Match List - I with List - II.

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

Match List - I with List - II.

List – I (Function y)		List – II (Derivative $\frac{dy}{dx}$)
(A)	$y=\cos \sqrt{x}$	(I)	$\frac{\sec (\tan \sqrt{x}) \tan (\tan \sqrt{x}) \sec ^2 \sqrt{x}}{2 \sqrt{x}}$
(B)	$y=\sqrt{\sin x}$	(II)	$-3 x^2 \cos \left(x^3\right) \sin \left(\sin \left(x^3\right)\right)$
(C)	$y=\sec (\tan \sqrt{x})$	(III)	$\frac{\cos x}{2 \sqrt{\sin x}}$
(D)	$y=\cos \left(\sin \left(x^3\right)\right)$	(IV)	$\frac{-1}{2 \sqrt{x}} \sin \sqrt{x}$

Choose the correct answer from the options given below :

Options:

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

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

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

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

Correct Answer:

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

Explanation:

Functions		Their Derivatives
(A)	$y=\cos \sqrt{x}$	$y' = \frac{-\sin \sqrt{x}}{2 \sqrt{x}}$ → (IV)
(B)	$y=\sqrt{\sin x}$	$y' = \frac{\cos x}{2 \sqrt{\sin x}}$ → (III)
(C)	$y=\sec (\tan \sqrt{x})$	$y' = \frac{\sec (\tan \sqrt{x}) \tan (\tan \sqrt{x}) \sec ^2 \sqrt{x}}{2 \sqrt{x}}$ → (I)
(D)	$y=\cos \left(\sin \left(x^3\right)\right)$	$y' = -\sin \left(\sin \left(x^3\right)\right) \cos \left(x^3\right) (3 x^2)$ → (II)