Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) A mixture contains benzoic acid and napthalene. The pure benzoic acid can be separated out by the use of benzene. Reason \(R:\) Benzoic acid is soluble in hot water. In the light of the above statements, choose the most appropriate answer from the options given below.

The complex that can show optical activity is:

The reaction of \(H _{2} O _{2}\) with potassium permanganate in acidic medium leads to the formation of mainly.

Consider the following reaction occurring in the blast furnace:
\(\mathrm{Fe}_3 \mathrm{O}_{4(\mathrm{~s})}+4 \mathrm{CO}_{(\mathrm{g})} \rightarrow 3 \mathrm{Fe}_{(\mathrm{l})}+4 \mathrm{CO}_{2(\mathrm{~g})}\)
' \(x\) ' kg of iron is produced when \(2.32 \times 10^3 \mathrm{~kg} \mathrm{Fe}_3 \mathrm{O}_4\) and \(2.8 \times 10^2 \mathrm{~kg} \mathrm{CO}\) are brought together in the furnace. The value of ' \(x\) ' is _____. (nearest integer)
Given:
molar mass of \(\mathrm{Fe}_3 \mathrm{O}_4=232 \mathrm{~g} \mathrm{~mol}^{-1}\)
molar mass of \(\mathrm{CO}=28 \mathrm{~g} \mathrm{~mol}^{-1}\)
molar mass of \(\left.\mathrm{Fe}=56 \mathrm{~g} \mathrm{~mol}^{-1}\right\}\)

The theory that can completely/properly explain the nature of bonding in \([Ni(CO)_4]\) is

The correct sequence of reagents used in the preparation of \(4 -\)bromo\(-2-\)nitroethyl benzene from benzene is :

Given below are two statements:
Statement I: Benzene is nitrated to give nitrobenzene, which on further treatment with \(CH_{3}COCl / AlCl_{3}\) will give

Statement II: \(NO_{2}\) group is a m-directing, and deactivating group.
In the light of the above statements, choose the most appropriate answer:

Consider the matrices \(A = \begin{bmatrix} 2 & -2 \\ 4 & -2 \end{bmatrix}\) and \(B = \begin{bmatrix} 3 & 9 \\ 1 & 3 \end{bmatrix}\). If matrices P and Q are such that \(PA = B\) and \(AQ = B\), then the absolute value of the sum of the diagonal elements of \(2(P + Q)\) is _______.

Due to cold weather a \(1\, {m}\) water pipe of cross-sectional area \(1\, {cm}^{2}\) is filled with ice at \(-10^{\circ} {C}\). Resistive heating is used to melt the ice. Current of \(0.5\, {A}\) is passed through \(4\, {k} \Omega\) resistance. Assuming that all the heat produced is used for melting, what is the minimum time required ? (In \({s}\)) (Given latent heat of fusion for water/ice \(=3.33 \times 10^{5}\, {J} {kg}^{-1}\), specific heat of ice \(=2 \times 10^{3}\, {J}\) \({kg}^{-1}\) and density of ice \(=10^{3}\, {kg} / {m}^{3}\)

The octahedral complex of a metal ion \(M^{3+}\) with four monodentate ligands \(L_1, L_2, L_3\) and \(L_4\) absorb wave lengths in the region of red, green, yellow and blue, respectively. The increasing order of ligand strength of the four ligands is :

A metallic rod of length ' \(L\) ' is rotated with an angular speed of ' \(\omega\) ' normal to a uniform magnetic field ' \(B\) ' about an axis passing through one end of rod as shown in figure. The induced emf will be :

If \(\int \frac{2 x^2+5 x+9}{\sqrt{x^2+x+1}} \mathrm{~d} x=x \sqrt{x^2+x+1}+\alpha \sqrt{x^2+x+1}+\beta \log _e\left|x+\frac{1}{2}+\sqrt{x^2+x+1}\right|+\mathrm{C}\), where \(C\) is the constant of integration, then \(\alpha+2 \beta\) is equal to \(\qquad\) _______.

The sum of all the roots of the equation \(\left|x^2-8 x+15\right|-2 x+7=0\) is: