List of top Questions asked in KEAM

A ring of radius 1.75 m stands vertically. A small sphere of mass 1kg rolls on the inside of this ring without slipping. If it has a velocity of 10m/s at the bottom of the ring,then its velocity when it reaches the top is:(Take g=10 m/s2)

An ideal diatomic gas is made up of molecules that do not vibrate. Its volume compressed by a factor of 32,without any exchange of heat. If the initial and final pressures are P1 and P2,respectively,the ratio P1:P2,is:

For a real number t ,the equation \((1+t)x^2 + (t-1)y^2 + t^2 - 1 = 0\) represents a hyperbola provided 
The set of points of the form(t^2+t+1,t^2-t+1),where t is a real number, represents a/an

Let A be an invertible matrix of size 4x4 with complex entries. If the determinant of adj(A) is 5,then the number of possible value of determinant of A is 

Let f(x)=πcosx+x2.The value of c∈(0,π) where f attains its local maximum/minumum is
A particle at rest starts from the origin with a constant acceleration a that makes an angle 60° with the positive y-axis. If its displacement along y-axis is 10m in time 2s,then the magnitude of a is:
If (2,-6),(5,2) and (-2,2) constitute the vertices of a triangle then the the line joining the origin and its orthocentre is
Let A and B be two independent events such that the odds in favour of A and B are \(1:1 \) and \(3:2\) respectively .Then the probability that only one of the two occurs is 
A Simple pendulum experiment is performed for the value of 'g',the acceleration due to the earth's gravity. The measured value of length of the pendulum is 25 cm with an accuracy of 1 mm and the measured time for 100 oscillations is found to be 100 sec with an accuracy of 1 sec. The percentage uncertainty in the determination of 'g' is:
\(∫_0^1 (5xe^{2x}-tan(π/4)) dx=\)
A six faced fair die is rolled for a large number of times. Then, the mean value of the outcome is 
A magnetic field of (10-4\(\hat{k}\))T exerts a force of (4\(\hat{i}\)-3\(\hat{j}\))x10-12N on a particle having a charge of 10-9 C. The speed of the particle is:

A small bar magnet lies along the x-axis with its Centre fixed at the origin. If the magnetic field at point (5\(\hat{i}\)) m due to this magnet is 4x106 T,then the magnetic field at point (10\(\hat{j}\)) m will be :

If \( α,β,γ\) are the cube roots of \(-2\) ,then the value of \(xα+yβ+zγ/xβ+yγ+zα\) is (\(x,y,z\) are variables)
An unpolarised light is incident on a glass slab such that the reflected ray is totally polarised. If the angle of refraction is 30°,the refractive index of the glass is:
Let \(a,b,c,d \) be an increasing sequence of real numbers,which are in geometric progression .If \(a+d=112\) and \(b+c=48\) ,then the value of \(\dfrac{a+c+8}{b}\) is 

The rod PQ slides along 2 parallel rails as shown in the figure. It has a length of 20 cm and is perpendicular to the 2 rails. It performs simple harmonic motion with amplitude 5 cm and frequency 10 Hz. The magnetic field is 10-4T and is directed perpendicular to the plane of paper. What is the peak induced electro-magnetic force?

Let the probability distribution of random variable X be
X-2-1123
P(X=x)k2k2kk3k

Then, the value of E(X2) is
\(∫\dfrac{1}{cosx(sinx+2cosx)} dx=\)
Let \(f:\R\rightarrow\R\) be defined by
\(f(x) =   \begin{cases} x & \text{if}\ x\leq1 \\  -x+2 & \text{if}\ x\gt1\end{cases}\)
Then \(\int^{2}_{0}f(x)dx=\)
\(∫xlog(1+x^2)dx=\)?
\(\int\frac{2\tan x+3}{\sin^2x+2\cos^2x}dx=\)
\(∫\dfrac{x+5}{x^{2}+1}dx=\)

\(∫sin^2 πx dx =\)?