CUET Mathematics 2025 22 May Shift 1 PYQs

$\int \frac{e^{7\log_e x} - e^{5\log_e x}}{e^{3\log_e x} - e^{3\log_e x}} dx$ is equal to:

(Here, c is an arbitrary constant)

The value of which of the following integrals is zero?

(A) $\int_0^1 x dx$

(B) $\int_{-1}^1 x dx$

(C) $\int_{-1}^1 x^2 dx$

(D) $\int_0^1 \log\left(\frac{x}{1-x}\right) dx$

Choose the correct answer from the options given below:

If $\int e^x\left(\frac{x-1}{(x+1)^3}\right)dx = \frac{Ae^x}{(x+1)^B} + C$, where C is constant of integration then which of the following are correct?

(A) $A = -1$

(B) $A = 1$

(C) $B = 3$

(D) $B = 2$

Choose the correct answer from the options given below: