\(20\,mL\) of calcium hydroxide was consumed when it was reacted with \(10\,mL\) of unknown solution of \(H _2 SO _4\). Also \(20 mL\) standard solution of \(0.5\,M\) \(HCl\) containing \(2\) drops of phenolphthalein was titrated with calcium hydroxide the mixture showed pink colour when burette displayed the value of \(35.5\,mL\) whereas the burette showed \(25.5\,mL\) initially. The concentration of \(H _2 SO _4\) is \(..........M\) (Nearest integer)

The formula of a gaseous hydrocarbon which requires \(6\) times of its own volume of \(O _{2}\) for complete oxidation and produces \(4\) times its own volume of \(CO _{2}\) is \(C _{ x } H _{ y }\). The value of \(y\) is ...... .

An organic compound gives \(0.220 g\) of \(CO _2\) and \(0.126 g\) of \(H _2 O\) on complete combustion. If the \(\%\) of carbon is 24 then the \(\%\) hydrogen is \(......\times 10^{-1} \cdot(\) Nearest integer \()\)

Which one of the following arrangements represents the correct order of solubilities of sparingly soluble salts \(Hg_2Cl_2,\,\,Cr_2(SO_4 )_3,\,\,BaSO_4\) and \(CrCl_3\) respectively ?

An organic compound is estimated through Dumus method and was found to evolve \(6\,mole\) of \(CO_2\,\,4\,moles\) of \(H_2O\) and \(1\,mole\) of nitrogen gas. The formula of the compound is

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:

Match the LIST-I with LIST-II

List-I (Compound)	List-II (Test)
A. Cyclohexanol	I. Hinsberg's reagent test
B. Cyclohexylamine	II. Phthalein dye test
C. Cyclohexanecarbaldehyde	III. Lucas test
D. Phenol	IV. Tollen's test

Choose the correct answer from the options given below:

If the sum of the first \(10\) terms of the series \(\dfrac{1}{1 + 1^4 \times 4} + \dfrac{2}{1 + 2^4 \times 4} + \dfrac{3}{1 + 3^4 \times 4} + \dfrac{4}{1 + 4^4 \times 4} + \ldots\) is \(\dfrac{m}{n}\), \(\gcd(m, n) = 1\), then \(m + n\) is equal to :

A hydrogen atom in ground state is given an energy of \(10.2 \mathrm{eV}\). How many spectral lines will be emitted due to transition of electrons?

A \(20\, Henry\) inductor coil is connected to a \(10\, ohm\) resistance in series as shown in figure. The time at which rate of dissipation of energy (Joule’s heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor, is

In two different experiments, an object of mass \(5\; kg\) moving with a speed of \(25\; ms ^{-1}\) hits two different walls and comes to rest within \((i)\) \(3\) second, \((ii)\) \(5\) seconds, respectively. Choose the correct option out of the following :

Match List-I with List-II

List - I (Complex)		List - II (Primary valency and Secondary valency)
(A)	[Co(en)2Cl2]Cl	(I)	3	6
(B)	[Pt(NH3)2Cl(NO2)]	(II)	3	4
(C)	Hg[Co(SCN)4]	(III)	2	6
(D)	[Mg(EDTA)]2-	(IV)	2	4

Choose the correct answer from the options given below :

A polyatomic ideal gas has \(24\) vibrational modes. What is the value of \(\gamma\) ?