List of top Questions asked in KEAM- 2024

PCl\(_5\)(g), PCl\(_3\)(g) and Cl\(_2\)(g) are at equilibrium at 500 K. The equilibrium concentrations of PCl\(_3\), Cl\(_2\) and PCl\(_5\) are respectively 4.0 M, 4.0 M and 2.0 M. Calculate \( K_c \) for the reaction: \[ {PCl}_5(g) \rightleftharpoons {PCl}_3(g) + {Cl}_2(g) \]
The half-life period of a radioactive element is 2 days. If \( \frac{1}{32} \) part of the initial amount remains undecayed after a time \( t \), then the value of \( t \) in days is

Ice is coated uniformly around a sphere of radius 15 cm. If ice is melting at the rate of \( 80 { cm}^3/{min} \) when the thickness is 5 cm, then the rate of change of thickness of ice is

Find the integrating factor of the differential equation: \[ (3 \sin x \cos x) \, dy = (1 + 3y \sin^2 x) \, dx, \quad {where} \quad 0<x<\frac{\pi}{2} \] is
If \[ f(x) = \sqrt[3]{x^2} + \sqrt{x}, \] then the value of \( f'(64) \) is equal to
The general solution of the differential equation \[ 2y \tan x + \frac{dy}{dx} = 5 \sin x \] is:
Let \( A = \{ 1, 3, 5, 7, \dots, 21 \} \). The number of ways 4 numbers, containing always 11, can be selected from the set A is equal to
Let \( z = x + iy \), where \( y>0 \). If \( z + \overline{z} = 6 \) and \( |z| + | \overline{z} | = 10 \), then \( z = \)
The conductivity of 0.02 mol L\(^{-1}\) KCl solution is 0.248 S m\(^{-1}\). Its molar conductivity is
The coefficient of friction between the road and the tyres of a cyclist is 0.1. The maximum speed with which he can take a circular turn of radius 2 m without skidding is ( \( g = 10 \) m/s\( ^2 \) )
When the number of molecules per unit volume of an ideal gas is \( 0.8 \times 10^{24} \), the mean free path length for its molecules is \( 2.2 \times 10^{-5} \, {m} \). If the number of molecules per unit volume is \( 1.0 \times 10^{24} \), then the mean free path is
The velocity (\( v \))-time (\( t \)) graph for the motion of a body is a straight line making an angle \( 60^\circ \) with the time axis. Then the body is moving with an acceleration (in m\( s^{-2} \)) of:
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
Lanthanides (Ln) when heated with carbon at 2773K form product with general formula
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
In a nuclear fusion process, the masses of the fusing nuclei are \( M_A \) and \( M_B \). Then the mass of the product nucleus \( M_C \) is related to \( M_A \) and \( M_B \) as
Radioactive decay follows
The electron concentration \( n_e \) and hole concentration \( n_h \) in semiconductor are related to the number of intrinsic charge concentration \( n_i \) as
Compound ‘X’ (C\(_6\)H\(_6\)O) reacts with aqueous NaOH to give compound ‘Y’. ‘Y’ reacts with CO\(_2\) followed by acidification to give compound ‘Z’. The compounds X, Y and Z are respectively
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
An intrinsic semiconductor at \( T = 0 \, {K} \) behaves like
The catalyst used in the Wacker process is

The energy stored in the capacitor after closing the key K is 

The decreasing order of basic strength in aqueous solution of amines is
If \[ \lim_{x \to 9} f(x) = 6 \quad {and} \quad \lim_{x \to 9} g(x) = 3, \] then \[ \lim_{x \to 9} \frac{f(x) - 2g(x)}{g(x)} \] is equal to