List of top Mathematics Questions asked in KEAM

If \( \cos \theta + \sin \theta = \sqrt{2} \), then \( \cos \theta - \sin \theta \) is equal to:
If \( |x - 2| \leq 4 \), then \( x \) lies in the interval:
If \( A = \begin{bmatrix} 3 & 7 \\ 2 & 5 \end{bmatrix} \), then \( A^2 (\text{adj} A) \) is:
If \( A = \begin{bmatrix} 4 & -1 \\ 12 & x \end{bmatrix} \) and \( A^2 = A \), 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:
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 coefficient of \( x^7 \) in the expansion of \( \left( \frac{1}{x + x^2} \right)^8 \) is
If \( \frac{|z - 5i|}{|z - 5i|} = 1 \), then
If \( x + iy = \frac{3 + 4i}{5 - 12i} \), then \( x + y \) is equal to
If the complex numbers \( (2 + i)x + (1 - i)y + 2i - 3 \) and \( x + (-1 + 2i)y + 1 + i \) are equal, then \( (x, y) \) is
If \( f(x) = \frac{x}{1 - x} \), \( x \neq 1 \), then the inverse of \( f \) is:
If \( f(x) = x + 8 \), and \( g(x) = 2x^2 \), then \( (g \circ f)(x) \) is equal to
The period of the function \( \sin\left( \frac{\pi x}{4} \right) \) is
The domain of the function \( f(x) = \sqrt{7 - 8x + x^2} \) is:
If \( f(x) = \lfloor x \rfloor \), where \( \lfloor x \rfloor \) denotes the greatest integer function, and if the domain of \( f \) is \( \{-3.01, 2.99\} \), then the range of \( f \) is
Let \( P \) and \( Q \) be two finite sets having 3 elements each. The total number of mappings from \( P \) to \( Q \) is
Find the integrating factor of the differential equation: \[ (3 \sin x \cos x) \, dy = (1 + 3y \sin^2 x) \, dx, \quad {where} \quad 0<x<\frac{\pi}{2} \] is
Evaluate the integral: \[ \int_{0}^{3} |x - 2| \,dx \] is equal to
Evaluate the integral: \[ \int \frac{6x^3 + 9x^2}{x^4 + 3x^3 - 9x^2} dx. \]
Evaluate the integral: \[ \int \frac{\sin \theta \sin 2\theta}{1 - \cos 2\theta} d\theta. \]
The general solution of the differential equation \[ 2y \tan x + \frac{dy}{dx} = 5 \sin x \] is:
The function \( f(x) = 6x^4 - 3x^2 - 5 \) is increasing in the set:
If \( f(x) = x^2 + 2x f'(1) + f''(2) \) for all \( x \), then \( f(0) \) is equal to:
Let \( \alpha \) and \( \beta \) be real numbers such that \( f(x) \) is defined as: \[ f(x) = \begin{cases} 2x^2 + 4x + \alpha, & \text{if } x < 1 \\ \beta x^2 + 5, & \text{if } x \geq 1 \end{cases} \] and is differentiable at \( x = 1 \). Then \( \alpha + \beta \) is equal to:
If \[ y = \log_e \left( \frac{1 + 2x^2}{1 - 3x^2} \right), \] then \( \frac{dy}{dx} \) is: