List of top Questions asked in KEAM

In the decomposition reaction AB\(_5\)(g)\(\rightleftharpoons\) AB\(_3\)(g) + B\(_2\)(g), at equilibrium in a 10-litre closed vessel at 227 C, 2 moles of AB\(_3\), 5 moles of B\(_2\) and 4 moles of AB\(_5\) are present. The equilibrium constant K\(_c\) for the formation of AB\(_5\)(g) is

Three numbers $x, y$ and $z $ are in arithmetic progression. If $x + y + z = - 3$ and $xyz= 8$, then $x^2 + y^2 + z^2$ is equal to
In a double slit experiment, the screen is placed at a distance of $1.25 \,m$ from the slits. When the apparatus is immersed in water $ ({{\mu }_{w}}=4/3) $ , the angular width of a fringe is found to be $ {{0.2}^{o}} $ . When the experiment is performed in air with same set up, the angular width of the fringe is
The decomposition of ${N_2O_5}$ in ${CCl_4}$ at 318 K is studied by monitoring the concentration of ${N2O5}$ in the solution. Initially the concentration of ${N2O5}$ is 2.4 mol $L^{-1}$ and after 200 minutes, it is reduced to 2.00 mol $L^{-1}$. What is the rate of production of $NO_2$ during this period in $mol\, L^{-1} min^{-1}$ ?
The output of the circuit is
Let $S_{n}$ denote the sum of first $n$ terms of an $A.P$. and $S_{2n} = 3S_{n}$. If $S_{3n} =k S_{n}$, then the value of $k$ is equal to
Let $ z=\frac{11-3i}{1+i}. $ If a is a real number such that $ z-i\alpha $ is real, then the value of $ \alpha $ is
The coefficient of $x$ in the expansion of $ (14+x)(1+2x)(1+3x)....(1+100x) $ is
A copper wire with a cross-section area of $2 \times 10^{-6} \, m^2$ has a free electron density equal to $5 \times 10^{22} /cm^{-3}$. If this wire carries a current of $16\,A$, the drift velocity of the electron is
The $pK_a$ of a weak acid $HA$ and $pK_b$ of a weak base $BOH$ are $4.60$ and $4.80$ respectively. The $pH$ of $0.1\, M$ solution of the salt, $BA$, formed from the acid $HA$ and base $BOH$ is
Which of the following compounds is most basic?
A metal conductor of length $1 \,m$ rotates vertically about one of its ends with an angular velocity $5 \,rad\, s^{-1}$. If the horizontal component of earths magnetic field is $0.2 \times10^{-4}\,T$, then the emf developed between the ends of the conductor is
An aqueous solution containing $3\, g$ of a solute of molar mass $111.6 \,g\, mol ^{-1}$ in a certain mass of water freezes at $-0.125^{\circ} C$. The mass of water in grams present in the solution is $\left(K_{f}=1.86\, Kkg \,mol ^{-1}\right)$
For the reaction, $C_{(s)}+CO_{2(g)} \rightarrow 2CO_{(g)},$ $K_p = 63$ atm at $1000\, K$. If at equilibrium $P_{CO} = 10\, P{co_2},$ than the total pressure of the gases at equilibrium is
The statement $p \rightarrow \left(\sim q\right)$ is equivalent to
$ \int{\frac{dx}{\sqrt{1-{{e}^{2x}}}}} $ is equal to
If $z^2 + z + 1 = 0$ where $z$ is a complex number, then the value of $\left(z+ \frac{1}{z}\right)^{2} + \left(z^{2} + \frac{1}{z^{2}}\right)^{2} + \left(z^{3} + \frac{1}{z^{3}}\right)^{2} $ equals
The boolean expression corresponding to the combinational circuit is
The coefficient of $x^2$ in the expansion of the determinant $\begin{vmatrix}x^{2}&x^{3}+1&x^{5}+2\\ x^{2}+3&x^{3}+x&x^{3}+x^{4}\\ x+4&x^{3}+x^{5}&2^{3}\end{vmatrix}$ is
The derivative of $ {{\sin }^{-1}}(2x\sqrt{1-{{x}^{2}}}) $ with respect to $ {{\sin }^{-1}}(3x-4{{x}^{3}}) $ is
If $\int \frac{f\left(x\right)}{log\,cos\,x}dx=-log\left(log\,cos\,x\right)+C$, then $f\left(x\right)$ is equal to
If the vectors $ \overrightarrow{a}=2\hat{i}+\hat{j}+4\hat{k},\overrightarrow{b}=4\hat{i}-2\hat{j}+3\hat{k} $ and $ \overrightarrow{c}=2\hat{i}-3\hat{j}-\lambda \hat{k} $ are coplanar, then the value of $\lambda$ is equal to
The roots of the equation $\begin{vmatrix}x-1&1&1\\ 1&x-1&1\\ 1&1&x-1\end{vmatrix} = 0 $ are
If $\left|z-\frac{3}{2}\right|=2$ , then the greatest value of $\left|z\right|$ is
$\displaystyle \lim_{x \to 2} $ $\frac{x^{100}-2^{100}}{x^{77}-2^{77}}$ is equal to