\(2 \mathrm{SO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{~g})\) In an equilibrium mixture, the partial pressures are \(P_{S O_{3}}=43\,\mathrm{kPa} ; \quad P_{O_{2}}=530 \,\mathrm{~Pa}\) and \(\mathrm{P}_{\mathrm{SO}_{2}}=45\, \mathrm{kPa}\) The equilibrium constant \(\mathrm{K}_{\mathrm{p}}=......\times 10^{-2} .\) (Nearest integer)

Which of the glycosidic linkage between galactose and glucose is present in lactose ?

Consider the following elements. Which of the following is/are true about \(\mathrm{A}^{\prime}, \mathrm{B}^{\prime}, \mathrm{C}^{\prime}\) and \(\mathrm{D}^{\prime}\) ? \(A\). Order of atomic radius: \(\mathrm{B}^{\prime}<\mathrm{A}^{\prime}<\mathrm{D}^{\prime}<\mathrm{C}^{\prime}\) \(B\). Order of metallic character: \(\mathrm{B}^{\prime}<\mathrm{A}^{\prime}<\mathrm{D}^{\prime}<\mathrm{C}^{\prime}\) \(C\). Size of the element : \(\mathrm{D}^{\prime}<\mathrm{C}^{\prime}<\mathrm{B}^{\prime}<\mathrm{A}^{\prime}\) \(D\). Order of ionic radius : \(\mathrm{B}^{\prime+}<\mathrm{A}^{\prime+}<\mathrm{D}^{\prime+}<\mathrm{C}^{\prime+}\) Choose the correct answer from the options given below :

The theory that can completely/properly explain the nature of bonding in \([Ni(CO)_4]\) is

\(\mathrm{R}-\mathrm{CN} \xrightarrow[\text { (ii) } \mathrm{H}_{2} \mathrm{O}]{\text { (i) DIBAL-H }} \mathrm{R}-\mathrm{Y}\) Consider the above reaction and identify \("Y"\)

The one that is not expected to show isomerism is:

The radius of the second Bohr orbit for hydrogen atom is  .......... \(\mathop A\limits^o \) (Plank's const. \( h = 6. \times 10^{-34}\, Js\,;\) mass of electron \(= 9.1091 \times 10^{-31}\, kg\,;\) charge of electron \(e= 1.60210 \times 10^{-19}\, C\,;\) permittivity of vaccum \(\epsilon _0 = 8.854185 \times 10^{-12} \,kg^{-1} \,m^{-3} A^2\))

If \(\alpha \) and \(\beta \) are the roots of the quadratic equation, \(x^2 + x\, sin\,\theta  -2sin\,\theta  = 0\), \(\theta  \in \left( {0,\frac{\pi }{2}} \right)\) then \(\frac{{{\alpha ^{12}} + {\beta ^{12}}}}{{\left( {{\alpha ^{ - 12}} + {\beta ^{ - 12}}} \right){{\left( {\alpha  - \beta } \right)}^{24}}}}\) is equal to

Let the shortest distance from \((\mathrm{a}, 0), \mathrm{a}\gt0\), to the parabola \(y^2=4 x\) be 4 . Then the equation of the circle passing through the point \((a, 0)\) and the focus of the parabola, and having its centre on the axis of the parabola is :

A cylinder with fixed capacity of \(67.2\, lit\) contains helium gas at \(STP\). The amount of heat needed to raise the temperature of the gas by \(20\,^oC\) is ..... \(J\) [Given that \(R = 8.31\, J\, mol^{-1}\, K^{-1}\)]

The electric field at point p due to an electric dipole is E . The electric field at point R on equitorial line will be \(\frac{E}{x}\). The value of \(x\) is _______.

In the cell  \(Pt(s)| H_2 (g,1\,bar)| HCl(aq)| AgCl(s)| Ag(s)| Pt(s)\) the cell potential is \(0.92\,V\) when a \(10^{-6}\) molal \(HCl\) solution is used. The standard electrode potential of \((AgCl / Ag,Cl^- )\) electrode is ............. \(\mathrm{V}\) \(\left\{ {Given,\frac{{2.303RT}}{F} = 0.06\,V\,at\,298\,K} \right\}\) 

Let \(Z\) be the set of all integers, \(\mathrm{A}=\left\{(\mathrm{x}, \mathrm{y}) \in \mathbb{Z} \times \mathbb{Z}:(\mathrm{x}-2)^{2}+\mathrm{y}^{2} \leq 4\right\}\) \(\mathrm{B}=\left\{(\mathrm{x}, \mathrm{y}) \in \mathbb{Z} \times \mathbb{Z}: \mathrm{x}^{2}+\mathrm{y}^{2} \leq 4\right\} \text { and }\) \(\mathrm{C}=\left\{(\mathrm{x}, \mathrm{y}) \in \mathbb{Z} \times \mathbb{Z}:(\mathrm{x}-2)^{2}+(\mathrm{y}-2)^{2} \leq 4\right\}\) If the total number of relation from \(\mathrm{A} \cap \mathrm{B}\) to \(\mathrm{A} \cap \mathrm{C}\) is \(2^{\mathrm{p}}\), then the value of \(\mathrm{p}\) is :