Sulphurous acid \(\left( H _{2} SO _{3}\right)\) has \(Ka _{1}=1.7 \times 10^{-2}\) and \(Ka _{2}=6.4 \times 10^{-8} .\) The \(pH\) of \(0.588 \,M\, H _{2} SO _{3}\) is ..... . (Round off to the Nearest Integer)

The product formed in the first step of the reaction of \(\begin{array}{*{20}{c}} {Br\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} \\ {|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} \\ {C{H_3} - C{H_2} - CH - C{H_2} - CH - C{H_3}} \\ {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,|} \\ {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,Br} \end{array}\) with excess \(Mg / Et _{2} O \left( Et = C _{2} H _{5}\right)\) is

The property/properties that show irregularity in first four elements of group-17 is/are :
(A) Covalent radius
(B) Electron affinity
(C) Ionic radius
(D) First ionization energy
Choose the correct answer from the options given below:

The anodic half-cell of lead-acid battery is recharged using electricity of \(0.05\, Faraday\). The amount of \(PbSO_4\) electrolyzed in \(g\) during the process is (Molar mass of \(PbSO_4 = 303\, g\, mol^{-1}\))

Given below are two statements :
Statement I : One mole of propyne reacts with excess of sodium to liberate half a mole of \(\mathrm{H}_2\) gas.
Statement II : Four g of propyne reacts with \(\mathrm{NaNH}_2\) to liberate \(\mathrm{NH}_3\) gas which occupies 224 mL at STP.
In the light of the above statements, choose the most appropriate answer from the options given below:

Consider the following equilibrium, \(\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_2(\mathrm{g}) \rightleftharpoons \mathrm{CH}_3 \mathrm{OH}(\mathrm{g})\) 0.1 mol of CO along with a catalyst is present in a \(2 \mathrm{dm}^3\) flask maintained at 500 K. Hydrogen is introduced into the flask until the pressure is 5 bar and 0.04 mol of \(\mathrm{CH}_3 \mathrm{OH}\) is formed. The \(\mathrm{K}_{\mathrm{p}}^0\) is ______ \(\times 10^{-3}\) (nearest integer).
Given : \(\mathrm{R}=0.08 \mathrm{dm}^3\) bar \(\mathrm{K}^{-1} \mathrm{~mol}^{-1}\)
Assume only methanol is formed as the product and the system follows ideal gas behaviour.

Amongst the following statements, that which was not proposed by Dalton was

A wire of resistance \(R\) is bent to form a square \(ABCD\) as shown in the figure. The effective resistance between \(E\) and \(C\) is ( \(E\) is mid-point of arm \(CD\) )

Choose the correct statement about two circles whose equations are given below \(x^{2}+y^{2}-10 x-10 y+41=0\) \(x^{2}+y^{2}-22 x-10 y+137=0\)

In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to

If \(\mathop {\lim }\limits_{x \to 2} \frac{{\tan \left( {x - 2} \right)\{ {x^2} + (k - 2)x - 2k\} }}{{{x^2} - 4x + 4}} = 5\) , then \(k\) is equal to

Let the ellipse \(E: \frac{x^{2}}{144}+\frac{y^{2}}{169}=1\) and the hyperbola \(H:\frac{x^{2}}{16}-\frac{y^{2}}{\lambda^{2}}=-1\) have the same foci. If e and L respectively denote the eccentricity and the length of the latus rectum of H, then the value of \(24(e+L)\) is:

Two capacitors \(C_1\) and \(C_2\) are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are \(U_1\) and \(U_2\), respectively. Which of the given statements is true?