Given below are two statements :
Statement (I) : For a given shell, the total number of allowed orbitals is given by \(\mathrm{n}^2\).
Statement (II) : For any subshell, the spatial orientation of the orbitals is given by \(-l\) to \(+l\) values including zero.
In the light of the above statements, choose the correct answer from the options given below :

The hybridization of \(P\) exhibited in \(P F_{5}\) is \(s p^{x} d^{y}\). The value of \(y\) is \(...\)

Given below are two statements: one is labelled as Assertion \((A)\) and the other is labelled as Reason \((R)\) : Assertion \((A)\) : \(\mathrm{S}_{\mathrm{N}} 2\) reaction of \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_2 \mathrm{Br}\) occurs more readily than the \(\mathrm{S}_{\mathrm{N}} 2\) reaction of \(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{Br}\). Reason \((R)\) : The partially bonded unhybridized p-orbital that develops in the trigonal bipyramidal transition state is stabilized by conjugation with the phenyl ring. In the light of the above statements, choose the most appropriate answer from the options given below:

Observation of "Rhumann 's purple " is a confirmatory test for the presence of

Consider the following first order gas phase reaction at constant temperature \(\mathrm{A}(\mathrm{g}) \rightarrow 2 \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})\) If the total pressure of the gases is found to be \(200\) torr after \(23 \mathrm{sec}\). and \(300\) torr upon the complete decomposition of \(\mathrm{A}\) after a very long time, then the rate constant of the given reaction is _______ \(\times 10^{-2} \mathrm{~s}^{-1}\) (nearest integer) [Given : \(\log _{10}(2)=0.301\) ]

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 given reaction can occur in the presence of: \((1)\) Bromine water        \((2)\) \(\mathrm{Br}_{2}\) in \(\mathrm{CS}_{2}, 273 \mathrm{~K}\)       \((3)\) \(\mathrm{Br}_{2} / \mathrm{FeBr}_{3}\)    \((4)\) \(\mathrm{Br}_{2}\) in \(\mathrm{CHCl}_{3}, 273 \,\mathrm{~K}\) Choose the correct answer from the options given below:

The energy released when \(\dfrac{7}{17.13}\) kg of \(^{7}_{3}\text{Li}\) is converted into \(^{4}_{2}\text{He}\) by proton bombardment is \(\alpha \times 10^{32}\) eV. The value of \(\alpha\) is _______. (Nearest integer) (Mass of \(^{7}_{3}\text{Li} = 7.0183\) u, mass of \(^{4}_{2}\text{He} = 4.004\) u, mass of proton \(= 1.008\) u and \(1\) u \(= 931\) MeV/c\(^2\) and Avogadro number \(= 6.0 \times 10^{23}\))

The freezing point of benzene decreases by \(0.45^o C\) when \(0.2\,g\) of acetic acid is added to \(20\, g\) of benzene. If acetic acid associates to form a dimer in benzene, percentage association of acetic acid in benzene will be .......... \(\%\) \((K_f \) for benzene \(= 5.12 \,K\, kg\, mol^{-1})\)

Let \(A=\left[\begin{array}{lll}x & y & z \\ y & z & x \\ z & x & y\end{array}\right], \quad\) where \(x, y\) and \(z\) are real numbers such that \(x + y + z >0\) and \(xyz =2\) If \(A ^{2}= I _{3},\) then the value of \(x ^{3}+ y ^{3}+ z ^{3}\) is ............

A \(\rightarrow\) products (First order reaction).
Three sets of experiment were performed for a reaction under similar experimental conditions.
Run \(1 \Rightarrow 100 mL\) of 10 M solution of reactant A
Run \(2 \Rightarrow 200 mL\) of 10 M solution of reactant A
Run \(3 \Rightarrow 100 mL\) of 10 M solution of reactant A+ 100 mL of \(H _2 O\) added.
The correct variation of rate of reaction is:

The velocity of the bullet becomes one third after it penetrates \(4\,cm\) in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at \((4+x)\,cm\) inside the block. The value of \(x\) is\(.....\)

Let \(\vec a\, = \,\hat i\, + \,2\hat j\, + 4\hat k\,,\,\vec b\, = \,\hat i\, + \,\lambda \hat j\, + 4\hat k\) and \(\vec c\, = \,2\hat i\, + \,4\hat j\, + ({\lambda ^2} - 1)\hat k\) be coplanar vectors. Then the non -zero vector \(\vec a\times \vec c\) is