The value of _0^1 _e(1/x - 1)dx is: Option 1: 1 Option 2: 0 Option 3: 3/2 Option 4: 2

The answer is '0'. View full solution:

CUET Mathematics - The value of _0^1 _e(1/x - 1)dx is: | PYQs + Solutions

CUET Mathematics 2025 2 June Shift 1

Calculus

Medium

common

3/2

$\log 2$

✅ Correct Option: 2

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Match the rational functions with the correct form of the partial fractions.

[ $p,q,r,a,b,c,A,B,C$ are arbitrary constants]

Match List-I with List-II

List-I (Rational Function)	List-II (Partial Fraction)
(A) $\dfrac{px^2+qx+r}{(x-a)(x^2+bx+c)}$	(I) $\dfrac{A}{x-a}+\dfrac{B}{(x-a)^2}+\dfrac{C}{x-b}$
(B) $\dfrac{px^2+qx+r}{(x-a)^2(x-b)}, a\neq b$	(II) $\dfrac{A}{x-a}+\dfrac{B}{(x-a)^2}$
(C) $\dfrac{px^2+qx+r}{(x-a)(x-b)(x-c)}, a\neq b\neq c$	(III) $\dfrac{A}{x-a}+\dfrac{Bx+C}{x^2+bx+c}$
(D) $\dfrac{px+q}{(x-a)^2}$	(IV) $\dfrac{A}{x-a}+\dfrac{B}{x-b}+\dfrac{C}{x-c}$

Choose the correct answer from the options given below: