Match List I with List II List I (Functions) List II (Derivatives) A. f(x)=sin -1 x I. $\frac{1}{1+x^2}$ , x ∈ R B. f(x)=tan -1 x II. $\frac{1}{\sqrt{1-x^2}}$ , x ∈ (-1, 1) C. f(x)=cos -1 x III. $-\frac{1}{\sqrt{1-x^2}}$ , x ∈ (-1, 1) D. f(x)=sin -1 x IV. $-\frac{1}{1+x^2}$ , x ∈ R Choose the correct answer from the options given below :

Question

cdquestions Admin · Accepted Answer

The correct option is (C) :A-II, B-I, C-III, D-IV.

Answer

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

Answer

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

Answer

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

Answer

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

List-I (Function)	List-II (Derivative w.r.t. x)
(A) \( \frac{5^x}{\ln 5} \)	(I) \(5^x (\ln 5)^2\)
(B) \(\ln 5\)	(II) \(5^x \ln 5\)
(C) \(5^x \ln 5\)	(III) \(5^x\)
(D) \(5^x\)	(IV) 0

The Correct Option is C

Solution and Explanation

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List I (Functions)		List II (Derivatives)
A.	f(x)=sin^-1x	I.	\(\frac{1}{1+x^2}\), x ∈ R
B.	f(x)=tan^-1x	II.	\(\frac{1}{\sqrt{1-x^2}}\), x ∈ (-1, 1)
C.	f(x)=cos^-1x	III.	\(-\frac{1}{\sqrt{1-x^2}}\), x ∈ (-1, 1)
D.	f(x)=sin^-1x	IV.	\(-\frac{1}{1+x^2}\), x ∈ R