List of top Mathematics Questions asked in KEAM

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 \( f(x) = \lfloor x \rfloor \), 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
If the sum of distances of a point from the origin and the line \( x = 3 \) is 8, then its locus is:
If \( A \) and \( B \) are two independent events such that \( P(A) = 0.4 \) and \( P(A \cup B) = 0.7 \), then \( P(B) \) is equal to:
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 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:
The length of perpendicular from the origin to the line \( \frac{x}{5} - \frac{y}{12} = 1 \) is:
The equation of the straight line passing through the point \( (1, 1) \) and perpendicular to the line \( x + y = 5 \) 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, intersecting the coordinate axes \( x \) and \( y \) are respectively 1 and 2, is:
If \( x_1, i=2, 3, \ldots, n \) are \( n \) observations such that \( \sum_{i=1}^{n} x_i^2 = 550 \), mean \( \bar{x} = 5 \) and variance is zero, then the number of observations is equal to:
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:
If \( \sin x = \frac{3}{5} \), then the value of \( \sec x + \tan x \) is equal to:
If \( 2 \sin \left( \frac{\pi}{3} - 2x \right) - 1 = 0 \), \( 0<x<\frac{\pi}{2} \), then the value of \( x \) is:
If \( \cos \theta + \sin \theta = \sqrt{2} \), then \( \cos \theta - \sin \theta \) 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:
Domain of the function \( \sin^{-1}(2x - 1) \) is:
If the mean of five observations \( x, 2x+5, 13, 2x-7, \) and 9 is 22, then the value of \( x \) is:
If \( 3 \tan^{-1}(x) + \cot^{-1}(x) = \pi \), then \( \sin^{-1}(x) \) is:
If \( A = \begin{bmatrix} 3 & 7 \\ 2 & 5 \end{bmatrix} \), then \( A^2 (\text{adj} A) \) is:
Let \( a, b, c \) be positive numbers. If \( a + b + c \geq K \left[ (a + b)(b + c)(c + a) \right]^{1/3} \), then the maximum value of \( K \) is:
If \( |x - 2| \leq 4 \), then \( x \) lies in the interval:
If \( z = 1 + i \), then the maximum value of \( |z + 12 + 9i| \) is
If \( \frac{|z - 5i|}{|z - 5i|} = 1 \), then