The order of decreasing reactivity towards an electrophilic reagent, for the following compounds, is

The \(\Delta_f \mathrm{H}^{\circ}\) of \(\mathrm{AO}(\mathrm{s}), \mathrm{BO}_2(\mathrm{~g})\) and \(\mathrm{ABO}_3(\mathrm{~s})\) is \(-635, x\) and \(-1210 \mathrm{~kJ} \mathrm{~mol}^{-1}\) respectively. \(\mathrm{ABO}_3(\mathrm{~s}) \rightarrow \mathrm{AO}(\mathrm{s})+\mathrm{BO}_2(\mathrm{~g}) ; \Delta_r \mathrm{H}^{\circ}=175 \mathrm{~kJ} \mathrm{~mol}^{-1}\).
What is the value of \(x\) (in \(\left.\mathrm{kJ} \mathrm{mol}^{-1}\right)\) ?

Which of the following statement is correct?

The reagent used in the Wolff-Kishner reduction is

Match the following methods for treating hardness of water with their corresponding reagents used. \begin{array}{|c|c|c|} \hline List-I & & List II \ \hline A. Treatment with washing soda & \mathrm{I}. & \mathrm{Ca}(\mathrm{OH})_2 \ \hline B. Calgon's method & II. & \mathrm{Na}_2 \mathrm{CO}_3 \ \hline C. Clark's method & III & \mathrm{NaAlSiO}_4 \ \hline D. Zeolite/permutit process & IV & \mathrm{Na}_6 \mathrm{P}_6 \mathrm{O}_{18} \ \hline \end{array} The correct match is \(\begin{array}{llllllll}\text { A } & \text { B } & \text { C } & \text { D } & \text { A } & \text { B } & \text { C } & \text { D }\end{array}\)

The most probable speed of \(\mathrm{O}_2\) molecules at \(T(\mathrm{~K})\) is

Iron crystalizes in $\mathrm{FCC}$ with an edge length of $400\mathrm{pm}$. If it contains $0.1\%$ Schottky defects, calculate its approximate density [$\mathrm{AW}$ of $\mathrm{Fe}=56 \mathrm{g}/\mathrm{mol}$]

In the meter bridge experiment, the length \(A B\) of the wire is \(1 \mathrm{~m}\). The resistors \(X\) and \(Y\) have values \(5 \Omega\) and \(2 \Omega\) respectively. When a shunt resistance \(S\) is connected to \(X\), the balancing point is found to be \(0.625 \mathrm{~m}\) from \(A\). Then, the resistance of the shunt is

Find the voltage \(V_2\) across \(R_2\) for the given circuit

If \(x_n=\cos \frac{\pi}{2^n}+i \sin \frac{\pi}{2^n}\), then \(\prod_{n=1}^{\infty} x_n\) is equal to

\(\begin{aligned} & \text { If } z=e^{i \theta} \text { and } \frac{3 \cos 3 \theta+2 \cos 2 \theta+5 \cos 5 \theta}{3 \sin 3 \theta+2 \sin 2 \theta+5 \sin 5 \theta} \ & =\frac{i \sum_{r=0}^{10} a_r z^r}{\sum_{r=0}^{10} b_r z^r} \text { then } \frac{\left(\sum_{r=0}^{10} a_r+\sum_{r=0}^{10} b_r\right)}{10}=\end{aligned}\)

Let \(\bar{a}\) and \(\bar{b}\) be two vectors such that \(|\bar{a}|=|\bar{b}|\) and \(|\bar{a}+2 \bar{b}|=|2 \bar{a}-\bar{b}|\). If \(\bar{c}\) is a vector parallel to \(\bar{a}\) then the angle between \(\bar{b}\) and \(\bar{c}\) is

If \(\alpha, \beta\) are the roots of quadratic equation \(x^2+b x+c=0\) such that \(\alpha^2+\beta^2=5\) and \(\alpha^3+\beta^3=9\), then \(b+c=\)