List of top Questions asked in KEAM

In the diagram given above, some of the algae have been labelled as a, b, c, d and e. These algae are respectively identified as :

The correct equation for the degree of association $'\alpha'$ of an associating solute, $'n'$ molecules of which undergoes association in solution, is

Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals

If $n\left(A\right)=43, n\left(B\right)=51\quad and \quad n\left(A\cup B\right)=75, then\quad n\left(A-B\right)\cup\left(B-A\right)$ is equal to

The increasing order of electronegativity of the three elements O,F and Na is

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

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