List of top Questions asked in KEAM

If $ y={{\tan }^{-1}}\left( \frac{\cos x}{1+\sin x} \right), $ then $ \frac{dy}{dx} $ is equal to

Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?

The value of $\displaystyle \lim_{y \to \infty} \left[y \, sin \left(\frac{1}{y}\right) - \frac{1}{y} \right]$ is equal to

If $ n=5, $ then $ {{{{(}^{n}}{{C}_{0}})}^{2}}+{{{{(}^{n}}{{C}_{1}})}^{2}}+{{{{(}^{n}}{{C}_{2}})}^{2}}+..... $ $ +{{{{(}^{n}}{{C}_{5}})}^{2}} $ is equal to

The number of words that can be formed by using all the letters of the word $PROBLEM$ only one is

A concave lens of focal length 20 cm produces an image half the size of the real object. The distance of the real object is

A body of mass $20\, g$ connected to spring of constant $k$ executes simple harmonic motion with a frequency of $\bigg(\frac{5}{\pi}\bigg)Hz$. The value of spring constant is

A monochromatic source of wavelength $60\, nm$ was used in Young?s double slit experiment to produce interference pattern. $I_1$ is the intensity of light at a point on the screen where the path difference is $150\, nm.$ The intensity of light at a point where the path difference is $200\, nm$ is given by

From a circular ring of mass $M$ and radius $R$, an arc corresponding to a $ {{90}^{o}} $ sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is $k$ times $ M{{R}^{2}} $ . Then the value of $k$ is

A $50\, Hz \,AC$ current of peak value $2\, A$ flows through one of the pair of coils. If the mutual inductance between the pair of coils is $150\, mH$, then the peak value of voltage induced in the second coil is

A particle of mass $m$ and charge $q$ is placed at rest in uniform electric field $E$ and then released. The kinetic energy attained by the particle after moving a distance $y$ is

A comet orbits around Sun in an elliptical orbit. Which of the following quantities remains constant during the course of its motion?

A force F is applied on a square plate of side L. If percentage error in determination of L is 2% and that in F is 4%, permissible error in pressure is

A body is thrown up with a speed $u$, at an angle of projection $\theta$. If the speed of the projectile becomes $\frac{u}{\sqrt{2}}$ on reaching the maximum height, then the maximum vertical height attained by the projectile is

A liquid is filled upto a height of $20\, cm$ in a cylindrical vessel. The speed of liquid coming out of a small hole at the bottom of the vessel is $(g = 10 \; ms^{-2})$

An engine of power $58.8\, kW$ pulls a train of mass $2 \times 10^{5}\, kg$ with a velocity of $36\, kmh ^{-1}$. The coefficient of friction is

If 10% of a radioactive material decays in 10 days the percentage of the material that decays in 20 days is

A plane electromagnetic wave travelling along the $ X- $ direction has a wavelength of $ 3 \,mm $ . The variation in the electric field occurs in the $ Y- $ direction with an amplitude $ 66\,V{{m}^{-1}} $ . The equations for the electric and magnetic fields as a function of $ x $ and $t$ are respectively.

A ball dropped from a height of $2\,m$ rebounds to a height of $1.5\,m$ after hitting the ground. Then the percentage of energy lost is

Choose the wrong statement.

A solid sphere and a hollow sphere, both of the same size and same mass roll down an inclined plane .Then

Which one of the following pairs consists of only paramagnetic species?

Which one of the following has the smallest bond angle ?

Which of the following is paramagnetic with bond order $ 0.5 $ ?