Q. The magnitude of the vector A = 4i - 3j + 12k is:
Solution
Magnitude |A| = √(4^2 + (-3)^2 + 12^2) = √(16 + 9 + 144) = √169 = 13.
Correct Answer:
B
— 14
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Q. The main function of the World Health Organization (WHO) is to: (1948)
-
A.
Regulate international trade
-
B.
Coordinate international health activities and responses
-
C.
Provide financial assistance to countries
-
D.
Promote cultural exchanges
Solution
The WHO, established in 1948, coordinates international health activities and responses to health emergencies.
Correct Answer:
B
— Coordinate international health activities and responses
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Q. The Man Booker International Prize is awarded for which type of literature?
-
A.
Fiction
-
B.
Non-Fiction
-
C.
Poetry
-
D.
Children's Literature
Solution
The Man Booker International Prize is awarded for outstanding fiction translated into English.
Correct Answer:
A
— Fiction
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Q. The Man Booker International Prize is awarded for which type of work?
-
A.
Fiction
-
B.
Non-Fiction
-
C.
Poetry
-
D.
All of the above
Solution
The Man Booker International Prize is awarded for a work of fiction translated into English, recognizing the best in international literature.
Correct Answer:
A
— Fiction
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Q. The mantle of the Earth is mainly composed of which type of rock? (2019)
-
A.
Igneous
-
B.
Sedimentary
-
C.
Metamorphic
-
D.
Basaltic
Solution
The mantle is primarily composed of silicate minerals, which are classified as igneous rocks.
Correct Answer:
A
— Igneous
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Q. The maximum displacement from the mean position in simple harmonic motion is called: (2019)
-
A.
Amplitude
-
B.
Frequency
-
C.
Wavelength
-
D.
Period
Solution
The maximum displacement is defined as the amplitude.
Correct Answer:
A
— Amplitude
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Q. The maximum displacement of a wave from its rest position is called what? (2022)
-
A.
Amplitude
-
B.
Wavelength
-
C.
Frequency
-
D.
Period
Solution
The maximum displacement from the rest position is defined as the amplitude of the wave.
Correct Answer:
A
— Amplitude
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Q. The maximum speed of a simple harmonic oscillator is 4 m/s. If the amplitude is 2 m, what is the angular frequency? (2019)
-
A.
2 rad/s
-
B.
4 rad/s
-
C.
1 rad/s
-
D.
8 rad/s
Solution
Maximum speed (v_max) = ωA => ω = v_max / A = 4 m/s / 2 m = 2 rad/s.
Correct Answer:
B
— 4 rad/s
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Q. The maximum strength of the Lok Sabha is?
-
A.
500
-
B.
550
-
C.
600
-
D.
700
Solution
The maximum strength of the Lok Sabha is 550 members.
Correct Answer:
B
— 550
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Q. The maximum value of the function f(x) = -x^2 + 4x + 1 is at x = ?
Solution
To find the maximum, we calculate f'(x) = -2x + 4. Setting f'(x) = 0 gives x = 2. Since f''(x) = -2 < 0, this is a maximum point.
Correct Answer:
B
— 2
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Q. The maximum value of the function f(x) = -x^2 + 4x + 1 is:
Solution
The vertex form of a parabola gives the maximum value at x = -b/(2a) = 2. Evaluating f(2) = -2^2 + 4*2 + 1 = 9.
Correct Answer:
A
— 5
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Q. The maximum value of the function f(x) = -x^2 + 4x + 1 occurs at:
-
A.
x = 2
-
B.
x = 4
-
C.
x = 1
-
D.
x = 3
Solution
The vertex of the parabola given by f(x) = -x^2 + 4x + 1 occurs at x = -b/(2a) = -4/(-2) = 2, which gives the maximum value.
Correct Answer:
A
— x = 2
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Q. The mean free path of gas molecules is defined as:
-
A.
The average distance traveled between collisions
-
B.
The distance traveled in one second
-
C.
The distance between two gas containers
-
D.
The average distance of gas molecules in a container
Solution
The mean free path is the average distance a molecule travels before colliding with another molecule.
Correct Answer:
A
— The average distance traveled between collisions
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Q. The mean of 10 numbers is 50. If one number is removed, the mean becomes 48. What is the removed number?
Solution
Total of 10 numbers = 10 * 50 = 500. Total of 9 numbers = 9 * 48 = 432. Removed number = 500 - 432 = 68.
Correct Answer:
A
— 52
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Q. The mean of 10, 20, 30, 40, and x is 25. What is the value of x? (2022)
Solution
Mean = (10 + 20 + 30 + 40 + x) / 5 = 25. Therefore, 100 + x = 125, so x = 25.
Correct Answer:
A
— 10
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Q. The mean of 4, 6, 8, and x is 7. What is the value of x?
Solution
Mean = (4 + 6 + 8 + x) / 4 = 7. Thus, 18 + x = 28, so x = 10.
Correct Answer:
D
— 10
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Q. The mean of 5, 10, 15, 20, and x is 12. What is the value of x?
Solution
Mean = (5 + 10 + 15 + 20 + x) / 5 = 12.\n\n50 + x = 60\n\nx = 60 - 50 = 10.
Correct Answer:
A
— 5
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Q. The mean of 5, 10, 15, and 20 is what?
-
A.
10
-
B.
12.5
-
C.
15
-
D.
17.5
Solution
Mean = (5 + 10 + 15 + 20) / 4 = 50 / 4 = 12.5.
Correct Answer:
C
— 15
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Q. The mean of 5, 10, 15, and x is 12. What is the value of x?
Solution
Mean = (5 + 10 + 15 + x) / 4 = 12. Therefore, 30 + x = 48, so x = 18.
Correct Answer:
A
— 8
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Q. The mean of 5, 15, 25, and x is 20. Find the value of x. (2023)
Solution
Mean = (5 + 15 + 25 + x) / 4 = 20. Solving gives x = 30.
Correct Answer:
C
— 30
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Q. The mean of 5, 15, and x is 10. What is the value of x? (2020)
Solution
Mean = (5 + 15 + x) / 3 = 10. Therefore, 20 + x = 30, so x = 10.
Correct Answer:
D
— 20
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Q. The mean of 6, 8, 10, and x is 9. What is the value of x? (2022)
Solution
Mean = (6 + 8 + 10 + x) / 4 = 9. Therefore, 24 + x = 36, so x = 12.
Correct Answer:
D
— 12
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Q. The mean of 7, 9, 11, 13, and x is 10. Find the value of x.
Solution
Mean = (7 + 9 + 11 + 13 + x) / 5 = 10. Solving gives x = 5.
Correct Answer:
A
— 5
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Q. The mean of 7, 9, 11, 13, and x is 10. What is the value of x?
Solution
Mean = (7 + 9 + 11 + 13 + x) / 5 = 10.\n\n40 + x = 50\n\nx = 50 - 40 = 10.
Correct Answer:
A
— 5
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Q. The mean of 7, 9, 11, and 13 is what? (2019)
Solution
Mean = (7 + 9 + 11 + 13) / 4 = 40 / 4 = 10.
Correct Answer:
B
— 10
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Q. The mean of 8, 12, 16, and 20 is what? (2019)
Solution
Mean = (8 + 12 + 16 + 20) / 4 = 56 / 4 = 14.
Correct Answer:
B
— 15
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Q. The mean of 8, 12, 16, and x is 14. Find the value of x.
Solution
Mean = (8 + 12 + 16 + x) / 4 = 14. Therefore, 36 + x = 56, so x = 20.
Correct Answer:
A
— 10
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Q. The mean of a data set is 10 and the variance is 4. What is the standard deviation? (2019)
Solution
Standard deviation is the square root of variance. Therefore, SD = √4 = 2.
Correct Answer:
A
— 2
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Q. The mean of a data set is 50 and the standard deviation is 5. What is the coefficient of variation?
-
A.
5%
-
B.
10%
-
C.
15%
-
D.
20%
Solution
Coefficient of Variation = (Standard Deviation / Mean) * 100 = (5 / 50) * 100 = 10%.
Correct Answer:
B
— 10%
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Q. The mean of a set of numbers is 15. If one number is removed, the mean becomes 12. What was the removed number?
Solution
Let the total number of items be n. Then, 15n - x = 12(n - 1). Solving gives x = 24.
Correct Answer:
C
— 24
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