A solution of aluminium chloride is electrolysed for 30 minutes using a current of 2 A . The amount of the aluminium deposited at the cathode is _______.
[Given : molar mass of aluminium and chlorine are \(27 \mathrm{~g} \mathrm{~mol}^{-1}\) and \(35.5 \mathrm{~g} \mathrm{~mol}^{-1}\) respectively. Faraday constant \(\left.=96500 \mathrm{C} \mathrm{mol}^{-1}\right]\)

Given below are two statements : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\): Assertion \(A\): In the photoelectric effect, the electrons are ejected from the metal surface as soon as the beam of light of frequency greater than threshold frequency strikes the surface. Reason \(R\) : When the photon of any energy strikes an electron in the atom, transfer of energy from the photon to the electron takes place. In the light of the above statements, choose the most appropriate answer from the options given below :

Given below are two statements: Statement \(I:\) Hyperconjugation is a permanent effect. Statement \(II:\) Hyper conjugation in ethyl cation \(\left(\mathrm{CH}_{3}-\mathrm{C^+H}_{2}\right)\) involves the over lapping of \(\mathrm{C}_{\mathrm{sp}^{2}}-\mathrm{H}_{1 \mathrm{~s}}\) bond with empty \(2 p\) orbital of other carbon. Choose the correct option:

In the above conversion of compound \(( X )\) to product \((Y)\), the sequence of reagents to be used will be:

For the reaction, \( N_{2}O_{4}\rightleftharpoons 2NO_{2}, \) graph is plotted as shown below. Identify correct statements.
A. Standard free energy change for the reaction is -5.40 kJ mol⁻¹.
B. As \( \Delta G^{\ominus} \) in graph is positive, \( N_{2}O_{4} \) will not dissociate into \( NO_{2} \) at all.
C. Reverse reaction will go to completion.
D. When 1 mole of \( N_{2}O_{4} \) changes into equilibrium mixture, value of \( \Delta G^{\ominus}=-0.84 \, kJ \, mol^{-1} \).
E. When 2 mole of \( NO_{2} \) changes into equilibrium mixture, \( \Delta G^{\ominus} \) for equilibrium mixture is -6.24 kJ mol⁻¹.

Choose the correct answer from the options given below:

In the given reactions identify the reagent \(A\) and reagent \(B\).

A gaseous mixture of two substances \(A\) and \(B\), under a total pressure of \(0.8\,atm\) is in equilibrium with an ideal liquid solution. The mole fraction of substance \(A\) is \(0.5\) in the vapour phase and \(0.2\) in the liquid phase. The vapour pressure of pure liquid \(A\) \(......\) is atm. (Nearest integer)

Let \(\alpha\) be a solution of \(x^2+x+1=0\), and for some \(a\) and \(b\) in
\(\mathbb{R},\left[\begin{array}{lll}4 & \mathrm{a} & \mathrm{b}\end{array}\right]\left[\begin{array}{ccc}1 & 16 & 13 \\ -1 & -1 & 2 \\ -2 & -14 & -8\end{array}\right]=\left[\begin{array}{ccc}0 & 0 & 0\end{array}\right]\). If \(\frac{4}{\alpha^4}\) \(+\frac{\mathrm{m}}{\alpha^{\mathrm{a}}}+\frac{\mathrm{n}}{\alpha^{\mathrm{b}}}=3\), then \(\mathrm{m}+\mathrm{n}\) is equal to

Let \(\quad S=109+\frac{108}{5}+\frac{107}{5^2}+\ldots \ldots . .+\frac{2}{5^{107}}+\frac{1}{5^{108}}\). Then the value of \(\left(16 S -(25)^{-34}\right)\) is equal to \(............\).

Given below are two statements :
Statement I : '\( C-Cl \)' bond is stronger in \( CH_{2}=CH-Cl \) than \( CH_{3}-CH_{2}-Cl \)
Statement II : The given optically active molecule

on hydrolysis gives a solution that can rotate the plane polarized light.
In the light of the above statements, choose the correct answer from the options given below

Which of the following sets includes all the species that will change the orange colour of \(K_2Cr_2O_7\) in acidic medium?

Three identical spheres of mass m , are placed at the vertices of an equilateral triangle of length a. When released, they interact only through gravitational force and collide after a time \(\mathrm{T}=4\) seconds. If the sides of the triangle are increased to length 2 a and also the masses of the spheres are made 2 m , then they will collide after _____ seconds.

Let \(\alpha, \beta(\alpha \neq \beta)\) be the values of m , for which the equations \(x+y+z=1 ; x+2 y+4 z=\mathrm{m}\) and \(x+4 y+10 z=m^2\) have infinitely many solutions. Then the value of \(\sum_{n=1}^{10}\left(n^\alpha+n^\beta\right)\) is equal to :