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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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  2. /Prelims Questions
Q.703·Miscellaneous·2024·Easy

How many 4-digit numbers are there having all digits as odd?

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Q.704·Miscellaneous·2024·Easy

The marks obtained by 10 students in a Statistics test are 24, 47, 18, 32, 19, 15, 21, 35, 50 and 41. What is the variance of the largest five observations ?

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Q.705·Miscellaneous·2024·Easy

Let A and B be two square matrices of same order. If AB is a null matrix, then which one of the following is correct?

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Q.706·Miscellaneous·2024·Easy

If then what is modulus of Z equal to?

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Q.707·Miscellaneous·2024·Easy

In how many ways can the letters of the word INDIA be permuted such that in each combination, vowels should occupy odd positions?

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Q.708·Miscellaneous·2024·Easy

The marks obtained by 10 students in a Statistics test are 24, 47, 18, 32, 19, 15, 21, 35, 50 and 41. What is the mean deviation of the largest five observations ?

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Q.709·Miscellaneous·2024·Easy

The letters of the word EQUATION are arranged in such a way that all vowels as well as consonants are together. How many such arrangements are there?

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Q.710·Miscellaneous·2024·Easy

Let A and B be two events such that P(AUB) ≥ 0-75 and 0-125 < P(ANB) 0-375. What is the maximum value of P(A) + P(B)?

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Q.711·Miscellaneous·2024·Easy

A, B and C are three events such that P(A) = 0-6, P(B) = 0-4, P(C) = 0-5, P(AUB) = 0-8, P(ANC) = 0-3 and P(ANBNC) = 0-2 and P(AUBUC) > 0-85. What is the minimum value of P(B|C)?

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Q.712·Miscellaneous·2024·Easy

Let A and B be two events such that P(AUB) ≥ 0-75 and 0-125 < P(ANB) 0-375. What is the minimum value of P(A) + P(B)?

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Q.713·Miscellaneous·2024·Easy

A, B and C are three events such that P(A) = 0-6, P(B) = 0-4, P(C) = 0-5, P(AUB) = 0-8, P(ANC) = 0-3 and P(ANBNC) = 0-2 and P(AUBUC) > 0-85. What is the maximum value of P(B|C)?

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Q.714·Miscellaneous·2024·Easy

From data (-4, 1), (-1, 2), (2, 7) and (3, 1), the regression line of y on x is obtained as y = a + bx, then what is the value of 2a + 15b?

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Q.715·Miscellaneous·2024·Easy

If two random variables X and Y are connected by relation 2X - 3Y = 4 and X follows Binomial distribution with parameters n = 10 and p = 1/2, then what is the variance of Y?

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Q.716·Miscellaneous·2024·Easy

A bag contains 5 black and 4 white balls. A man selects two balls at random. What is the probability that both of these are of the same colour?

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Q.717·Miscellaneous·2024·Easy

If a, b, c are in HP, then what is b - 1/a + b - 1/c equal to?

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Q.718·Miscellaneous·2024·Easy

Let f(x) and g(x) be two functions such that g(x)=x- 1/x and f o g(x) = x^3 - 1/x^3 What is f'(x) equal to?

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Q.719·Miscellaneous·2024·Easy

Let f(x) and g(x) be two functions such that g(x)=x- 1/x and f o g(x) = x^3 - 1/x^3 What is g(f(x) - 3x) equal to?

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Q.720·Miscellaneous·2024·Easy

Let f(x)=|x| + 1 and g(x)=[x] − 1, where [.] is the greatest integer function. Let h(x) = f(x)/g(x) Consider the following statements: 1.f(x) is differentiable for all x < 0 2.g(x) is continuous at x = 0.0001 3.The derivative of g(x) at x = -2.5 is 1 Which of the statements given above are correct?

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