500 J of energy is transferred as heat to 0.5 mol of Argon gas at 298 K and 1.00 atm. The final temperature and the change in internal energy respectively are:
Given : \(\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\)

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:

On charging the lead storage battery, the oxidation state of lead changes from \(x_1\) to \(y_1\) at the anode and from \(x_2\) to \(y_2\) at the cathode. The values of \(x_1, y_1, x_2, y_2\) are respectively :

Phthalic acid reacts with resorcinol in the presence of concentrated \(H_2SO_4\) to give

While preparing crystals of Mohr's salt, dil \(H _2 SO _4\) is added to a mixture of ferrous sulphate and ammonium sulphate, before dissolving this mixture in water, dil \(H _2 SO _4\) is added here to for _______.

The number of moles of methane required to produce \(11 \mathrm{~g} \mathrm{CO}_2(\mathrm{~g})\) after complete combustion is _______. (Given molar mass of methane in \(\mathrm{g} \mathrm{mol}^{-1}: 16\) )

Which among the above compound/s does/do not form Silver mirror when treated with Tollen's reagent?

The radius of a sphere is measured to be \((7.50 \pm 0.85) \,cm .\) Suppose the percentage error in its volume is \(x\). The value of \(x\), to the nearest integer is .....\(\%\)

The dimensional formula of \(\dfrac{1}{2}\epsilon_0 E^2\) (\(\epsilon_0\) = permittivity of vacuum and \(E\) = electric field) is \(M^a L^b T^c\). The value of \(2a - b + c = \) _______.

The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is

The coordination geometry around the manganese in decacarbonyldimanganese\((0)\) :

For the hyperbola \(H : x ^{2}- y ^{2}=1\) and the ellipse \(E: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1, a>b>0\), let the \((1)\) eccentricity of \(E\) be reciprocal of the eccentricity of \(H\), and \((2)\) the line \(y=\sqrt{\frac{5}{2}} x+K\) be a common tangent of \(E\) and \(H\) Then \(4\left(a^{2}+b^{2}\right)\) is equal to

Let \( \alpha, \beta \in \mathbb{R} \) be such that the function
\( f(x)=\begin{cases}2\alpha(x^{2}-2)+2\beta x&,x<1\\ (\alpha+3)x+(\alpha-\beta)&,x\ge1\end{cases} \)
be differentiable at all \( x \in \mathbb{R} \). Then \( 34(\alpha+\beta) \) is equal to