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:
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:
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:
Let \( P \) and \( Q \) be two finite sets having 3 elements each. The total number of mappings from \( P \) to \( Q \) is
The value of \( \int_0^1 x(1 - x)^{10} \, dx \) is equal to:
A vector of magnitude 6 and perpendicular to \( \vec{a} = 2i + 2j + k \) and \( \vec{b} = i - 2j + 2k \), is:
If the parametric form of the circle is \( x = 3\cos\theta + 3 \) and \( y = 3\sin\theta \), then the Cartesian form of the equation of the circle 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:
The length of perpendicular from the origin to the line \( \frac{x}{5} - \frac{y}{12} = 1 \) 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:
The equation of the straight line passing through the point \( (1, 1) \) and perpendicular to the line \( x + y = 5 \) is:
The integral \( \int \frac{1 + x^2 + x^4}{(1 - x^3)(1 + x^3)} \, dx \) is equal to:
If \( \sin x = \frac{3}{5} \), then the value of \( \sec x + \tan x \) is equal to:
If \( 3 \tan^{-1}(x) + \cot^{-1}(x) = \pi \), then \( \sin^{-1}(x) \) is:
sin\(^{-1} \left( \sin \left( \frac{5\pi}{6} \right) \right) \) is equal to:
tan\(^{-1} 2 - \) tan\(^{-1} \frac{1}{3}\) is equal to:
The integral \( \int \sqrt{1 + \sin 2x} \, dx \) is equal to:
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:
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 equation of the straight line, intersecting the coordinate axes \( x \) and \( y \) are respectively 1 and 2, is:
The value of \( \cos 26^\circ + \cos 54^\circ + \cos 126^\circ + \cos 206^\circ + \cos 240^\circ \) is:
If \( 2 \sin \left( \frac{\pi}{3} - 2x \right) - 1 = 0 \), \( 0<x<\frac{\pi}{2} \), then the value of \( x \) is:
If \( \cos x - \sin x = 0 \), \( 0 \leq x \leq \pi \), then the value(s) of \( x \) is/are:
The integral \( \int_{-2}^4 x^2 |x| \, dx \) is equal to: