Question

Match List-I with List-II: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

Choose the correct answer from the options given below.

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

Answer 1

Answer: (D)

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

Answer 2

To match the functions in List-I with their derivatives in List-II , calculate the derivatives:

For (A) $f(x) = \frac{5^x}{\log_e 5}$:

$f'(x) = 5^x.$

Thus, (A) matches with (III).

For (B) $f(x) = \log_e 5$:

$f'(x) = 0.$

Thus, (B) matches with (IV).

For (C) $f(x) = 5^x \log_e 5$:

$f'(x) = 5^x \log_e 5.$

Thus, (C) matches with (II).

For (D) $f(x) = 5^x$:

$f'(x) = 5^x (\log_e 5)^2.$

Thus, (D) matches with (I).

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