Match List-I with List-II | List-I | List-II | | --- | --- | | Functions | Integrals | | --- | --- | | (A) dx/x^2 - 4, x ≠ ± 2 | (I) x + sqrt(4 + x^2) + C, where C is an arbitrary constant | | (B) 1sqrt(16 - x^2) dx; x

Question

Match List-I with List-II | List-I | List-II | | --- | --- | | Functions | Integrals | | --- | --- | | (A) dx/x^2 - 4, x ≠ ± 2 | (I) x + sqrt(4 + x^2) + C, where C is an arbitrary constant | | (B) 1sqrt(16 - x^2) dx; x < 4 | (II) ^-1 ( x/4 ) + C, where C is an arbitrary constant | | (C) 1/16 + x^2 dx | (III) 1/4 x-2/x+2 + C, where C is an arbitrary constant | | (D) 1sqrt(4 + x^2) dx | (IV) 1/4 ^-1 ( x/4 ) + C, where C is an arbitrary constant | Choose the correct answer from the options given below:

Option 1: (A) - (IV), (B) - (III), (C) - (II), (D) - (I)

Option 2: (A) - (III), (B) - (II), (C) - (IV), (D) - (I)

Option 3: (A) - (III), (B) - (IV), (C) - (II), (D) - (I)

Option 4: (A) - (IV), (B) - (III), (C) - (I), (D) - (II)

AfterBoards · Accepted Answer

The answer is '(A) - (III), (B) - (II), (C) - (IV), (D) - (I)'. View full solution:

List-I	List-II
(A) $\int \frac{dx}{\sqrt{a^2 - x^2}} =$	(I) $\log_e \vert x + \sqrt{x^2 - a^2}\vert + c$
(B) $\int \sqrt{a^2 - x^2} dx =$	(II) $\sin^{-1} \frac{x}{a} + c$
(C) $\int \sqrt{x^2 - a^2} dx =$	(III) $\frac{x}{2} \sqrt{a^2 - x^2} + \frac{a^2}{2} \sin^{-1} \frac{x}{a} + c$
(D) $\int \frac{dx}{\sqrt{x^2 - a^2}} =$	(IV) $\frac{x}{2} \sqrt{x^2 - a^2} - \frac{a^2}{2} \log_e \vert x + \sqrt{x^2 - a^2}\vert + c$

CUET Mathematics 2025 16 May Shift 1 PYQs

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