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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.3979·Miscellaneous·2021·Easy

What is the derivative of e^(e^x) with respect to e^x?

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Q.3980·Miscellaneous·2021·Easy

What is the condition that f(x) = x^3 + x^2 + kx has no local extremum?

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Q.3981·Miscellaneous·2021·Easy

What is the area bounded by y = [x], the x-axis and the lines x = -1.5 and x = -1.8?

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Q.3982·Miscellaneous·2021·Easy

The tangent to the curve x^2 = y at (1,1) makes an angle:

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Q.3983·Miscellaneous·2021·Easy

Consider the following relations for two events E and F: 1. P(E ∩ F) ≥ P(E) + P(F) − 1 2. P(E ∪ F) = P(E) + P(F) + P(E ∩ F) 3. P(E ∪ F) ≤ P(E) + P(F) Which of the above relations is/are correct?

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Q.3984·Miscellaneous·2021·Easy

If P(A|B) < P(A), then which one of the following is correct?

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Q.3985·Miscellaneous·2021·Easy

When the measure of central tendency is available in the form of mean, which one of the following is the most reliable and accurate measure of variability?

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Q.3986·Miscellaneous·2021·Easy

A problem is given to three students A, B and C, whose probabilities of solving the problem independently are 1/2, 3/4 and p respectively. If the probability that the problem can be solved is 29/32, then what is the value of p?

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Q.3987·Miscellaneous·2021·Easy

In a cricket match, a batsman hits a six 8 times out of 60 balls he plays. What is the probability that on a ball played he does not hit a six?

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Q.3988·Miscellaneous·2021·Easy

Two regression lines are given as 3x − 4y + 8 = 0 and 4x − 3y − 1 = 0. Consider the following statements : 1. The regression line of y on x is y = (3/4)x + 2 . 2. The regression line of x on y is x = (3/4)y + 1/4 . Which of the above statements is/are correct?

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Q.3989·Miscellaneous·2021·Easy

Two regression lines are given as 3x -4y+8=0 and 4x - 3y– 1= 0. Consider the following statements : 1. The coefficient of correlations r is 3/4. 2. The means of x and y are 3 and 4 respectively. Which of the above statements is/are correct?

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Q.3990·Miscellaneous·2021·Easy

The marks obtained by 60 students in a certain subject out of 75 are given below : What is the mode?

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Q.3991·Miscellaneous·2021·Easy

For the set of numbers x, x, x+2, x+3, x+10 where x is a natural number, which of the following is/are correct? 1. Mean > Mode 2. Median > Mean Select the correct answer using the code given below.

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Q.3992·Miscellaneous·2021·Easy

If g is the geometric mean of 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, then which one of the following is correct?

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Q.3993·Miscellaneous·2021·Easy

If the harmonic mean of 60 and x is 48, then what is the value of x ?

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Q.3994·Miscellaneous·2021·Easy

What is the mean deviation of the first 10 even natural numbers?

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Q.3995·Miscellaneous·2021·Easy

3-digit numbers are formed using the digits 1, 3, 7 without repetition of digits. A number is randomly selected. What is the probability that the number is divisible by 3?

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Q.3996·Miscellaneous·2021·Easy

If A and B are two events such that P(not A) = 7/10, P(not B) = 3/10 and P(A|B) = 3/14, then what is P(B|A) equal to?

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