List of top Questions asked in KEAM

A projectile is given an initial velocity of $(\hat{i} + \hat{j})$ m/s, where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical direction. The equation of its trajectory is $(g = 10 \, \text{m/s}^2)$.

In the travelling plane wave equation given by $ y = A \sin \omega \left( \frac{x}{v} - t \right) $, where $ \omega $ is the angular velocity and $ v $ is the linear velocity.
The dimension of $ \omega t $ is:

Which of the following are the conditions for a reaction spontaneous at all temperatures?

The general solution of the differential equation $ \frac{dy}{dx} = xy - 2x - 2y + 4 $ is:

The product of the total electric flux emanating from a closed surface enclosing a charge $ q $ in free space is ($ \epsilon_0 $ - electrical permittivity of free space):

A parallel plate capacitor with a dielectric medium of dielectric constant 1.5 has a capacitance of $C$. If the dielectric is removed, then the capacitance of the capacitor becomes

Which one of the following phenomena does not occur when a white light falls on an equilateral glass prism?

Let \[ f(x) = \frac{|5 - x|(x + 5)}{\tan(x - 5)} \quad {for} \quad x \neq 5. \] Then \[ \lim_{x \to 5} f(x) { is equal to:} \]

A person travels in a car from p to q with uniform speed u and returns to p with uniform speed v. The average speed for his round trip is

The first term and the 6th term of a G.P. are 2 and $ \frac{64}{243} $ respectively. Then the sum of first 10 terms of the G.P. is:

The period of the function $ f(x) = \sin\left( \frac{3x}{2} \right) $ is equal to:

If $ \cos \theta = \frac{2 \cos \alpha + 1}{2 + \cos \alpha} $, then $ \tan^2 \left( \frac{\theta}{2} \right) $ is equal to:

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:

A ball is projected in still air. With respect to the ball the streamlines appear as shown in the figure. If speed of air passing through the region 1 and 2 are $ v_1 $ and $ v_2 $, respectively and the respective pressures, $ P_1 $ and $ P_2 $, respectively, then

If the voltage across a bulb rated 220V – 60W drops by 1.5% of its rated value, the percentage drop in the rated value of the power is:

The electric power delivered by a transmission cable of resistance $ R_c $ at a voltage $ V $ is $ P $. The power dissipated is

Mobility $ \mu $ of an electron is related to average collision time $ \tau $ as: \[ \mu = \frac{e \tau}{m} \] (where $ e $ is the electronic charge, and $ m $ is the mass of the electron)

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:

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 vapour pressure of H$_2$O at 323K is 95 mm of Hg. 176g of sucrose (Molar mass = 342 gmol$^{-1}$) is added to 900g of H$_2$O at 323K.
The vapour pressure of solution is about

1 g of ice at 0°C is converted into water by supplying a heat of 418.72 J. The quantity of heat that is used to increase the temperature of water from 0°C is (Latent heat of fusion of ice = $ 3.35 \times 10^5 \, {Jkg}^{-1} $):

The number of positive integers that have at most seven digits and contain only the digits 0 and 9 is

When n-hexane is heated to 773K at 10-20 atmosphere pressure in the presence of $Cr_2O_3$, benzene is formed. This reaction is called

The ratio of the velocities of the electron in the second, third and fourth Bohr’s orbits of the hydrogen atom is:

The quantum number which determines the shape of the subshell is: