List of top Questions asked in KEAM

If t$_5$, t$_{10}$ and t$_{25}$ are 5$^{th}$, 10$^{th}$, and 25$^{th}$ terms of an A.P. respectively, then the value of $\begin{vmatrix}t_{5}&t_{10}&t_{25}\\ 5&10&25\\ 1&1&1\end{vmatrix}$ is equal to

Exponential growth in plants can 'be expressed as :

If $\left(1+ax\right)^{n} =1+6x+\frac{27}{2}x^{2}+\cdots+a^{n}\, x^{n}$, then the values of $a$ and $n$ are respectively

If $|x - 3| < 2x + 9$ then $x$ lies in the interval

Let $s_n = \cos \left(\frac{n\pi}{10}\right), n=1,2,3,\ldots$ Then the value of $\frac{s_{1}s_{2}\ldots s_{10}}{s_{1}+s_{2}+\ldots+s_{10}}$ is equal to

If $1.5$ moles of oxygen combines with $Al$ to form $Al_2O_3$, the mass of $Al$ in g [Atomic mass of $Al = 27$] used in the reaction is

Two particles $ A $ and $ B $ are projected with same speed so that the ratio of their maximum heights reached is $ 3:1 $ . If the speed of $ A $ is doubled without altering other parameters, the ratio of the horizontal ranges attained by $ A $ and $ B $ is

If $cos x = -\frac{4}{5}$, where $x\in\left[0, \pi\right]$, then the value of $cos \left(\frac{x}{2}\right)$ is equal to

If $x=sin^{-1}\left(3t-4t^{3}\right)$ and $y=cos^{-1}\left(\sqrt{1-t^{2}}\right)$, then $\frac{dy}{dx}$ is equal to

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 $V(t) = V_0 - 5t + 5t^2$

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

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?

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

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