\(10 \mathrm{~mL}\) of gaseous hydrocarbon on combustion gives \(40 \mathrm{~mL}\) of \(\mathrm{CO}_2(\mathrm{~g})\) and \(50 \mathrm{~mL}\) of water vapour. Total number of carbon and hydrogen atoms in the hydrocarbon is _______.

Given below are two statements: Statement- \(I\): Along the period, the chemical reactivity of the element gradually increases from group \(1\) to group \(18\). Statement - \(II\): The nature of oxides formed by group \(1\) element is basic while that of group \(17\) elements is acidic.In the the light above statements, choose the most appropriate from the questions given below:

The set of meta directing functional groups from the following sets is _______.

A monoatomic anion \((A^-)\) has \(45\) neutrons and \(36\) electrons. Atomic mass, group in the periodic table and physical state at room temperature of the element \((A)\) respectively are

Given below are two statements: one is labelled as Assertion \((A)\) and the other is labelled as Reason \((R)\) : Assertion \((A)\) : \(\mathrm{S}_{\mathrm{N}} 2\) reaction of \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_2 \mathrm{Br}\) occurs more readily than the \(\mathrm{S}_{\mathrm{N}} 2\) reaction of \(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{Br}\). Reason \((R)\) : The partially bonded unhybridized p-orbital that develops in the trigonal bipyramidal transition state is stabilized by conjugation with the phenyl ring. In the light of the above statements, choose the most appropriate answer from the options given below:

Increasing rate of \(S_N1\) reaction in the following compounds is

The standard free energy change \(\left(\Delta G ^{\circ}\right)\) for \(50 \%\) dissociation of \(N _{2} O _{4}\) into \(NO _{2}\) at \(27^{\circ} C\) and \(1\, atm\) pressure is \(- x\, J \,mol ^{-1}\). The value of \(x\) is \(......\) (Nearest Integer) [Given \(: R =8.31 \,J \,K ^{-1} \,mol ^{-1}, \log 1.33=0.1239\) \(\ln 10=2.3]\)

Initial pressure and volume of a monoatomic ideal gas are \(P\) and \(V\). The change in internal energy of this gas in adiabatic expansion to volume \(V_{final}=27V\) is ________ J.

Three Carnot engines operate in series between a heat source at a temperature \(T_1\) and a heat sink at temperature \(T_4\) (see figure). There are two other reservoirs at temperature \(T_2\) and \(T_3\), as shown, with \(T_1 > T_2 > T_3 > T_4\). The three engines are equally efficient if

The \(pH\) of a \(0.02\,M\,\,NH_4Cl\) solution will be [given \(K_b\,(NH_4OH) = 10^{-5}\) and \(log\,2 = 0.301\) ]

The number of incorrect statement \(/ s\) about the black body from the following is \(........\). \((A)\) Emit or absorb energy in the form of electromagnetic radiation \((B)\) Frequency distribution of the emitted radiation depends on temperature \((C)\) At a given temperature, intensity vs frequency curve passes through a maximum value \((D)\) The maximum of the intensity vs frequency curve is at a higher frequency at higher temperature compared to that at lower temperature

Let \(B _{i}(i=1,2,3)\) be three independent events in a sample space. The probability that only \(B _{1}\) occur is \(\alpha,\) only \(B _{2}\) occurs is \(\beta\) and only \(B _{3}\) occurs is \(\gamma\). Let \(p\) be the probability that none of the events \(B _{i}\) occurs and these \(4\) probabilities satisfy the equations \((\alpha-2 \beta) p =\alpha \beta\) and \((\beta-3 \gamma) p =2 \beta \gamma\) (All the probabilities are assumed to lie in the interval \((0,1))\). Then \(\frac{ P \left( B _{1}\right)}{ P \left( B _{3}\right)}\) is equal to ..........

A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their magnetic moment parallel to their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are \(T_h\) and \(T_c\) respectively, then the relation between them is....