List of top Questions asked in KEAM

The pressure of an ideal gas is proportional to the cube of its temperature (on absolute scale) in an adiabatic process. Then the value of the ratio $C_p/C_v$ is

For the reaction:

$3Fe_{(s)} + 2O_2{(g)} \rightarrow Fe_3O_4{(s)}$

$\Delta H = -1650\,\text{kJ mol}^{-1}$, $\Delta S = -600\,\text{J K}^{-1} \text{mol}^{-1}$ at $300\,\text{K}$. What is the value of free energy change for the reaction at $300\,\text{K}$?

The numbers $ a, b, c, d $ are in G.P. with common ratio $ r $. If $ \frac{1}{a^3 + b^3} + \frac{1}{b^3 + c^3} + \frac{1}{c^3 + d^3} $ are also in G.P., then the common ratio is:

The minimum value of $ f(x) = 7x^4 + 28x^3 + 31 $ is:

A block of mass $ M $ is placed on the floor of a lift at the center. The acceleration required for the lift to descend so that the block exerts a force of $ \frac{Mg}{4} $ on the lift floor is:

Evaluate $ \binom{10}{1} + \binom{10}{2} + \dots + \binom{10}{10} $:

A tennis ball of mass 50g thrown vertically up at a speed of 25 m s$^{-1}$ reaches a maximum height of 25 m. The work done by the resistance forces on the ball is:

For a given radioactive material of mean life $\tau$ and half-life $t_{1/2}$, the relationship between $t_{1/2}$ and $\tau$ is:

The coefficient of $ x^3 $ in the binomial expansion of $ \left( \frac{1}{\sqrt{x}} - x \right)^6 $ is:

The common ratio of a G.P. is $ \frac{1}{2} $. If the product of the first three terms is 64, then the sum of the first 10 terms is:

If $ \left( \frac{1 - i}{1 + i} \right)^{10} = a + ib $, then the values of $ a $ and $ b $ are, respectively:

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):

If $ _nP_r = 480 $ and $ _nC_r = 20 $, then the value of $ r $ is equal to:

The second term of a G.P. is 4, then the product of the first three terms is:

Two similar metallic rods of the same length $ l $ and area of cross section $ A $ are joined and maintained at temperatures $ T_1 $ and $ T_2 $ ($ T_1>T_2 $) at one of their ends as shown in the figure. If their thermal conductivities are $ K $ and $ \frac{K}{2} $ respectively. The temperature at the joining point in the steady state is: