Q. The following scores were obtained in a quiz: 10, 10, 20, 20, 20, 30, 30, 40. What is the mode?
Solution
The mode is 20, as it appears most frequently (3 times) in the data set.
Correct Answer:
B
— 20
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Q. The following scores were recorded in a game: 10, 20, 10, 30, 20, 10, 40. What is the mode?
Solution
The mode is 10, as it appears 3 times, which is more than any other score.
Correct Answer:
A
— 10
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Q. The function f(x) = 1/(x-1) is continuous on which of the following intervals?
-
A.
(-∞, 1)
-
B.
(1, ∞)
-
C.
(-∞, ∞)
-
D.
(-∞, 0)
Solution
The function f(x) = 1/(x-1) is discontinuous at x = 1, hence it is continuous on (1, ∞).
Correct Answer:
B
— (1, ∞)
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Q. The function f(x) = 2x + 1 is continuous at which of the following intervals?
-
A.
(-∞, ∞)
-
B.
(0, 1)
-
C.
(1, 2)
-
D.
(2, 3)
Solution
f(x) = 2x + 1 is a linear function and is continuous over the entire real line (-∞, ∞).
Correct Answer:
A
— (-∞, ∞)
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Q. The function f(x) = 2x + 3 is continuous at which of the following intervals?
-
A.
(-∞, ∞)
-
B.
[0, 1]
-
C.
[1, 2]
-
D.
[2, 3]
Solution
f(x) = 2x + 3 is a linear function and is continuous over the entire real line (-∞, ∞).
Correct Answer:
A
— (-∞, ∞)
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Q. The function f(x) = 2x + 3 is continuous at which of the following? (2023)
-
A.
x = -1
-
B.
x = 0
-
C.
x = 1
-
D.
All of the above
Solution
f(x) = 2x + 3 is a linear function and is continuous for all x.
Correct Answer:
D
— All of the above
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Q. The function f(x) = sin(x) + cos(x) has a maximum value at which point? (2022)
-
A.
π/4
-
B.
π/2
-
C.
0
-
D.
3π/4
Solution
To find the maximum, set f'(x) = cos(x) - sin(x) = 0. This occurs at x = π/4.
Correct Answer:
A
— π/4
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Q. The function f(x) = x^2 + 3 is continuous for which of the following intervals? (2023)
-
A.
(-∞, ∞)
-
B.
(0, 1)
-
C.
(1, 2)
-
D.
(2, 3)
Solution
f(x) = x^2 + 3 is a polynomial function and is continuous for all x in (-∞, ∞).
Correct Answer:
A
— (-∞, ∞)
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Q. The function f(x) = x^2 is continuous at which of the following points? (2023)
-
A.
x = -1
-
B.
x = 0
-
C.
x = 1
-
D.
All of the above
Solution
The function f(x) = x^2 is a polynomial function and is continuous at all points, including -1, 0, and 1.
Correct Answer:
D
— All of the above
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Q. The function f(x) = x^3 - 3x is continuous at which of the following points? (2023)
-
A.
x = -2
-
B.
x = 0
-
C.
x = 2
-
D.
All of the above
Solution
The function f(x) = x^3 - 3x is a polynomial function and is continuous at all points, including -2, 0, and 2.
Correct Answer:
D
— All of the above
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Q. The function f(x) = { x + 1, x < 1; 2, x = 1; x^2, x > 1 } is continuous at x = 1?
-
A.
Yes
-
B.
No
-
C.
Only left continuous
-
D.
Only right continuous
Solution
Left limit as x approaches 1 is 2, right limit is 1, but f(1) = 2. Hence, it is discontinuous at x = 1.
Correct Answer:
B
— No
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Q. The function f(x) = { x^2, x < 0; 0, x = 0; x + 1, x > 0 } is:
-
A.
Continuous
-
B.
Not continuous
-
C.
Continuous from the left
-
D.
Continuous from the right
Solution
The left limit as x approaches 0 is 0, but the right limit is 1. Hence, it is not continuous at x = 0.
Correct Answer:
B
— Not continuous
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Q. The function f(x) = { x^2, x < 0; 2, x = 0; x + 1, x > 0 } is continuous at x = 0?
-
A.
Yes
-
B.
No
-
C.
Only left continuous
-
D.
Only right continuous
Solution
At x = 0, lim x→0- f(x) = 0 and lim x→0+ f(x) = 1, hence it is discontinuous at x = 0.
Correct Answer:
B
— No
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Q. The Fundamental Duties were added to the Constitution by which amendment? (2023)
-
A.
42nd Amendment
-
B.
44th Amendment
-
C.
61st Amendment
-
D.
73rd Amendment
Solution
The Fundamental Duties were added to the Constitution by the 42nd Amendment.
Correct Answer:
A
— 42nd Amendment
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Q. The Indian Independence Act was enacted in which year? (1947)
-
A.
1947
-
B.
1945
-
C.
1946
-
D.
1948
Solution
The Indian Independence Act was enacted in 1947, leading to the partition of India and the establishment of two independent dominions.
Correct Answer:
A
— 1947
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Q. The Indian Independence Act was passed in which year? (1947)
-
A.
1945
-
B.
1947
-
C.
1946
-
D.
1948
Solution
The Indian Independence Act was passed by the British Parliament in July 1947.
Correct Answer:
B
— 1947
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Q. The Lahore Resolution was passed in which year? (1940)
-
A.
1940
-
B.
1935
-
C.
1929
-
D.
1947
Solution
The Lahore Resolution was passed in 1940, calling for greater autonomy for Muslim-majority regions in India.
Correct Answer:
A
— 1940
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Q. The Lahore Resolution, which called for a separate nation for Muslims, was passed in which year? (1940)
-
A.
1940
-
B.
1930
-
C.
1929
-
D.
1947
Solution
The Lahore Resolution was passed in 1940.
Correct Answer:
A
— 1940
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Q. The Lahore Resolution, which called for the creation of a separate nation for Muslims, was passed in which year? (1940)
-
A.
1940
-
B.
1930
-
C.
1929
-
D.
1947
Solution
The Lahore Resolution was passed in 1940, demanding a separate nation for Muslims in India.
Correct Answer:
A
— 1940
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Q. The lengths of the sides of triangle ABC are 5 cm, 12 cm, and 13 cm. What is the area of the triangle? (2019)
-
A.
30 cm²
-
B.
60 cm²
-
C.
24 cm²
-
D.
40 cm²
Solution
Using Heron's formula, s = (5 + 12 + 13)/2 = 15. Area = √[s(s-a)(s-b)(s-c)] = √[15(15-5)(15-12)(15-13)] = √[15*10*3*2] = √[900] = 30 cm².
Correct Answer:
A
— 30 cm²
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Q. The lengths of the sides of triangle ABC are 7 cm, 24 cm, and 25 cm. Is this triangle a right triangle? (2020)
-
A.
Yes
-
B.
No
-
C.
Cannot be determined
-
D.
Only if angle A is 90 degrees
Solution
Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625 = 25^2. Therefore, triangle ABC is a right triangle.
Correct Answer:
A
— Yes
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Q. The lengths of the sides of triangle GHI are 5 cm, 12 cm, and 13 cm. What is the area of the triangle? (2019)
-
A.
30 cm²
-
B.
60 cm²
-
C.
65 cm²
-
D.
78 cm²
Solution
This is a right triangle. Area = 1/2 * base * height = 1/2 * 5 * 12 = 30 cm².
Correct Answer:
A
— 30 cm²
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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 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 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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