CUET Mathematics 2022 16 July Shift 2 PYQs

If $\int \frac{dx}{(x-1)^3/^4,(x+2)^5/^4} = a[1 - g(x)]^b + c$, where $c$ is a constant of integration, then which of the following are true?

(A) $a = \frac{2}{3}$

(B) $\beta = \frac{3}{4}$

(C) $3\alpha + 4\beta = 5$

(D) $g(x) = \frac{3}{(x+2)}$

Choose the correct answer from the options given below:

The value of $\int_{0}^{1} \frac{a-b x^{2}}{\left(a+b x^{2}\right)^{2}} d x$ is :

$\int_{0}^{\pi} \frac{e^{\cos x}}{e^{\cos x} + e^{-\cos x}} dx =$