The conductivity of a weak acid \(HA\) of concentration \(0.001\, \mathrm{~mol}\, \mathrm{~L}^{-1}\) is \(2.0 \times 10^{-5}\, \mathrm{~S} \,\mathrm{~cm}^{-1} .\) If \(\Lambda_{\mathrm{m}}^{\circ}\) \((\mathrm{HA})=190 \,\mathrm{~S} \,\mathrm{~cm}^{2} \mathrm{~mol}^{-1}\), the ionization constant \(\left(\mathrm{K}_{\mathrm{a}}\right)\) of \(\mathrm{HA}\) is equal to \(....\,\times 10^{-6} .\) (Round off to the Nearest Integer)

It has been found that for a chemical reaction with rise in temperature by \(9\, K\) the rate constant gets doubled. Assuming a reaction to be occurring at \(300\, K\), the value of activation energy is found to be \(......\,k\,J \,mol ^{-1}\). [nearest integer] (Given \(\ln 10=2.3, R =8.3 JK ^{-1} mol ^{-1}, \log 2=0.30\) )

The product \((c)\) in the following sequence of reactions has _______\(\pi\) bonds.

Identify correct statement from the following:
A. Propanal and propanone are functional isomers.
B. Ethoxyethane and methoxypropane are metamers.
C. But-2-ene shows optical isomerism.
D. But-1-ene and but-2-ene are functional isomers.
E. Pentane and 2, 2-dimethyl propane are chain isomers.
Choose the correct answer from the options given below:

The statements that are incorrect about the nickel (II) complex of dimethylglyoxime are:
A. It is red in colour
B. It has a high solubility in water at \(pH =9\)
C. The Ni ion has two unpaired d-electrons
D. The \(N - Ni - N\) bond angle is almost close to \(90^{\circ}\)
E. The complex contains four five-membered metallacycles (metal containing rings)
Choose the correct answer from the options given below :

The rate of a certain biochemical reaction at physiological temperature \((T)\) occurs \(10^{6}\) times faster with enzyme than without. The change in the activation energy upon adding enzyme is

At 298 K, the mole percentage of \(N_{2}(g)\) in air is 80%. Water is in equilibrium with air at a pressure of 10 atm. What is the mole fraction of \(N_{2}(g)\) in water at 298 K ? (\(K_{H}\) for \(N_{2}\) is \(6.5 \times 10^{7}\) mm Hg)

Given below are two statements :
Statement (I): Experimentally determined oxygen-oxygen bond lengths in the \(\mathrm{O}_3\) are found to be same and the bond length is greater than that of a \(\mathrm{O}=\mathrm{O}\) (double bond) but less than that of a single \((O-O)\) bond.
Statement (II) : The strong lone pair-lone pair repulsion between oxygen atoms is solely responsible for the fact that the bond length in ozone is smaller than that of a double bond \((\mathrm{O}=\mathrm{O})\) but more than that of a single bond \((\mathrm{O}-\mathrm{O})\).
In the light of the above statements, choose the correct answer from the options given below :

At \(300\,K\), the rms speed of oxygen molecules is \(\sqrt{\frac{\alpha+5}{\alpha}}\) times to that of its average speed in the gas. Then, the value of \(\alpha\) will be (used \(\pi=\frac{22}{7}\) )

In the given figure the blocks \(A , B\) and C weigh \(4 kg, 6 kg\) and 8 kg respectively. The co-efficient of sliding friction between any two surfaces is 0.5 . The force \(\overrightarrow{ F }\) required to slide the block C with constant speed is _________ N . (Used \(g =10 m / s ^2\) )

Let \(f\) be a differentiable function defined on \(\left[0, \frac{\pi}{2}\right]\) such that \(f(x) > 0\) and \(f(x)+\int \limits_0^x f(t) \sqrt{1-\left(\log _e f(t)\right)^2} d t=e, \forall x \in\left[0, \frac{\pi}{2}\right]\) Then \(\left(6 \log _{ e } f \left(\frac{\pi}{6}\right)\right)^2\) is equal to \(.............\)

When a metal surface is illuminated by light of wavelength \(\lambda\), the stopping potential is \(8 \mathrm{~V}\). When the same surface is illuminated by light of wavelength \(3 \lambda\), stopping potential is \(2 \mathrm{~V}\). The threshold wavelength for this surface is _______.

A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is