List of top Questions asked in KEAM

A bullet of 10 g, moving at 250 m/s, penetrates 5 cm into a tree limb before coming to rest. Assuming uniform force being exerted by the tree limb, the magnitude of the force is:
The function \( f(x) = 2x^3 + 9x^2 + 12x - 1 \) is decreasing in the interval:
The lines \( \frac{x + 3}{-2} = \frac{y}{1} = \frac{z - 4}{3} \) and \( \frac{x - 1}{\mu} = \frac{y - 1}{\mu + 1} = \frac{z}{\mu + 2} \) are perpendicular to each other. Then the value of \( \mu \) is:
The INCORRECT statement is:
The efficiency of a Carnot engine operating between steam point and ice point is:
The domain of the function \( f(x) = \frac{\sin^{-1} \left( x-3 \right)}{\sqrt{9 - x^2}} \) is:
If \( \frac{1 + 3p}{4}, \frac{1 - p}{3}, \frac{1 - 3p}{2} \) are the probabilities of three mutually exclusive and exhaustive events, then the value of \( p \) is:
The value of \( \tan \left[ \tan^{-1} \left( \frac{3}{4} \right) + \tan^{-1} \left( \frac{2}{3} \right) \right] \) is:
The period of \( 2 \sin 4x \cos 4x \) is:
If \( \sin \theta = \frac{b}{a} \), then \( \frac{\sqrt{a+b}} {\sqrt{a-b}} + \frac{\sqrt{a-b}} {\sqrt{a+b}} \) is equal to:
If the determinant of the matrix \( \begin{bmatrix} |x| & 1 & 2 \\ 4 & 1 & x \\ 1 & -1 & 3 \end{bmatrix} \) equals -10, then the values of \( x \) are:
If the points \( (2, -3), (\lambda, -1) \) and \( (0, 4) \) are collinear, then the value of \( \lambda \) is equal to:
If \( B = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix} \) is the adjoint of a \( 3 \times 3 \) matrix \( A \) and \( |A| = 4 \), then the value of \( \alpha \) is:
If \( 3 \sin \theta + 5 \cos \theta = 5 \), then the value of \( 5 \sin \theta - 3 \cos \theta \) is:
If \( \frac{\sec^2 15^\circ - 1}{\sec^2 15^\circ} \) equals:
Let \( A = (a_{ij}) \) be a square matrix of order 3 and let \( M_{ij} \) be the minors of \( a_{ij} \). If \( M_{11} = -40, M_{12} = -10, M_{13} = 35 \), and \( a_{11} = 1, a_{12} = 3, a_{13} = -2 \), then the value of \( |A| \) is equal to:

If 

then the value of \( x - y \) is:

Evaluate \( \cos \left( \cot^{-1} \left( \frac{7}{24} \right) \right) \):
The constant term in the expansion of \( \left( x^3 + \frac{1}{x^2} \right)^{10} \) is:
If \( _nP_r = 480 \) and \( _nC_r = 20 \), then the value of \( r \) is equal to:
The coefficient of \( x^3 \) in the binomial expansion of \( \left( \frac{1}{\sqrt{x}} - x \right)^6 \) is:
Evaluate \( \binom{10}{1} + \binom{10}{2} + \dots + \binom{10}{10} \):
The minimum value of \( f(x) = 7x^4 + 28x^3 + 31 \) is:
If \( \cos \theta = \frac{2 \cos \alpha + 1}{2 + \cos \alpha} \), then \( \tan^2 \left( \frac{\theta}{2} \right) \) is equal to:
Magnitude of drift velocity per unit electric field is known as: