\(2.4\,g\) coal is burnt in a bomb calorimeter in excess of oxygen at \(298\,K\) and \(1\,atm\) pressure.The temperature of the calorimeter rises from \(298\,K\) to \(300\,K\). The enthalpy change during the combustion of coal is \(- x\,kJ\,mol ^{-1}\). The value of \(x\) is . (Nearest Integer)(Given : Heat capacity of bomb calorimeter \(20.0\,kJ\) \(K ^{-1}\). Assume coal to be pure carbon)

Copper reduces \(NO _{3}^{-}\) into \(NO\) and \(NO _{2}\) depending uponthe concentration of \(HNO _{3}\) insolution. (Assuming fixed \(\left[ Cu ^{2+}\right]\) and \(\left. P _{ NO }= P _{ NO _{2}}\right),\) the \(HNO _{3}\) concentration at which the thermodynamic tendency for reduction of \(NO _{3}^{-}\) into \(NO\) and \(NO _{2}\) by copper is same is \(10^{ x }\, M\). The value of \(2 x\) is ...... . \(\left[\right.\) Given \(, E_{C u^{2+} / C u}^{o}=0.34\, V , E _{ NO _{3}^{-} / NO_2 }^{\circ}=0.96\, V\) (Rounded-off to the nearest integer) \(E _{ NO _{3} / NO _{2}}^{\circ}=0.79 \,V\) and at \(298 \,K\)  \(\left.\frac{ RT }{ F }(2.303)=0.059\right]\)

The number of \(f\) electrons in the ground state electronic configuration of \(\mathrm{Np}(\mathrm{Z}=93)\) is ....... .

Number of stereo centers present in linear and cyclic structures of glucose are respectively

Consider the following elements. Which of the following is/are true about \(\mathrm{A}^{\prime}, \mathrm{B}^{\prime}, \mathrm{C}^{\prime}\) and \(\mathrm{D}^{\prime}\) ? \(A\). Order of atomic radius: \(\mathrm{B}^{\prime}<\mathrm{A}^{\prime}<\mathrm{D}^{\prime}<\mathrm{C}^{\prime}\) \(B\). Order of metallic character: \(\mathrm{B}^{\prime}<\mathrm{A}^{\prime}<\mathrm{D}^{\prime}<\mathrm{C}^{\prime}\) \(C\). Size of the element : \(\mathrm{D}^{\prime}<\mathrm{C}^{\prime}<\mathrm{B}^{\prime}<\mathrm{A}^{\prime}\) \(D\). Order of ionic radius : \(\mathrm{B}^{\prime+}<\mathrm{A}^{\prime+}<\mathrm{D}^{\prime+}<\mathrm{C}^{\prime+}\) Choose the correct answer from the options given below :

A \(0.5\) percent solution of potassium chloride was found to freeze at \(-0.24^{\circ} C\). The percentage dissociation of potassium chloride is .... (Nearest integer) (Molal depression constant for water is \(1.80\, K\, kg\,mol ^{-1}\) and molar mass of \(KCl\) is \(74.6 \,g\, mol ^{-1}\) )

The number of tripeptides formed by three different amino acids using each amino acid once is _______.

In the figure, a very large plane sheet of positive charge is shown. \(P _{1}\) and \(P _{2}\) are two points at distance \(l\) and \(2 \,l\) from the charge distribution. If \(\sigma\) is the surface charge density, then the magnitude of electric fields \(E_{1}\) and \(E_{2}\) at \(P _{1}\) and \(P _{2}\) respectively are

Consider the lines \(L _1\) and \(L _2\) given by \(L_1: \frac{ x -1}{2}=\frac{ y -3}{1}=\frac{ z -2}{2}\) \(L _2: \frac{ x -2}{1}=\frac{ y -2}{2}=\frac{ z -3}{3}\) A line \(L _3\) having direction ratios \(1,-1,-2\), intersects \(L _1\) and \(L _2\) at the points \(P\) and \(Q\) respectively. Then the length of line segment \(PQ\) is

The equation of the curve passing through the origin and satisfying the differential equation \(\left( {1 + {x^2}} \right)\,\frac{{dy}}{{dx}} + 2xy = 4{x^2}\) is

Given below are two statements :
Statement (I) : Potassium hydrogen phthalate is a primary standard for standardisation of sodium hydroxide solution.
Statement (II) : In this titration phenolphthalein can be used as indicator.
In the light of the above statements, choose the most appropriate answer from the options given below:

Consider a circular loop that is uniformly charged and has a radius \(\mathrm{a} \sqrt{2}\). Find the position along the positive z -axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin :

A fair die is thrown until \(2\) appears. Then the probability, that \(2\) appears in even number of throws, is