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Prelims

UPSC Prelims Questions

Practice UPSC Prelims MCQs by subject and year. Free questions with explanations for focused revision.

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Q.37·Miscellaneous·2025·Easy

The mode of the set {5, 8, 8, 10, 11, 11, 11, 12, 13, 14, 15} is: What is the mode of the given set?

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Q.38·Miscellaneous·2025·Easy

The mode of the set {5, 8, 8, 10, 11, 11, 11, 12, 13, 14, 15} is: What is the mean of the given set?

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Q.39·Miscellaneous·2025·Easy

ABC is an equilateral triangle and AD is the altitude on BC. If coordinates of A are (1, 2) and D are (-2, 6), then what is the equation of BC?

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Q.40·Miscellaneous·2025·Easy

The standard deviation of 100 observations is 10. If 5 is added to each observation and then divided by 20, then what will be the new standard deviation?

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Q.41·Miscellaneous·2025·Easy

The probability of a man hitting a target is 1/5. If the man fires 7 times, then what is the probability that he hits the target at least twice?

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Q.42·Miscellaneous·2025·Easy

Let X be a random variable following binomial distribution whose mean and variance are 200 and 160 respectively. What is the value of the number of trials (n)?

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Q.43·Miscellaneous·2025·Easy

Consider the following for the two (02) items that follow: In a triangle ABC, two sides BC and CA are in the ratio 2:1 and their opposite corresponding angles are in the ratio 3:1. One of the angles of the triangle is

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Q.44·Miscellaneous·2025·Easy

Consider the following for the two (02) items that follow: In a triangle ABC, two sides BC and CA are in the ratio 2:1 and their opposite corresponding angles are in the ratio 3:1. Consider the following statements: I. The triangle is right-angled. II. One of the sides of the triangle is 3 times the other. III. The angles A, C and B of the triangle are in AP. Which of the statements given above is/are correct ?

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Q.45·Miscellaneous·2025·Easy

If p and q are real numbers between 0 and 1 such that the points (p, 1), (1, q) and (0, 0) form an equilateral triangle, then what is (p + q) equal to ?

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Q.46·Miscellaneous·2025·Easy

The vertices of a triangle are A(1, 1), B(0, 0) and C(2, 0). The angular bisectors of the triangle meet at P. What are the coordinates of P?

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Q.47·Miscellaneous·2025·Easy

How many positive integer solutions for x + y + z = 5?

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Q.48·Miscellaneous·2025·Easy

What is (pq + qr + rp) equal to?

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Q.49·Miscellaneous·2025·Easy

What is (p + q + r) equal to? Let p = sin 35°, q = sin 25° and r = sin (–95°)

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Q.50·Miscellaneous·2025·Easy

Consider for a non-singular matrix M: I. |M²| = |M|² II. |M| = |M⁻¹| III. |M| = |Mᵗ| How many are correct?

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Q.51·Miscellaneous·2025·Easy

If then x = ?

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Q.52·Miscellaneous·2025·Easy

If number of selections of r and (n + r) from 5n things are equal, what is r?

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Q.53·Miscellaneous·2025·Easy

How many sides are there in a polygon with 20 diagonals?

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Q.54·Miscellaneous·2025·Easy

How many 7-letter words can be formed from "CAPITAL" such that all consonants come together?

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