List of top Mathematics Questions asked in KEAM

The integral \( \int xe^x \, dx \) is equal to:
If the sum of distances of a point from the origin and the line \( x = 3 \) is 8, then its locus is:
If \( f(x) = \frac{1}{2 - x} \) and \( g(x) = \frac{1}{1 - x} \), then the point(s) of discontinuity of the function \( g(f(x)) \) is (are):
The equation of the straight line, intersecting the coordinate axes \( x \) and \( y \) are respectively 1 and 2, is:
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
The area of the triangle formed by the coordinate axes and a line whose perpendicular from the origin makes an angle of 45° with the x-axis is 50 square units. Then the equation of the line is:
A line makes angles \( \alpha, \beta, \gamma \) with \( x, y \), and \( z \)-axes respectively. Then the value of \( \sin^2\alpha + \sin^2\beta - \cos^2\gamma \) is:
sin\(^{-1} \left( \sin \left( \frac{5\pi}{6} \right) \right) \) is equal to:
If \( \sin x = \frac{3}{5} \), then the value of \( \sec x + \tan x \) is equal to:
If \( \vec{a} \) and \( \vec{b} \) are non-collinear unit vectors and \( |\vec{a} + \vec{b}|^2 = 3 \), then \( (3\vec{a} + 2\vec{b}) \cdot (3\vec{a} - \vec{b}) \) is equal to:
Domain of the function \( \sin^{-1}(2x - 1) \) is:
The eccentricity of an ellipse is \( \frac{1}{3} \) and its center is at the origin. If one of the directrices is \( x = 9 \), then the equation of the ellipse is:
If \( P(-3, 4) \) and \( Q(3, 1) \) are points on a straight line, then the slope of the straight line perpendicular to PQ is:
If \( 3 \tan^{-1}(x) + \cot^{-1}(x) = \pi \), then \( \sin^{-1}(x) \) is:
tan\(^{-1} 2 - \) tan\(^{-1} \frac{1}{3}\) is equal to:
If \( \cos x - \sin x = 0 \), \( 0 \leq x \leq \pi \), then the value(s) of \( x \) is/are:
If \( \tan \left( \frac{\pi}{12} + 2x \right) = \cot 3x \), where \( 0<x<\frac{\pi}{2} \), then the value of \( x \) is:
The value of \( \cos 26^\circ + \cos 54^\circ + \cos 126^\circ + \cos 206^\circ + \cos 240^\circ \) is:
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:
The length of perpendicular from the origin to the line \( \frac{x}{5} - \frac{y}{12} = 1 \) is:
If \( 2 \sin \left( \frac{\pi}{3} - 2x \right) - 1 = 0 \), \( 0<x<\frac{\pi}{2} \), then the value of \( x \) is:
The probability that at least one of \( A \) or \( B \) occurs is 0.6. If \( A \) and \( B \) occur simultaneously with probability 0.2, then \( P(A') + P(B') \) is:
If \( \frac{|z - 5i|}{|z - 5i|} = 1 \), then