List of top Questions asked in KEAM

If the straight line \( \frac{x - a}{1} = \frac{y - b}{2} = \frac{z - 3}{-1} \) passes through \( (-1, 3, 2) \), then the values of \( a \) and \( b \) are, respectively:
The energy required by the electron to cross the forbidden band for Germanium is:
The radius of gyration of a circular disc of radius \( R \), rotating about its diameter is:
If two vectors \( \vec{a} = \cos \alpha \hat{i} + \sin \alpha \hat{j} + \sin \frac{\alpha}{2} \hat{k} \) and \( \vec{b} = \sin \alpha \hat{i} - \cos \alpha \hat{j} + \cos \frac{\alpha}{2} \hat{k} \) are perpendicular, then the values of \( \alpha \) are:
If \( f(x) = \left\{ \begin{array}{ll} mx + 1, & \text{when } x \leq \frac{\pi}{2} \\ \sin x + n, & \text{when } x > \frac{\pi}{2} \end{array} \right. \) is continuous at \( x = \frac{\pi}{2} \), then the values of \( m \) and \( n \) are:
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:
A tuning fork vibrating at 300 Hz, initially in air, is then placed in a trough of water. The ratio of the wavelength of the sound waves produced in air to that in water is (Given that the velocity of sound in water and in air at that place are 1500 m/s and 350 m/s respectively):
The dimensions of torque are:
A particle is projected at an angle \( \theta \) with the x-axis in the xy-plane with a velocity \( \mathbf{v} = 6\hat{i} - 4\hat{j} \). The velocity of the body on reaching the x-axis again is:
Magnitude of drift velocity per unit electric field is known as:
Evaluate \( \cos \left( \cot^{-1} \left( \frac{7}{24} \right) \right) \):
If \( 3 \sin \theta + 5 \cos \theta = 5 \), then the value of \( 5 \sin \theta - 3 \cos \theta \) is:
The coefficient of linear expansion of aluminum is \( 2.5 \times 10^{-5} \, {K}^{-1} \). Its coefficient of volume expansion in \( {K}^{-1} \) is:
The valence electron MO configuration of \( {C}_2 \) (atomic number of C = 6) molecule is:
Which of the following is true for a reaction that is spontaneous only at high temperature?
If \( \cos \theta = \frac{2 \cos \alpha + 1}{2 + \cos \alpha} \), then \( \tan^2 \left( \frac{\theta}{2} \right) \) is equal to:
The rate constant of a first order reaction is \(4.606 \times 10^{-3} \, {s}^{-1}\). The time taken to reduce 20 g of reactant into 2 g is:
The rate law for the reaction, A + B → Product, is: \[ {rate} = [A][B]^{3/2} \] The total order of the reaction is:
The domain of the function \( f(x) = \frac{\sin^{-1} \left( x-3 \right)}{\sqrt{9 - x^2}} \) is:
If \( 2z = 7 + i\sqrt{3} \), then the value of \( z^2 - 7z + 4 \) is:
Let \( z \) be a complex number satisfying \( |z + 16| = 4|z + 1| \). Then:
If \( f(x) = \begin{cases} x^2 & \text{for } x < 0 \\ 5x - 3 & \text{for } 0 \leq x \leq 2 \\ x^2 + 1 & \text{for } x > 2 \end{cases} \), then the positive value of \( x \) for which \( f(x) = 2 \) is:
Let a relation \( R \) on the set of natural numbers be defined by \( (x, y) \in R \) if and only if \( x^2 - 4xy + 3y^2 = 0 \) for all \( x, y \in \mathbb{N} \). Then the relation is:
If a vector makes angles \( \frac{\pi}{3}, \frac{\pi}{4} \) and \( \gamma \) with \( \hat{i}, \hat{j} \), and \( \hat{k} \), respectively, where \( \gamma \in \left( \frac{\pi}{2}, \pi \right) \), then the angle \( \gamma \) is:
The value of \( \tan \left[ \tan^{-1} \left( \frac{3}{4} \right) + \tan^{-1} \left( \frac{2}{3} \right) \right] \) is: