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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.14491·Miscellaneous·2011·Easy

The students of a class are offered three languages (Hindi, English and French). 15 students learn all the three languages whereas 28 students do not learn any language. The number of students learning Hindi and English but not French is twice the number of students learning Hindi and French but not English. The number of students learning English and French but not Hindi is thrice the number of students learning Hindi and French but not English. 23 students learn only Hindi and 17 students learn only English. The total number of students learning French is 46 and the total number of students learning only French is 11. What is the total strength of the class?

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Q.14492·Miscellaneous·2011·Easy

There are 4 letters and 4 directed envelopes. These 4 letters are randomly inserted into the 4 envelopes. What is the probability that the letters are inserted into the corresponding envelopes ?

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Q.14493·Miscellaneous·2011·Easy

What is the degree of the following differential equation?

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Q.14494·Miscellaneous·2011·Easy

What does the differential equation (y(dy/dx) + x = a), (where a is a constant) represent?

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Q.14495·Miscellaneous·2011·Easy

What is the value of n, if P(15, n-1) : P(16, n-2) = 3 : 4 ?

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Q.14496·Miscellaneous·2011·Easy

What is the value of the determinant |x+1 x+2 x+4|; |x+3 x+5 x+8|; |x+7 x+10 x+14| ?

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Q.14497·Miscellaneous·2011·Easy

If 5 and 7 are the roots of the equation |x 4 5|; |7 x 7|; |5 8 x| = 0, then what is the third root ?

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Q.14498·Miscellaneous·2011·Easy

In a GP of positive terms, any term is equal to one-third of the sum of next two terms. What is the common ratio of the GP ?

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Q.14499·Miscellaneous·2011·Easy

What is the value of k for which the system of equations kx + 2y = 5 and 3x + y = 1 has no solution ?

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Q.14500·Miscellaneous·2011·Easy

In the binary system of numbers let a = 00111 and b = 01110, then in decimal system what is b/a equal to ?

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Q.14501·Miscellaneous·2011·Easy

If 1/(b – a) + 1/(b – c) = 1/a + 1/c then a, b, c are in

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Q.14502·Miscellaneous·2011·Easy

What is the total number of combinations of n different things taken 1, 2, 3, ..., n at a time ?

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Q.14503·Miscellaneous·2011·Easy

If the solution of the differential equation dy/dx = (ax + 3)/(2y + f) represents a circle, then what is the value of a ?

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Q.14504·Miscellaneous·2011·Easy

The points with position vectors 10i + 3j, 12i – 5j, ai + 11j are collinear, if the value of a is

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Q.14505·Miscellaneous·2011·Easy

What is the sine of angle between the vectors i + 2j + 3k and –i + 2j + 3k ?

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Q.14506·Miscellaneous·2011·Easy

5 books are to be chosen from a lot of 10 books. If m is the number of ways of choice when one specified book is always included and n is the number of ways of choice when a specified book is always excluded, then which one of the following is correct ?

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Q.14507·Miscellaneous·2011·Easy

In how many ways can 6 girls be seated in 2 empty chairs ?

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Q.14508·Miscellaneous·2011·Easy

I bought from your shop (P) a week ago (Q) to send the books (R) you have not cared (S)

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