In the given compound, the number of \(2^{\circ}\) carbon atom is _______.

Identify the molecule \(( X )\) with maximum number of lone pairs of electrons (obtained using Lewis dot structure) among \(HNO _3, H _2 SO _4, NF _3\) and \(O _3\). Choose the correct bond angle made by the central atom of the molecule (X).

The activation energy of one of the reactions in a biochemical process is \(532611\, J\,  mol ^{-1}\). When the temperature falls from \(310 \, K\) to \(300\,  K\), the change in rate constant observed is \(k _{300}= x \times 10^{-3}\,  k _{310}\). The value of \(x\) is \(.....\) [Given: \(\ln 10=2.3\) \(R =8.3\,  J \, K ^{-1}\,  mol ^{-1}\)

The correct sequence of reagents for the conversion of X to Y is :

Two isomers \('A'\) and \('B'\) with molecular formula \(C _{4} H _{8}\) give different products on oxidation with \(KMnO _{4}\) in acidic medium. Isomer ' \(A\) ' on reaction with \(KMnO _{4} / H ^{+}\)results in effervescence of a gas and gives ketone. The compound ' \(A\) ' is ...... .

\(HF\) has highest boiling point among hydrogen halides, because it has

\(40\, \mathrm{~g}\) of glucose (Molar mass \(=180\) ) is mixed with \(200\, \mathrm{~mL}\) of water. The freezing point of solution is \(.....\,\mathrm{K}\). (Nearest integer) [Given : \(\mathrm{K}_{\mathrm{f}}=1.86 \,\mathrm{~K} \,\mathrm{~kg} \,\mathrm{~mol}^{-1} ;\) Density of water \(=\) \(1.00 \,\mathrm{~g}\, \mathrm{~cm}^{-3} ;\) Freezing point of water \(\left.=273.15\, \mathrm{~K}\right]\)

If the minimum area of the triangle formed by a tangent to the ellipse \(\frac{x^{2}}{b^{2}}+\frac{y^{2}}{4 a^{2}}=1\) and the co-ordinate axis is \(kab,\) then \(\mathrm{k}\) is equal to ..... .

A \(100\,m\) long wire having cross-sectional area \(6.25 \times 10^{-4}\,m ^2\) and Young's modulus is \(10^{10}\,Nm ^{-2}\) is subjected to a load of \(250\,N\), then the elongation in the wire will be :

Dichromate ion is treated with base, the oxidation number of \(Cr\) in the product formed is .... .

Let \(f\left( x \right) = {\sin ^4}\,x + {\cos ^4}\,x\). Then \(f\) is an increasing function in the interval 

Combustion of \(1\) mole of benzene is expressed at \(\mathrm{C}_6 \mathrm{H}_6(1)+\frac{15}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2 \mathrm{O}(1) \text {. }\) The standard enthalpy of combustion of \(2 \mathrm{~mol}\) of benzene is - ' \(x\) ' \(k J\). \(\mathrm{x}=\) _______ \((1)\) standard Enthalpy of formation of \(1 \mathrm{~mol}\) of \(\mathrm{C}_6 \mathrm{H}_6(1)\), for the reaction \(6 \mathrm{C}\) (graphite) \(+3 \mathrm{H}_2(\mathrm{~g}) \rightarrow \mathrm{C}_6 \mathrm{H}_n(1)\) is \(48.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\). \((2)\) Standard Enthalpy of formation of \(1 \mathrm{~mol}\) of \(\mathrm{CO}_2(\mathrm{~g})\), for the reaction \(\mathrm{C}\) (graphite) \(+\mathrm{O}_{2(\mathrm{~g})} \rightarrow \mathrm{CO}_2(\mathrm{~g})\) is \(-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1}\). \((3)\) Standard and Enthalpy of formation of \(1 \mathrm{~mol}\) of \(\mathrm{H}_2 \mathrm{O}(1)\), for the reaction \(\mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(1)\) is \(-286 \mathrm{~kJ} \mathrm{~mol}^{-1}\).

A particle which is experiencing a force, given by \(\vec F = 3\vec i -12\vec j\), undergoes a displacement of \(\vec d = 4\vec i\) . If the particle had a kinetic energy of \(3\, J\) at the beginning of the displacement, what is its kinetic energy at the end of the displacement?