List of top Mathematics Questions asked in KEAM

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 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 integral \( \int xe^x \, dx \) is equal to:
The integral \( \int \frac{1 + x^2 + x^4}{(1 - x^3)(1 + x^3)} \, dx \) is equal to:
sin\(^{-1} \left( \sin \left( \frac{5\pi}{6} \right) \right) \) is equal to:
The value of \( \cos 26^\circ + \cos 54^\circ + \cos 126^\circ + \cos 206^\circ + \cos 240^\circ \) is:
The value of \( \int_{-1}^{1} x^2 \sin x \, dx \) is equal to:
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 \( \sin x = \frac{3}{5} \), then the value of \( \sec x + \tan x \) is equal to:
If \( \vec{a} = 2\vec i + 4\vec j + 7\vec k \) and \( \vec {b} = 4\vec i + 7\vec j + 2\vec k \), then the angle between \( \vec{a} + \vec{b} \) and \( \vec{a} - \vec{b} \) is equal to:
If \( z = 1 + i \), then the maximum value of \( |z + 12 + 9i| \) 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:
The domain of the function \( f(x) = \sqrt{7 - 8x + x^2} \) is:
If \( |x - 2| \leq 4 \), then \( x \) lies in the interval:
Find the equation of the line perpendicular to the line \[ 7x - 5y = 11 \] and passing through the point \( (7, -9) \).

The value of \( \cosec x + \cot x \) is

The value of \( \sin \left( 2 \cos^{-1} \left( \frac{5}{12} \right) + \sin^{-1} \left( \frac{5}{12} \right) \right) \) is equal to
The function \( f(x) = 6x^4 - 3x^2 - 5 \) is increasing in the set:
The standard deviation of a data set \( x_1, x_2, \dots, x_6 \) (\( x_i>0 \)) is 2. If \[ \sum_{i=1}^{9} x_i^2 = 360, \] then the mean of the data set is
Let \( \alpha, \beta, \gamma \) be the direction cosines of a vector \( \vec{a} = x \hat{i} + y \hat{j} + z \hat{k} \), where \( z<0 \). If \( \alpha = \frac{-4}{\sqrt{105}} \) and \( \beta = \frac{\sqrt{5}}{\sqrt{21}} \), then \( \gamma \) is equal to
Let \( A(0,3,-3) \), \( B(1,1,1) \) and \( C(2,0,3) \) be three points in space. Then the projection of \( \overrightarrow{AB} \) on \( \overrightarrow{AC} \) is equal to
If \( \vec{a} = 5\hat{i} - 7\hat{j} + 9\hat{k} \) and \( \vec{b} = -5\hat{i} + 7\hat{j} - 9\hat{k} \), then \( \vec{a} \cdot (\vec{a} \times \vec{b}) + (\vec{a} + \vec{b}) \cdot \hat{b} \) is equal to
The angle between the vectors \( \vec{a} \) and \( \vec{b} \) is \( \frac{\pi}{3} \). If \( | \vec{a} \cdot \vec{b} |^2 = 15 \), then \( | \vec{a} \times \vec{b} |^2 \) is equal to
Evaluate the limit: $$ \lim_{x \to 4} \left( \frac{1}{x - 4} - \frac{5}{x^2 - 3x - 4} \right) $$ is equal to 
Find the values of \( \alpha \) for which the circle \[ x^2 + y^2 + \alpha x - 8y + 56 = 0 \] has radius 3.