The internal energy change (in \(J\) ) when \(90\, g\) of water undergoes complete evaporation at \(100^{\circ} C\) is........ (Given: \(\Delta H _{\text {vap }}\) for water at \(373\, K =41\, kJ / mol\), \(\left. R =8.314\, JK ^{-1} mol ^{-1}\right)\)

Elevation in boiling point for \(1.5\) molal solution of glucose in water is \(4 \,K\). The depression in freezing point for \(4.5\) molal solution of glucose in water is \(4\, K\) The ratio of molal elevation constant to molal depression constant \(\left( K _{ b } / K _{ f }\right)\) is \(....\)

Following figure shows dependence of molar conductance of two electrolytes on concentration. \(\Lambda \stackrel{0}{ m }\) is the limiting molar conductivity.The number of Incorrect statement(s) from the following is \(...........\) \((A)\) \(\Lambda \stackrel{0}{ m }\) for electrolyte \(A\) is obtained by extrapolation \((B)\) For electrolyte B, vx \(\Lambda m\) vs \(\sqrt{ c }\) graph is a straight line with intercept equal to \(\Lambda \stackrel{0}{ m }\) \((C)\) At infinite dilution, the value of degree of dissociation approach zero for electrolyte \(B\). \((D)\) \(\Lambda \stackrel{0}{ m }\) for any electrolyte \(A\) or \(B\) can be calculated using \(\lambda^{\circ}\) for individual ions.

\(2.8 \times 10^{-3} \mathrm{~mol}\) of \(\mathrm{CO}_2\) is left after removing \(10^{21}\) molecules from its ' \(x\) ' mg sample. The mass of \(\mathrm{CO}_2\) taken initially is
Given: \(\mathrm{N}_{\mathrm{A}}=6.02 \times 10^{23} \mathrm{~mol}^{-1}\)

Which one of the following metals forms interstitial hydride easily ?

Half life of zero order reaction \(\mathrm{A} \rightarrow\) product is 1 hour, when initial concentration of reaction is \(2.0 \mathrm{~mol} \mathrm{~L} \mathrm{~L}^{-1}\). The time required to decrease concentration of A from 0.50 to \(0.25 \mathrm{~mol} \mathrm{~L}^{-1}\) is _______.

The equilibrium \(\mathrm{Cr}_2 \mathrm{O}_7^{2-} \rightleftharpoons 2 \mathrm{CrO}_4^{2-}\) is shifted to the right in _______.

In a group of 3 girls and 4 boys, there are two boys \(B_1\) and \(B_2\). The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but \(B_1\) and \(B_2\) are not adjacent to each other, is :

Let \(L_{1}\) be a tangent to the parabola \(y ^{2}=4( x +1)\) and \(L _{2}\) be a tangent to the parabola \(y ^{2}=8( x +2)\) such that \(L _{1}\) and \(L _{2}\) intersect at right angles. Then \(L_{1}\) and \(L_{2}\) meet on the straight line

The sum of all local minimum values of the function is
\(
f(x)=\left\{\begin{array}{lr}
1-2 x, & x \lt -1 \\
\frac{1}{3}(7+2|x|), & -1 \leq x \leq 2 \\
\frac{11}{18}(x-4)(x-5), & x\gt2
\end{array}\right.
\)

For the equilibrium \(A\left( g \right) \rightleftharpoons B\left( g \right)\), \(\Delta H\) is \(-40\, k\,J/mol\). If the ratio of the activation energies of the forward \((E_f)\) and reverse \((E_b)\) reactions is \(\frac{2}{3}\) then

The relation between time ' \(t\) ' and distance ' \(x\) ' is \(t=\) \(\alpha x^2+\beta x\), where \(\alpha\) and \(\beta\) are constants. The relation between acceleration \((a)\) and velocity \((v)\) is _______.

\(\tan \left(2 \tan ^{-1} \frac{1}{5}+\sec ^{-1} \frac{\sqrt{5}}{2}+2 \tan ^{-1} \frac{1}{8}\right)\) is equal to.