List of top Mathematics Questions asked in KEAM

The direction ratios of the line joining the points \( (2, 3, 4) \) and \( (-1, 4, -3) \) 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:
If the sum of distances of a point from the origin and the line \( x = 3 \) is 8, then its locus is:
The integral \( \int_{-2}^4 x^2 |x| \, dx \) is equal to:
The integral \( \int \sqrt{1 + \sin 2x} \, dx \) is equal to:
The general solution of the differential equation \( (x + y)^2 \frac{dy}{dx} = 1 \) is:
Equation of the line parallel to the line \( \frac{x-2}{2} = \frac{y-2}{3} = \frac{z-1}{-2} \) and passing through the point \( (3, 2, -1) \) is:
The equation of the straight line, intersecting the coordinate axes \( x \) and \( y \) are respectively 1 and 2, is:
The equation of the straight line passing through the point \( (1, 1) \) and perpendicular to the line \( x + y = 5 \) is:
If the lines \( \frac{x-1}{2} = \frac{y-2}{\alpha} = \frac{z-3}{2} \) and \( \frac{x-1}{2} = \frac{y-2}{1} = \frac{z-3}{-2} \) are perpendicular, then the value of \( \alpha \) 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:
Domain of the function \( \sin^{-1}(2x - 1) \) is:
If \( f(x) = \int_0^{x^3} (t + 4)^2 \, dt \), then \( f'(2) \) is equal to:
If \( \tan \left( \frac{\pi}{12} + 2x \right) = \cot 3x \), where \( 0<x<\frac{\pi}{2} \), then the value of \( x \) is:
The coordinates of the vertex of the parabola \[ y = 2x^2 - 12x + 26 \] are
If the complex number \( \frac{2 + i}{\lambda + i} \) lies on the line \( y = x \) of the first quadrant, then the value of \( \lambda \) is equal to
Find the equation of the line perpendicular to the line \[ 7x - 5y = 11 \] and passing through the point \( (7, -9) \).
If the complex number \( 2 + i \) is rotated through an angle \( 90^\circ \) in the anti-clockwise direction about the origin in the complex plane, then the resulting complex number is
Let \( A \) be a \( 3 \times 3 \) matrix with \( |A| = 7 \). If \( B = 3A \), then the value of \[ \left| \frac{{adj } A}{B} \right| \] is equal to
If \[ A = \begin{bmatrix} -7 & 3 \\ 3 & -1 \end{bmatrix} \] then \( \det(A^5) \) is equal to:
Let \[ \sum_{k=1}^{15} \sin (t_k) = 0 \quad {and} \quad \sum_{k=1}^{15} \sin (3t_k) = \frac{-24}{5}, \] where \( t_1, t_2, t_3, \dots \) are real numbers. Then the value of the sum \[ \sum_{k=1}^{15} \sin^3 (t_k) \] is equal to
Let \( f(x) = 6x^2 + 9x + 10 \) and \( g(x) = x^2 - 9x - 9 \). Then the value of \( (f \circ g)(10) \) is
If \( (a,-6) \) lies on the perpendicular bisector of the line segment joining \( (-2,-1) \) and \( (4,-13) \), then the value of \( a \) is equal to
The line joining the points $ (2,2,2) $ and $ (6,6,6) $ meets the line $$ \frac{x - 1}{3} = \frac{y - 2}{2} = \frac{z - 5}{-1} $$ at the point 
The value of \( \int_{-2}^{2} x |x| \,dx \) is: