, 0).
Correct Answer:
A
— (2, 0)
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Q. The coordinates of the foot of the perpendicular from the point (3, 4) to the line 2x + 3y = 6 are:
A.
(2, 0)
B.
(1, 2)
C.
(0, 2)
D.
(2, 2)
Show solution
Solution
Using the formula for foot of perpendicular, we find the coordinates to be (2, 0).
Correct Answer:
A
— (2, 0)
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Q. The critical angle for total internal reflection occurs when light travels from: (2019)
A.
Air to water
B.
Water to air
C.
Glass to air
D.
Air to glass
Show solution
Solution
The critical angle occurs when light travels from a denser medium (water) to a less dense medium (air).
Correct Answer:
B
— Water to air
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Q. The critical points of the function f(x) = x^3 - 6x^2 + 9x + 1 are:
A.
x = 1, 3
B.
x = 0, 2
C.
x = 2, 4
D.
x = 1, 2
Show solution
Solution
Finding f'(x) = 3x^2 - 12x + 9 and solving gives critical points at x = 1 and x = 3.
Correct Answer:
A
— x = 1, 3
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Q. The Dadasaheb Phalke Award is associated with which industry?
A.
Theater
B.
Television
C.
Film
D.
Literature
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Solution
The Dadasaheb Phalke Award is the highest award in Indian cinema.
Correct Answer:
C
— Film
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Q. The Dandi March of 1930 was a significant event in the Indian independence movement. What was its primary purpose? (1930)
A.
To protest against the Rowlatt Act
B.
To oppose the Simon Commission
C.
To defy the salt laws imposed by the British
D.
To demand the right to self-governance
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Solution
The Dandi March was primarily aimed at defying the salt laws imposed by the British, symbolizing the broader struggle for independence.
Correct Answer:
C
— To defy the salt laws imposed by the British
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Q. The Dandi March was a significant event in which movement? (1930)
A.
Non-Cooperation Movement
B.
Civil Disobedience Movement
C.
Quit India Movement
D.
Swadeshi Movement
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Solution
The Dandi March in 1930 was a key event in the Civil Disobedience Movement, led by Gandhi to protest against the salt tax.
Correct Answer:
B
— Civil Disobedience Movement
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Q. The Dandi March was a significant event in which year? (1930)
A.
1930
B.
1942
C.
1920
D.
1947
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Solution
The Dandi March took place in 1930 as a non-violent protest against the salt tax imposed by the British.
Correct Answer:
A
— 1930
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