2 moles each of ethylene glycol and glucose are dissolved in 500 g of water. The boiling point of the resulting solution is _______.
(Given : Ebullioscopic constant of water \(\left.=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)\)

If the radius of the \(3^{\text {rd }}\) Bohr's orbit of hydrogen atom is \(r_{3}\) and the radius of \(4^{\text {th }}\) Bohr's orbit is \(r_{4}\). Then ....

Given below are two statements :
Statement (I) : Potassium hydrogen phthalate is a primary standard for standardisation of sodium hydroxide solution.
Statement (II) : In this titration phenolphthalein can be used as indicator.
In the light of the above statements, choose the most appropriate answer from the options given below:

\(2 IO _3^{-}+ xI ^{-}+12 H ^{+} \rightarrow 6 I _2+6 H _2 O\) What is the value of \(x\) ?

Among the following species
\(N _{2}, N _{2}^{+}, N _{2}^{-}, N _{2}{ }^{2-}, O _{2}, O _{2}{ }^{+}, O _{2}^{-}, O _{2}{ }^{2-}\) the number of species showing diamagnetism is.

Given below are two statements: One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) Butan\(-1-\)ol has higher boiling point than ethoxyethane. Reason \(R:\) Extensive hydrogen bonding leads to stronger association of molecules. In the light of the above statements, choose the correct answer from the options given below:

The reaction of ozone with oxygen atoms in the presence of chlorine atoms can occur by a two step process shown below \({O_3}(g)\, + \,C{l^ * }(g)\, \to \,{O_2}(g) + Cl{O^ * }(g)\) ..... \((i)\)               \([{K_i} = 5.2 \times {10^9}\,\,L\,mo{l^{ - 1}}\,{s^{ - 1}}]\) \(Cl{O^ * }(g) + {O^ * }(g)\, \to \,{O_2}(g) + \,C{l^ * }(g)\) ..... \((ii)\)                \([{K_{ii}} = 2.6 \times {10^{10}}\,\,L\,mo{l^{ - 1}}\,{s^{ - 1}}]\) The closest rate constant for the overall reaction  \({O_3}(g){\mkern 1mu}  + {\mkern 1mu} {O^*}(g){\mkern 1mu}  \to {\mkern 1mu} 2{O_2}(g)\) is  ........... \(L\,\,mo{l^{ - 1}}\,{s^{ - 1}}\)

Let \(M\) be a \(3 \times 3\) matrix such that \(M \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}\), \(M \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix} = \begin{pmatrix} 0 \\ 1 \\ 2 \end{pmatrix}\) and \(M \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} = \begin{pmatrix} -1 \\ 1 \\ 1 \end{pmatrix}\). If \(M \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 1 \\ 7 \\ 11 \end{pmatrix}\), then \(x + y + z\) equals :

The figure shows two solid discs with radius \({R}\) and \({r}\) respectively. If mass per unit area is same for both, what is the ratio of \({MI}\) of bigger disc around axis \({AB}\) (Which is \(\perp\) to the plane of the disc and passing through its centre) of MI of smaller disc around one of its diameters lying on its plane? Given \('M'\) is the mass of the larger disc. (\(MI\) stands for moment of inertia)

A circular disc \(D_1\) of mass \(M\) and radius \(R\) has two identical discs \(D_2\) and \(D_3\) of the same mass \(M\) and radius \(R\) attached rigidly as its opposite ends (see figure). The moment of inertia of the system about the axis \(OO\)’, passing through the centre of \(D_1\) as shown in the figure, will

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : Boric acid is a weak acid Reason \(R\) : Boric acid is not able to release \(H ^{+}\)ion on its own. It receives \(OH ^{-}\)ion from water and releases \(H ^{+}\)ion. In the light of the above statements, choose the most appropriate answer from the options given below.

Water flows into a large tank with flat bottom at the rate of \({10^{ - 4}}\,{m^3}{s^{ - 1}}\). Water is also leaking out of a hole of area \(1\, cm^2\) at its bottom. If the height of the water in the tank remains steady, then this height is........ \(cm\)

Consider the lines \(\mathrm{L}_1: \mathrm{x}-1=\mathrm{y}-2=\mathrm{z}\) and \(\mathrm{L}_2: \mathrm{x}-2=\mathrm{y}=\mathrm{z}-1\). Let the feet of the perpendiculars from the point \(\mathrm{P}(5,1,-3)\) on the lines \(\mathrm{L}_1\) and \(\mathrm{L}_2\) be \(Q\) and \(R\) respectively. If the area of the triangle PQR is A , then \(4 \mathrm{~A}^2\) is equal to :