Match Column I with Column II

MATHEMATICS · Subjective · CBSE · Mathematics · Integrals · Integrals

Problem

Match Column I with Column II.

Column I	Statement	Column II
(a)	If $\int \frac{2^x}{\sqrt{1 - 4^x}}\,dx = k \sin^{-1}(f(x)) + C$ , then $k$ is greater than	(p)	0
(b)	If $\int \frac{(\sqrt{x})^5}{(\sqrt{x})^7 + x^6}\,dx = a \ln \frac{x^k}{x^k + 1} + c$ , then $ak$ is less than	(q)	1
(c)	If $\int \frac{x^4 + 1}{x(x^2 + 1)^2}\,dx = k \ln x + \frac{m}{1 + x^2} + n$ , where $n$ is the constant of integration, then $mk$ is greater than	(r)	3
(d)	If $\int \frac{dx}{5 + 4 \cos x} = k \tan^{-1}\left(m \tan \frac{x}{2}\right) + C$ , then $k/m$ is greater than	(s)	4