When equal volume of \(1 \mathrm{M}\) \(\mathrm{HCl}\) and \(1 \mathrm{M}\) \(\mathrm{H}_2 \mathrm{SO}_4\) are separately neutralised by excess volume of \(1 \mathrm{M}\) \(\mathrm{NaOH}\) solution. \(\mathrm{X}\) and \(\mathrm{y}\) \(\mathrm{J}\) of heat is liberated respectively. The value of \(y / x \) is _______.

Match the LIST-I with LIST-II

No.	LIST-I (Reagent)	No.	LIST-II (Functional Group detected)
A.	Sodium bicarbonate solution	I.	double bond/unsaturation
B.	Neutral ferric chloride	II.	carboxylic acid
C.	Ceric ammonium nitrate	III.	phenolic - OH
D.	Alkaline KMnO	IV.	alcoholic - OH

Choose the correct answer from the options given below :

Consider the oxides of group \(14\) elements \(\mathrm{SiO}_2, \mathrm{GeO}_2, \mathrm{SnO}_2, \mathrm{PbO}_2, \mathrm{CO}\) and \(\mathrm{GeO}\). The amphoteric oxides are _______.

Some \(\mathrm{CO}_2\) gas was kept in a sealed container at a pressure of 1 atm and at 273 K . This entire amount of \(\mathrm{CO}_2\) gas was later passed through an aqueous solution of \(\mathrm{Ca}(\mathrm{OH})_2\). The excess unreacted \(\mathrm{Ca}(\mathrm{OH})_2\) was later neutralized with 0.1 M of 40 mL HCl . If the volume of the sealed container of \(\mathrm{CO}_2\) was \(x\), then \(x\) is ________ \(\mathrm{cm}^3\) (nearest integer).
[Given : The entire amount of \(\mathrm{CO}_2(\mathrm{~g})\) reacted with exactly half the initial amount of \(\mathrm{Ca}(\mathrm{OH})_2\) present in the aqueous solution.]

One mole of the octahedral complex compound \(\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{Cl}_3\) gives 3 moles of ions on dissolution in water. One mole of the same complex reacts with excess of \(\mathrm{AgNO}_3\) solution to yield two moles of \(\mathrm{AgCl}_{(\mathrm{s})}\). The structure of the complex is which?

The complete combustion of \(0.492\, g\) of an organic compound containing \('C', 'H'\) and \('O'\) gives \(0.793\, g\) of \(CO _{2}\) and \(0.442\,g\) of \(H _{2} O\). The percentage of oxygen composition in the organic compound is .... (nearest integer)

The cell potential for the given cell at \(298 \,K\) \(Pt\) \(\mid H _{2}\) \((g,1 \,bar)\) \(\left| H ^{+}( aq ) \| Cu ^{2+}( aq )\right| Cu ( s )\) is \(0.31\, V\). The \(pH\) of the acidic solution is found to be \(3 ,\) whereas the concentration of \(Cu ^{2+}\) is \(10^{- x } \,M\). The value of \(x\) is \(.....\) (Given: \(E _{ Cu ^{2+} / Cu }^{\ominus}=0.34 \,V\) and \(\frac{2.303 RT }{ F }=0.06\, V\) )

There are three bags \(X\), \(Y\) and \(Z\). Bag \(X\) contains \(5\) one-rupee coins and \(4\) five-rupee coins; Bag \(\mathrm{Y}\) contains \(4\) one-rupee coins and \(5\) five-rupee coins and Bag \(\mathrm{Z}\) contains \(3\) one-rupee coins and \(6\) five-rupee coins. A bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability, that it came from bag \(\mathrm{Y}\), is :

Let the Mean and Variance of five observations \(x_1=1, x_2=3, x_3=a, x_4=7\) and \(x_5=b, a \gt b\), be 5 and 10 respectively. Then the Variance of the observations \(n+x_n, n=1,2, \ldots \ldots . .5\) is

Given below are two statements
Statement I : The N-N single bond is weaker and longer than that of \(\mathrm{P}-\mathrm{P}\) single bond
Statement II : Compounds of group 15 elements in +3 oxidation states readily undergo disproportionation reactions.
In the light of above statements, choose the correct answer from the options given below

The rate of a reaction \(A\) doubles on increasing the temperature from \(300\) to \(310\, K\). By how much, the temperature of reaction \(B\) should be increased from \(300\, K\) so that rate doubles if activation energy of the reaction \(B\) is twice to that of reaction \(A\). ......... \(K\)

A student determined Young's Modulus of elasticity using the formula \(Y=\frac{M g L^{3}}{4 b d^{3} \delta} .\) The value of \(g\) is taken to be \(9.8 \,{m} / {s}^{2}\), without any significant error, his observation are as following.

Physical Quantity	Least count of the Equipment used for measurement	Observed value
Mass \(({M})\)	\(1\; {g}\)	\(2\; {kg}\)
Length of bar \((L)\)	\(1\; {mm}\)	\(1 \;{m}\)
Breadth of bar \((b)\)	\(0.1\; {mm}\)	\(4\; {cm}\)
Thickness of bar \((d)\)	\(0.01\; {mm}\)	\(0.4 \;{cm}\)
Depression \((\delta)\)	\(0.01\; {mm}\)	\(5 \;{mm}\)

Then the fractional error in the measurement of \({Y}\) is

A value of \(x\) satisfying the equation \(\sin \left[ {{{\cot }^{ - 1}}\left( {1 + x} \right)} \right] = \cos \left[ {{{\tan }^{ - 1}}\,x} \right]\) , is