Q. The area of a triangle is 60 cm². If the base is 10 cm, what is the height? (2019)
A.
8 cm
B.
10 cm
C.
12 cm
D.
15 cm
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Solution
Area = (1/2) * base * height. Thus, 60 = (1/2) * 10 * height, giving height = 12 cm.
Correct Answer:
A
— 8 cm
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Q. The area of a triangle is 60 square units. If the base is 10 units, what is the height? (2019)
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Solution
Area = 1/2 * base * height. Thus, 60 = 1/2 * 10 * height. Solving gives height = 12.
Correct Answer:
A
— 6
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Q. The average of 10 numbers is 50. If one number is removed, the average becomes 48. What is the removed number?
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Solution
Total of 10 numbers = 10 * 50 = 500.\n\nTotal of 9 numbers = 9 * 48 = 432.\n\nRemoved number = 500 - 432 = 68.
Correct Answer:
A
— 60
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Q. The average of 10, 20, 30, and x is 25. What is the value of x?
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Solution
Mean = (10 + 20 + 30 + x) / 4 = 25. Solving gives x = 50.
Correct Answer:
C
— 40
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Q. The average of 4 numbers is 15. If one number is increased by 5, what will be the new average? (2019)
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Solution
Total of 4 numbers = 4 * 15 = 60. New total = 60 + 5 = 65. New average = 65 / 4 = 16.25.
Correct Answer:
B
— 16
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Q. The average of 4, 6, 8, and x is 7. What is the value of x?
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Solution
Mean = (4 + 6 + 8 + x) / 4 = 7.\n\n18 + x = 28\n\nx = 28 - 18 = 10.
Correct Answer:
C
— 10
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Q. The average of 7 numbers is 14. If one number is added which is 10 more than the average, what will be the new average?
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Solution
New total = 7 * 14 + (14 + 10) = 98 + 24 = 122. New average = 122 / 8 = 15.25.
Correct Answer:
B
— 16
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Q. The average of 8 numbers is 15. If one number is excluded, the average of the remaining numbers becomes 12. What is the excluded number?
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Solution
The total sum of the 8 numbers is 8 * 15 = 120. Let the excluded number be x. The sum of the remaining 7 numbers is 120 - x, and their average is (120 - x)/7 = 12. Thus, 120 - x = 84, leading to x = 36.
Correct Answer:
B
— 20
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Q. The average of five consecutive integers is 12. What is the smallest of these integers?
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Solution
Let the integers be x, x+1, x+2, x+3, x+4.\n\nMean = (5x + 10) / 5 = 12\n\n5x + 10 = 60\n\n5x = 50\n\nx = 10.
Correct Answer:
B
— 11
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Q. The average of five numbers is 20. If one number is excluded, the average of the remaining numbers becomes 18. What is the excluded number?
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Solution
Total of five numbers = 5 * 20 = 100. Total of remaining four = 4 * 18 = 72. Excluded number = 100 - 72 = 28.
Correct Answer:
A
— 22
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Q. The average of five numbers is 20. If one number is removed, the average becomes 18. What is the number removed?
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Solution
Total of five numbers = 5 * 20 = 100. Total of four numbers = 4 * 18 = 72. Number removed = 100 - 72 = 28.
Correct Answer:
A
— 22
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Q. The average of three consecutive integers is 20. What are the integers?
A.
19, 20, 21
B.
18, 19, 20
C.
20, 21, 22
D.
17, 18, 19
Show solution
Solution
Let the integers be x, x+1, x+2. (x + (x + 1) + (x + 2)) / 3 = 20. Therefore, 3x + 3 = 60, so x = 19.
Correct Answer:
A
— 19, 20, 21
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Q. The average of three numbers is 15. If one number is increased by 5, what will be the new average?
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Solution
Total of three numbers = 3 * 15 = 45.\n\nNew total = 45 + 5 = 50.\n\nNew average = 50 / 3 = 16.67.
Correct Answer:
B
— 16
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Q. The average of three numbers is 40. If the first number is increased by 10, what will be the new average?
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Solution
The sum of the three numbers is 3 * 40 = 120. Increasing the first number by 10 gives a new sum of 120 + 10 = 130. The new average is 130 / 3 = 43.33, which rounds to 42.
Correct Answer:
A
— 42
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Q. The average of two numbers is 30. If one number is 20, what is the other number?
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Solution
Mean = (20 + x) / 2 = 30.\n\n20 + x = 60\n\nx = 60 - 20 = 40.
Correct Answer:
A
— 40
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Q. The Ayushman Bharat scheme is primarily aimed at providing which of the following? (2018)
A.
Free education for all
B.
Health insurance for the poor
C.
Housing for the homeless
D.
Employment for youth
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Solution
The Ayushman Bharat scheme aims to provide health insurance coverage to economically vulnerable families.
Correct Answer:
B
— Health insurance for the poor
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Q. The Beti Bachao Beti Padhao scheme primarily focuses on which of the following? (2015)
A.
Promoting women's entrepreneurship
B.
Preventing female foeticide and promoting education for girls
C.
Providing financial aid for women's health
D.
Encouraging women in sports
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Solution
The Beti Bachao Beti Padhao scheme aims to prevent female foeticide and promote education for girls.
Correct Answer:
B
— Preventing female foeticide and promoting education for girls
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Q. The circumference of a circle is 31.4 cm. What is the radius of the circle? (Use π = 3.14) (2019)
A.
5 cm
B.
10 cm
C.
7 cm
D.
15 cm
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Solution
Circumference = 2πr => r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm
Correct Answer:
A
— 5 cm
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Q. The concept of 'Judicial Review' in the Indian Constitution is derived from which country's Constitution? (2022)
A.
USA
B.
UK
C.
Canada
D.
Australia
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Solution
The concept of 'Judicial Review' in the Indian Constitution is derived from the Constitution of the United States of America.
Correct Answer:
A
— USA
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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, 7) are:
A.
(4, 5)
B.
(3, 4)
C.
(5, 6)
D.
(6, 5)
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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 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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Q. The Digital India initiative aims to transform India into a digitally empowered society and knowledge economy. What is one of its key components? (2015)
A.
Skill development
B.
Financial inclusion
C.
E-governance
D.
Rural development
Show solution
Solution
E-governance is a key component of the Digital India initiative, aimed at making government services accessible electronically.
Correct Answer:
C
— E-governance
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Q. The Directive Principles of State Policy are enshrined in which part of the Constitution? (2019)
A.
Part III
B.
Part IV
C.
Part V
D.
Part VI
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Solution
The Directive Principles of State Policy are contained in Part IV of the Indian Constitution.
Correct Answer:
B
— Part IV
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Q. The equation of a line with slope 2 passing through the point (1, 3) is?
A.
y = 2x + 1
B.
y = 2x + 2
C.
y = 2x + 3
D.
y = 2x - 1
Show solution
Solution
Using point-slope form: y - 3 = 2(x - 1) => y = 2x + 1.
Correct Answer:
C
— y = 2x + 3
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Q. The equation of a parabola with vertex at (0, 0) and directrix y = -3 is?
A.
x^2 = -12y
B.
y^2 = -12x
C.
x^2 = 12y
D.
y^2 = 12x
Show solution
Solution
The distance from the vertex to the directrix is 3, so the equation is x^2 = -12y.
Correct Answer:
A
— x^2 = -12y
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