List of top Questions asked in KEAM

If the position vectors of three consecutive vertices, of a parallelogram are $ \vec{i}+\vec{j}+\vec{k}, $ $ \vec{i}+3\vec{j}+5\vec{k} $ and $ 7\vec{i}+9\vec{j}+11\vec{k}, $ then the coordinates of the fourth vertex are

If $ \sqrt{x+iy}=\pm (a+ib), $ then $ \sqrt{-x-iy} $ is equal to

The slope of the normal to the curve $x=t^{2}+3t-8, y=2t^{2}-2t-5$ at the point $(2,-1)$ is

The angle between the straight lines $x-1=\frac{2y+3}{3}=\frac{z+5}{2}$ and $x-3r+2; y=-2r-1; z=2,$ where $r$ is a parameter, is

The $A$.$M$. of $9$ terms is $15$. If one more term is added to this series, then the $A$.$M$. becomes $16$. The value of the added term is

If the mean of the numbers $a, b, 8,5,10$ is $6$ and their variance is $6.8$, then $ab$ is equal to

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?

If the mean of six numbers is $41$, then the sum of these numbers is

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

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

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 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 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 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

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

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

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 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 $(g = 10 \; ms^{-2})$

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

Ampere?s circuital law can be derived from

According to Kepler's law of planetary motion if $ T $ represents time period and $ r $ is orbital radius, then for two planets these are related as :