The compound (X) on
(i) on heating in the presence of anhydrous \(AlCl_3\) and HCl gas gives \(2,4\)-dimethyl pentane
(ii) aromatization gives toluene and
(iii) cyclisation gives methyl cyclohexane
The correct name of compound (X) is:

The mole fraction of a solvent in aqueous solution of a solute is \(0.8\). The molality (in \(mol\, kg^{-1}\)) of the aqueous solution is

Consider the following reactions. From these reactions which reaction will give carboxylic acid
as a major product ?
(A) \(\mathrm{R}-\mathrm{C} \equiv \mathrm{N} \xrightarrow[\text { mild condition }]{\text { (i) } \mathrm{H}^{+} / \mathrm{H}_2 \mathrm{O}}\)
(B) \(\mathrm{R}-\mathrm{MgX} \xrightarrow[\text { (ii) } \mathrm{H}_3 \mathrm{O}^{+}]{\text {(i) } \mathrm{CO}_2}\)
(C) \(\mathrm{R}-\mathrm{C} \equiv \mathrm{N} \xrightarrow[\text { (ii) } \mathrm{H}_3 \mathrm{O}^{+}]{\text {(i) } \mathrm{SnCl}_2 / \mathrm{HCl}}\)
(D) \(\mathrm{R} \cdot \mathrm{CH}_2 \cdot \mathrm{OH} \xrightarrow{\mathrm{PCC}}\)
(E)

Choose the correct answer from the options given below:

The one giving maximum number of isomeric alkenes on dehydrohalogenation reaction is (excluding rearrangement)

Which of the following pair of molecules contain odd electron molecule and an expanded octet molecule?

\(2 O _{3}( g ) \rightleftharpoons 3 O _{2}( g )\) At \(300 \,K\), ozone is fifty percent dissociated. The standard free energy change at this temperature and \(1\, atm\) pressure is \((-)\) \(........\,J\, mol ^{-1}\) (Nearest integer) [Given: \(\ln 1.35=0.3\) and \(R =8.3 J K ^{-1} mol ^{-1}\) ]

Standard entropies of \(\mathrm{X}_2, \mathrm{Y}_2\) and \(\mathrm{XY}_5\) are 70,50 and \(110 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\) respectively. The temperature in Kelvin at which the reaction
\(\frac{1}{2} \mathrm{X}_2+\frac{5}{2} \mathrm{Y}_2 \rightleftharpoons \mathrm{XY}_5 \Delta \mathrm{H}^{\Theta}=-35 \mathrm{~kJ} \mathrm{~mol}^{-1}\)
will be at equilibrium is_______. (Nearest integer)

The number of molecules/ion/s having trigonal bipyramidal shape is _______. \(\mathrm{PF}_5, \mathrm{BrF}_5, \mathrm{PCl}_5,\left[\mathrm{PtCl}_4\right]^{2-}, \mathrm{BF}_3, \mathrm{Fe}(\mathrm{CO})_5\)

Consider a \(\Delta A B C\) where \(A(1,3,2), B(-2,8,0)\) and \(C(3,6,7)\). If the angle bisector of \(\angle B A C\) meets the line \(B C\) at \(D\), then the length of the projection of the vector \(\overrightarrow{A D}\) on the vector \(\overrightarrow{A C}\) is :

If the tangent to the curve \(y=x^{3}-x^{2}+x\) at the point \((a, b)\) is also tangent to the curve \(y=5 x^{2}+\) \(2 x -25\) at the point \((2,-1)\), then \(|2 a +9 b |\) is equal to \(........\)

A parallel plate capacitor with plate area \(A\) and plate separation \(d =2 \,m\) has a capacitance of \(4 \,\mu F\). The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant \(K =3\) (as shown in figure) will be .........\( \mu \,F\)

A coil of negligible resistance is connected in series with \(90 \Omega\) resistor across \(120 \mathrm{~V}, 60 \mathrm{~Hz}\) supply. A voltmeter reads \(36 \mathrm{~V}\) across resistance. Inductance of the coil is _______.

Let \(f\) and \(g\) be twice differentiable functions on \(R\) such that \(f^{\prime \prime}(x)=g^{\prime \prime}(x)+6 x\) \(f^{\prime}(1)=4 g^{\prime}(1)-3=9\) \(f(2)=3 g(2)=12\) Then which of the following is NOT true ?