For a strong electrolyte, a plot of molar conductivity against (concentration) \({ }^{1 / 2}\) is a straight line, with a negative slope, the correct unit for the slope is _______.

Which one of the following does not have a pyramidal shape?

Consider the following half cell reaction
\(\mathrm{Cr}_2 \mathrm{O}_7^{2-}(\mathrm{aq})+6 \mathrm{e}^{-}+14 \mathrm{H}^{+}(\mathrm{aq})\) \(\rightarrow 2 \mathrm{Cr}^{3+}(\mathrm{aq})+7 \mathrm{H}_2 \mathrm{O}(\mathrm{l})\)
The reaction was conducted with the ratio of \(\frac{\left[\mathrm{Cr}^{3+}\right]^2}{\left[\mathrm{Cr}_2 \mathrm{O}_7^{2-}\right]}=10^{-6}\). The pH value at which the EMF of the half cell will become zero is ________. (nearest integer value)
[Given : standard half cell reduction potential
\(\left.\mathrm{E}_{\mathrm{Cr}_2 \mathrm{O}_7^{2-}, \mathrm{H}^{+} / \mathrm{Cr}^{3+}}^{\mathrm{o}}=1.33 \mathrm{~V}, \frac{2.303 \mathrm{RT}}{\mathrm{~F}}=0.059 \mathrm{~V}\right]\)

One mole of an alkane (x) requires \(8\) mole oxygen for complete combustion. Sum of number of carbon and hydrogen atoms in the alkane (x) is _______.

Regarding the hydrides of group 15 elements \( EH_{3} \) (E = N, P, As, Sb), select the correct statement from the following:
A. The stability of hydrides decreases down the group.
B. The basicity of hydrides decreases down the group.
C. The reducing character increases down the group.
D. The boiling point increases down the group.
Choose the correct answer from the options given below:

The isomer(s) of \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]\) that has/have a \(\mathrm{Cl}-\mathrm{Co}-\mathrm{Cl}\) angle of \(90^{\circ},\) is/are

One mole each of He and \(A(g)\) are taken in a \(10\) L closed flask and heated to \(400\) K to establish the following equilibrium. \(A(g) \rightleftharpoons B(g)\). \(K_c\) for this reaction at \(400\) K is \(4.0\). The partial pressures (in atm) of He and \(B(g)\) are respectively (at equilibrium) (Assume He, \(A(g)\) and \(B(g)\) behave as ideal gases) (Given: \(R = 0.082\) L atm K\(^{-1}\) mol\(^{-1}\))

Given below are two statements: Statement \(I:\) According to Bohr's model of hydrogen atom, the angular momentum of an electron in a given stationary state is quantised. Statement \(II:\) The concept of electron in Bohr's orbit, violates the Heisenberg uncertainty principle. In the light of the above statements, choose the most appropriate answer from the options given below:

Given below are two statements: Statement\(- I\) : Susceptibilities of paramagnetic and ferromagnetic substances increase with decrease in temperature. Statement\(- II\): Diamagnetism is a result of orbital motions of electrons developing magnetic moments opposite to the applied magnetic field. Choose the \(CORRECT\) answer from the options given below : -

The value of \(\frac{e^{-\frac{\pi}{4}}+\int \limits_0^{\frac{\pi}{4}} e^{-x} \tan ^{50} x d x}{\int \limits_0^{\frac{\pi}{4}} e^{-x}\left(\tan ^{49} x+\tan ^{51} x\right) d x}\) is

How many electrons are involved in the following redox reaction? \(C{r_2}O_7^{2 - } + F{e^{2 + }} + {C_2}O_4^{2 - } \to C{r^{3 + }} + F{e^{3 + }} + C{O_2}\) (Unbalanced)

If \(S _{ n }=4+11+21+34+50+\ldots\) to \(n\) terms, then \(\frac{1}{60}\left( S _{29}- S _9\right)\) is equal to \(.......\).

If \(a=\lim _{x \rightarrow 0} \frac{\sqrt{1+\sqrt{1+x^4}}-\sqrt{2}}{x^4}\) and \(b=\lim _{x \rightarrow 0} \) \(\frac{\sin ^2 x}{\sqrt{2}-\sqrt{1+\cos x}}\), then the value of \(a b^3\) is