Consider the following reactions (not balanced) \(mathrm{BF}_3+\mathrm{NaH} \xrightarrow{450 \mathrm{~K}} \mathrm{X}+\mathrm{NaF}\) \(mathrm{X}+\mathrm{H}_2 \mathrm{O} \longrightarrow \mathrm{Y}+\mathrm{H}_2 \uparrow\)
The correct statements about X and Y are I. X is an electron deficient molecule II. In X, B-B bond is present III. \(Y\) is a weak tribasic acid IV. Y acts as a Lewis acid

The degree of dissociation of $0.1 \mathrm{N} {\mathrm{CH}}_3\mathrm{COOH}$ is (given ${\mathrm{K}}_a=1\times {10}^{-5}$) approximately _________

Consider the following reaction, \(\mathrm{C}_2 \mathrm{H}_5 \mathrm{Cl}+\mathrm{AgCN} \stackrel{\mathrm{EtOH} / \mathrm{H}_2 \mathrm{O}}{\longrightarrow} \underline{X} \text { (major) }\) Which one of the following statements is true for \(\underline{X} ?\)
(I) It gives propionic acid on hydrolysis
(II) It has an ester functional group
(III) It has a nitrogen linked to ethyl carbon
(IV) It has a cyanide group

\(\mathrm{SiO}_2\) reacts with

The first order decomposition of \(\mathrm{H}_2 \mathrm{O}_2\) in an appropriate medium is characterised by a rate constant of \(0.2303 \mathrm{~min}^{-1}\). What is the time (in min) required to complete \(9 / 10\) fraction of the reaction?

From the following sets of quantum numbers, which set is possible?

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 \(\begin{array}{llllllll}\text { A } & \text { B } & \text { C } & \text { D } & \text { A } & \text { B } & \text { C } & \text { D }\end{array}\)

If \(\sin ^{-1}\left(\frac{12}{x}\right)+\sin ^{-1}\left(\frac{5}{x}\right)=\frac{\pi}{2}\), then \(x=\)

The number of five digit numbers divisible by 5 that can be formed using the numbers \(0,1,2,3,4,5\) without repetition is

Let \(x=\left\{\left[\begin{array}{ll}a & b \ c & d\end{array}\right]: a, b, c, d \in \mathbb{R}\right\}\). If \(f: X \rightarrow \mathbb{R}\) is defined by \(\mathrm{f}(\mathrm{A})=\operatorname{det}(\mathrm{A}) \forall \mathrm{A} \in \mathrm{X}\), then \(\mathrm{f}\) is

Consider a steady flow of oil in a pipeline. The cross-sectional radius of the pipeline decreases gradually as \(r=r_0 e^{-\alpha x}\), where \(\alpha=\frac{1}{3} \mathrm{~m}^{-1}\) and \(x\) is the distance from the pipeline inlet. If \(R_1\) is the Reynold's number for a certain pipeline cross-section at a distance \(x_1\) metre from the inlet and \(R_2\) is for distance \(\left(x_1+3\right)\) metre, then the ratio \(\frac{R_1}{R_2}\) is

A parallel beam of monochromatic light of frequency \(v\) is incident on a surface. The intensity of the beam is \(I\) and area of the surface is \(A\). Find the force exerted by the light of beam on the surface is perfectly reflecting and the light beam is incident at an angle of incidence \(\theta\). (The speed of light is denoted as \(c\).)

If \(R\) is the set of all real numbers and \(f: R-\{2\} \rightarrow R\) is defined by \(f(x)=\frac{2+x}{2-x}\) for \(x \in R-\{2\}\)