List of top Mathematics Questions asked in KEAM

If the sum of distances of a point from the origin and the line \( x = 3 \) is 8, then its locus 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:
The direction ratios of the line joining the points \( (2, 3, 4) \) and \( (-1, 4, -3) \) is:
The equation of the straight line, intersecting the coordinate axes \( x \) and \( y \) are respectively 1 and 2, 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 integral \( \int_5^{10} \left\lfloor x \right\rfloor dx \) is equal to (where \( \left\lfloor x \right\rfloor \) denotes the greatest integer function):
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:
If \( x = r \cos \theta, y = r \sin \theta \), then \( \frac{dy}{dx} \) at \( \theta = \frac{\pi}{4} \), where \( r \) is a constant and \( \theta \) is a parameter, is equal to:
If \( 3 \tan^{-1}(x) + \cot^{-1}(x) = \pi \), then \( \sin^{-1}(x) \) is:
If the point \( (2, k) \) lies on the circle \( (x - 2)^2 + (y + 1)^2 = 4 \), then the value of \( k \) is:
The solution of the differential equation \( x + y \frac{dy}{dx} = 0 \), given that at \( x = 0 \), \( y = 5 \), 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 value of \( \cos 26^\circ + \cos 54^\circ + \cos 126^\circ + \cos 206^\circ + \cos 240^\circ \) is:
Find the equation of the line perpendicular to the line \[ 7x - 5y = 11 \] and passing through the point \( (7, -9) \).
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
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:
Evaluate the limit: \[ \lim\limits_{x \to 6} \frac{\sqrt{x^2 + 13} - 7}{x^2 - 36}. \]
The value of \[ \tan^{-1} \left( \frac{1}{3} \right) + \tan^{-1} \left( \frac{2}{3} \right) + \cot^{-1} \left( \frac{9}{7} \right) \] 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
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 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
If \( x \) satisfies the inequality \( -3<\frac{1}{2} + \frac{-3x}{2} \leq 6 \), then \( x \) lies in the interval