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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.13789·Miscellaneous·2012·Easy

What is the geometric mean of the sequence 1, 2, 4, 8, …., 2^n ?

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Q.13790·Miscellaneous·2012·Easy

ABCD is a parallelogram. If AB = a, BC = b, then what is BD equal to ?

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Q.13791·Miscellaneous·2012·Easy

The vector 2j - k lies :

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Q.13792·Miscellaneous·2012·Easy

The magnitude of the scalar p for which the vector p(-3i - 2j + 13k) is of unit length is :

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Q.13793·Miscellaneous·2012·Easy

Consider the following : 1. 4i×3i = 0 2. (4i/3i) = 4/3 Which of the above is/are correct ?

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Q.13794·Miscellaneous·2012·Easy

EFGH is a rhombus such that the angle EFG is 60°. The magnitude of vectors FH and (m EG) are equal where m is a scalar. What is the value of m ?

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Q.13795·Miscellaneous·2012·Easy

What is the general solution of the differential equation e^x tan y dx + (1 - e^x) sec^2 y dy = 0 ?

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Q.13796·Miscellaneous·2012·Easy

What is the general solution of the differential equation x^2 dy + y^2 dx = 0 ?

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Q.13797·Miscellaneous·2012·Easy

For the differential equation (dy/dx)^2 - x(dy/dx) + y = 0, which one of the following is not its solution ?

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Q.13798·Miscellaneous·2012·Easy

The differential equation y dy/dx + x = a where ‘a’ is any constant represents :

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Q.13799·Miscellaneous·2012·Easy

Consider a differential equation of order m and degree n. Which one of the following pairs is not feasible ?

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Q.13800·Miscellaneous·2012·Easy

What is the degree of the differential equation d^3y/dx^3 + 2(d^2y/dx^2)^2 - dy/dx + y = 0 ?

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Q.13801·Miscellaneous·2012·Easy

What is the area of the region bounded by the lines y = x, y = 0 and x = 4 ?

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Q.13802·Miscellaneous·2012·Easy

What is the minimum value of |x| ?

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Q.13803·Miscellaneous·2012·Easy

If y = ln(e^x + e^-x), then what is dy/dx at x = 0 equal to ?

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Q.13804·Miscellaneous·2012·Easy

Consider the following statements : 1.If f(x) = x^3 and g(y) = y^3 then f = g. 2.Identity function is not always a bijection. Which of the above statements is/are correct ?

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Q.13805·Miscellaneous·2012·Easy

The function f(x) = x^3 - 3x^2 + 6 is an increasing function for :

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Q.13806·Miscellaneous·2012·Easy

If f(x) = 2^(sin x), then what is the derivative of f(x) ?

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