\(N_2O_5\) decomposes to \(NO_2\) and \(O_2\) and follows first order kinetics . After \(50\, minutes\), the pressure inside the vessel increases from \(50\, mm\,Hg\) to \(87 .5\, mm \,Hg\). The pressure of the gaseous mixture after \(100\, minutes\) at constant temperature will be ........... \(mm\,Hg\)

When concentrated \(HCl\) is added to an aqueous solution of \(CoCl_2\), its colour changes from reddish pink to deep blue . Which complex ion gives blue colour in this reaction?

Match List \(- I\) with List \(- II.\)

List \(- I\)	List \(- II\)
\((a)\) Zymase	\((i)\) Stomach
\((b)\) Diastase	\((ii)\) Yeast
\((c)\) Urease	\((iii)\) Malt
\((d)\) Pepsin	\((iv)\) Soyabean

Choose the correct answer from the options given below

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 :

\(1\, L\) aqueous solution of \(H _{2} SO _{4}\) contains \(0.02\, m\) mol \(H _{2} SO _{4} .50\, \%\) of this solution is diluted with deionized water to give \(1\, L\) solution \((A).\) In solution \((A)\), \(0.01\, m \,mol\) of \(H _{2} SO _{4}\) are added. Total \(m\) \(mols\) of \(H _{2} SO _{4}\) in the final solution is \(......\times 10^{3}\, m\, mols.\)

The equilibrium constant at \(298\, K\) for a reaction \(A + B \rightleftharpoons C + D\) is \(100.\) If the initial concentration of all the four species were \(1\, M\) each, then equilibrium concentration of \(D\) ( in \(mol\, L^{-1}\) ) will be :

Which one of the following when dissolved in water gives coloured solution in nitrogen atmosphere?

Match List-I with List-II.

List-I	List-II
(A) Isothermal	(I) \(\Delta W(\text{work done}) = 0\)
(B) Adiabatic	(II) \(\Delta Q(\text{supplied heat}) = 0\)
(C) Isobaric	(III) \(\Delta U(\text{change in internal energy}) \neq 0\)
(D) Isochoric	(IV) \(\Delta U = 0\)

Choose the correct answer from the options given below :

Given below are two statements: Statement \(I :\) Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an \(AC\) source, when resonance occurs Statement \(II :\) Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage. In the light of the above statements, choose the correct answer from the options given below :

If \(\Delta=\left|\begin{array}{ccc}x-2 & 2 x-3 & 3 x-4 \\ 2 x-3 & 3 x-4 & 4 x-5 \\ 3 x-5 & 5 x-8 & 10 x-17\end{array}\right|=\) \(Ax ^{3}+ Bx ^{2}+ Cx + D ,\) then \(B + C\) is equal to

Number of paramagnetic oxides among the following given oxides is ..... . \(\mathrm{Li}_{2} \mathrm{O}, \mathrm{CaO}, \mathrm{Na}_{2} \mathrm{O}_{2}, \mathrm{KO}_{2}, \mathrm{MgO}\) and \(\mathrm{K}_{2} \mathrm{O}\)

Two \(10 \; cm\) long, straight wires, each carrying a current of \(5 \; A\) are kept parallel to each other. If each wire experienced a force of \(10^{-5} \; N\), then separation between the wires is \(\dots \; cm\).

Let \(y=y(x)\) be the solution of the differential equation \(\frac{d y}{d x}=1+x e^{y-x},-\sqrt{2}\,<\,x\,<\,\sqrt{2}, y (0)=0\) then, the minimum value of \(y(x)\) , \(\mathrm{x} \in(-\sqrt{2}, \sqrt{2})\) is equal to: