List of top Questions asked in KEAM

The particle which is expected to be emitted along with $ Y $ in the following nuclear reaction is \[ { }^{198}_{80}X \rightarrow { }^{197}_{79}Y + ? \]

The value of $ \int_{-2}^{2} x |x| \,dx $ is:

If the complex number $ 2 + i $ is rotated through an angle $ 90^\circ $ in the anti-clockwise direction about the origin in the complex plane, then the resulting complex number 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

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

The relation $ R $ in the set of integers $ \mathbb{Z} $ is given by $ R = \{(a, b) : b = 2a + 3 \} $. Then the relation $ R $ is:

Which of the following molecule is paramagnetic?

Let $ A $ be a $ 3 \times 3 $ matrix with $ |A| = 7 $. If $ B = 3A $, then the value of \[ \left| \frac{{adj } A}{B} \right| \] is equal to

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

Evaluate the limit: $$ \lim_{x \to 4} \left( \frac{1}{x - 4} - \frac{5}{x^2 - 3x - 4} \right) $$ is equal to

The angle between the lines $$ \frac{x-1}{2} = \frac{2y+3}{4} = \frac{z+5}{-2} \quad \text{and} \quad \frac{x-3}{4} = \frac{y+1}{-4} = \frac{z+3}{-4} $$ is equal to

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 conductivity of 0.02 mol L$^{-1}$ KCl solution is 0.248 S m$^{-1}$. Its molar conductivity is

Lanthanides (Ln) when heated with carbon at 2773K form product with general formula

A body of weight $ W $ is suspended from the ceiling of a room through a chain of weight $ w $. The ceiling pulls the chain by a force.

The catalyst used in the Wacker process is

Evaluate the integral \[ \int x^5 e^{x^3} \,dx. \]

Evaluate the integral \[ \int \frac{e^x}{2^x} dx. \]

The IUPAC name of HOCH$_2$(CH$_2$)$_3$CH$_2$COCH$_3$ is

Evaluate the integral: \[ \int_{0}^{3} |x - 2| \,dx \] is equal to

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

Let \[ g(x) = 4x + 3 \quad {and} \quad f(g(x)) = x^2 + 9. \] Then the value of $ f(7) $ is equal to

The general solution of the differential equation \[ 2y \tan x + \frac{dy}{dx} = 5 \sin x \] is:

Evaluate \[ \frac{\cosec^2(\theta) - 1}{\cosec^2(\theta)} - \frac{\sec^2(\theta) - 1}{\sec^2(\theta)} \]

The value of $ \cosec x + \cot x $ is