List of top Mathematics Questions on Integration asked in KEAM

Evaluate the following integral: $ \int \frac{\sec x}{(\sec x + \tan x)^2} \, dx $
Evaluate the following integral: $ \int e^{2\theta} \left( 2 \cos^2 \theta - \sin 2\theta \right) \, d\theta $
Evaluate the integral: $ \int e^{x + \frac{1}{x}} \frac{x^2 - 1}{x^2} \, dx $
Evaluate the integral: $ \int_0^{\frac{\pi}{2}} \frac{1}{1 + \sin x} \, dx $
If \( a_1 = 3 \) and \( a_n = n \cdot a_{n-1} \), for \( n \geq 2 \), then \( a_6 \) is equal to
If \( A = \begin{bmatrix} 4 & -1 \\ 12 & x \end{bmatrix} \) and \( A^2 = A \), then the value of \( x \) is:
The value of \( \lim_{x \to 0} \frac{\sin(5x)}{\sin(3x)} \) is:
The period of the function \( \sin\left( \frac{\pi x}{4} \right) \) is
If \( f(x) = x + 8 \), and \( g(x) = 2x^2 \), then \( (g \circ f)(x) \) is equal to
The domain of the function \( f(x) = \sqrt{7 - 8x + x^2} \) is:
If \( f(x) = \frac{x}{1 - x} \), \( x \neq 1 \), then the inverse of \( f \) is:
If \( x + iy = \frac{3 + 4i}{5 - 12i} \), then \( x + y \) is equal to
If \( z = 1 + i \), then the maximum value of \( |z + 12 + 9i| \) is
If \( \frac{|z - 5i|}{|z - 5i|} = 1 \), then
The coefficient of \( x^7 \) in the expansion of \( \left( \frac{1}{x + x^2} \right)^8 \) is
If \( \frac{1}{\log_2 x} + \frac{1}{\log_3 x} + \frac{1}{\log_4 x} + \frac{1}{\log_5 x} + \frac{1}{\log_6 x} = 1 \), then the value of \( x \) is
The common ratio of a G.P. is 10. Then the ratio between its 11th term and its 6th term is:
Let \( a, b, c \) be positive numbers. If \( a + b + c \geq K \left[ (a + b)(b + c)(c + a) \right]^{1/3} \), then the maximum value of \( K \) is:
If \( A = \begin{bmatrix} 3 & 7 \\ 2 & 5 \end{bmatrix} \), then \( A^2 (\text{adj} A) \) is:
If \( |x - 2| \leq 4 \), then \( x \) lies in the interval:
If \( \tan \left( \frac{\pi}{12} + 2x \right) = \cot 3x \), where \( 0<x<\frac{\pi}{2} \), then the value of \( x \) is:
If \( \cos \theta + \sin \theta = \sqrt{2} \), then \( \cos \theta - \sin \theta \) is equal to:
The value of \( \cos 26^\circ + \cos 54^\circ + \cos 126^\circ + \cos 206^\circ + \cos 240^\circ \) is:
If \( \cos x - \sin x = 0 \), \( 0 \leq x \leq \pi \), then the value(s) of \( x \) is/are:
If \( 2 \sin \left( \frac{\pi}{3} - 2x \right) - 1 = 0 \), \( 0<x<\frac{\pi}{2} \), then the value of \( x \) is: