List of top Questions asked in KEAM

If $log_e\,5$, $log_e(5^x-1)$ and $log_e$ $\left(5^{x}-\frac{11}{5}\right)$ are in $A.P.$, then the values of $x$ are

Two forces in the ratio 1 : 2 act simultaneously on a particle. The resultant of these forces is three times the first force. The angle between them is

Among the following species, identify the pair having same bond order $ C{{N}^{-}},O_{2}^{-},N{{O}^{+}},C{{N}^{+}} $

If $f(x) = \sqrt{2x} + \frac{4}{\sqrt{2x}}$ , then $f'(2) $ is equal to

The variation of speed (in m/s) of an object with time (in seconds) is given by the expression $V(t) = V_0 - 5t + 5t^2$

A man of mass 60 kg is standing on a spring balance inside a lift. lf the lift falls freely downwards, then the reading of the spring balance will be

If $X=\{1,2,3, \ldots, 10\}$ and $A=\{1,2,3,4,5\}$. Then, the number of subsets $B$ of $X$ such that $A-B=\{4\}$ is

A train of length $L$ move with a constant speed $V_t$. A person at the back of the train fires a bullet at time $t = 0$ towards a target which is at a distance of $D$ (at time $t =0$) from the front of the train (on the same direction of motion). Another person at the front of the train fires another bullet at time $t\, = \,T$ towards the same target. Both bullets reach the target at the same time. Assuming the speed of the bullets, $V_b$, are same, the length of the train is

$\int_{0}^{1} \frac{1}{\left(x^{2}+16\right)\left(x^{2}+25\right)} \,dx$ is equal to

In a first order reaction, the concentration of reactant is reduced to $1/8$ of the initial concentration in $75$ minutes at $298 \,K$. What is the half-life period of the reaction in minutes?

Let $a, b, c$ be in $AP$. If $ 0 < a,b,c < 1 ,x=\sum\limits_{n=0}^{\infty }{{{a}^{n}}}, $ $ y=\sum\limits_{n=0}^{\infty }{{{b}^{n}}} $ and $ z=\sum\limits_{n=0}^{\infty }{{{c}^{n}}}, $ then

A system consisting of two masses connected by a massless rod lies along the x-axis. A 0.4 kg mass is at a distance x = 2 m while a 0.6 kg mass is at a distance x = 7 m. The x-coordinate of the center of mass is

The nuclear structure observed by Henkings in 50% of the insect sperm after spermatogenesis was

When a gas is bubbled through water at $298\, K$, a very dilute solution of the gas is obtained. Henry?s law constant for the gas at $298 \,K$ is $100\, kbar$. If the gas exerts a partial pressure of $1\, bar$, the number of millimoles of the gas dissolved in one litre of water is

The partial pressure of nitrogen in air is $0.76\, atm$. and its Henry?s law constant is $7.6 \times 10^4$ atm at 300 K. What is the mole fraction of $N_2$ in the solution obtained when air is bubbled through water at 300 K?

The graph between resistivity and temperature, for a limited range of temperatures, is a straight line for a material like

If $A = \begin{bmatrix}log\,x&-1\\ -log\,x&2\end{bmatrix}$ and if $det (A) = 2$, then the value of $x$ is equal to

The remainder when $2^{2016}$ is divided by $63$, is

Let $ A(1,-1,2) $ and $ B(2,3,-1) $ be two points. If a point $P$ divides $AB$ internally in the ratio $ 2:3, $ then the position vector of $P$ is

The letter ?$D$? in $D$-carbohydrates represents

If $f \left(z\right)=\frac{1-z^{3}}{1-z} ,$ where $z=x+iy$ with $z\ne1,$ then $Re\left\{\overline{f \left(z\right)}\right\}=0$ reduces to

If $ {{(\sqrt{5}+\sqrt{3}i)}^{33}}={{2}^{49}}z, $ then modulus of the complex number $z$ is equal to

A potentiometer wire of length $10\, m$ and resistance $ 20\,\Omega $ is connected in series with a $15\, V$ battery and an external resistance $ 40\,\Omega $ . A secondary cell of emf in the secondary circuit is balanced by $240 \,cm$ long potentiometer wire. The emf $E$ of the cell is

The value of $\frac{1}{i}+\frac{1}{i^{2}}+\frac{1}{i^{3}}+\cdots+\frac{1}{i^{102}}$ is

Two identical thin rings, each of radius $10\,cm$ carrying charges $10\,C$ and $5\,C$ are coaxially placed at a distance $10\,cm$ apart. The work done in moving a charge $q$ from the centre of the first ring to that of the second is