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 stepwise formation of \(\left[ Cu \left( NH _{3}\right)_{4}\right]^{2+}\) is given below \(Cu ^{2+}+ NH _{3} \stackrel{ K _{1}}{\rightleftharpoons}\left[ Cu \left( NH _{3}\right)\right]^{2+}\) \(\left[ Cu \left( NH _{3}\right)\right]^{2+}+ NH _{3} \stackrel{ K _{2}}{\rightleftharpoons}\left[ Cu \left( NH _{3}\right)_{2}\right]^{2+}\) \(\left[ Cu \left( NH _{3}\right)_{2}\right]^{2+}+ NH _{3} \stackrel{ K _{3}}{\rightleftharpoons}\left[ Cu \left( NH _{3}\right)_{3}\right]^{2+}\) \(\left[ Cu \left( NH _{3}\right)_{3}\right]^{2+}+ NH _{3} \stackrel{ K _{4}}{\rightleftharpoons}\left[ Cu \left( NH _{3}\right)_{4}\right]^{2+}\) The value of stability constants \(K _{1}, K _{2}, K _{3}\) and \(K _{4}\) are \(10^{4}, 1.58 \times 10^{3}, 5 \times 10^{2}\) and \(10^{2}\) respectively. The overall equilibrium constants for dissociation of \(\left[ Cu \left( NH _{3}\right)_{4}\right]^{2+}\) is \(x \times 10^{-12}\) The value of \(x\) is ............... (Rounded off to the nearest integer)

For elements \(B , C , N , Li , Be , O\) and \(F\) the correct order of first ionization enthalpy is

For a chemical reaction \(A + B \rightarrow\) Product, the order is \(1\) with respect to \(A\) and \(B\).

Rate \(mol\,L^{-1}\,s^{-1}\)	\([A]\) \(mol\,L^{-1}\)	\([B]\) \(mol\,L^{-1}\)
\(0.10\)	\(20\)	\(0.5\)
\(0.40\)	\(x\)	\(0.5\)
\(0.80\)	\(40\)	\(y\)

What is the value of \(x\) and \(y ?\)

Match List I with List II

List - I Type	List - II Name
A. Antifertility drug	I. Norethindrone
B. Tranquilizer	II. Meprobomate
C. Antihistamine	III. Seldane
D. Antibiotic	IV. Ampicillin

Choose the correct answer from the options given below :

\(M_3 A_2\) is a sparingly soluble salt of molar mass \(y\) g mol\(^{-1}\) and solubility \(x\) g L\(^{-1}\). The ratio of the molar concentration of the anion (\(A^{3-}\)) to the solubility product of the salt is

One mole of an ideal gas expands isothermally and reversibly from \(10 \mathrm{dm}^3\) to \(20 \mathrm{dm}^3\) at \(300 \mathrm{~K}. \Delta \mathrm{U}\), q and work done in the process respectively are :
Given : \(\mathrm{R}=8.3 \mathrm{JK}^{-1}\) and \(\mathrm{mol}^{-1}\)
\(\begin{aligned}
& \text { In } 10=2.3 \\
& \log 2=0.30 \\
& \log 3=0.48
\end{aligned}\)

Two balls \(A\) and \(B\) are placed at the top of \(180 \,m\) tall tower. Ball \(A\) is released from the top at \(t =0 \,s\). Ball \(B\) is thrown vertically down with an initial velocity \(u\)' at \(t=2\, s\). After a certain time, both balls meet \(100 \,m\) above the ground. Find the value of \(u\) in ............... \(ms ^{-1}\). [use \(g =10 \,ms ^{-2}\) ]

Among the following basic oxide is .....

Given; A circle \(2{x^2} + 2{y^2} = 5\) and parabola \({y^2} = 4\sqrt 5 x\) Statement \(-1\):An equation of a common tangent to these curve is  \(y = x + \sqrt 5 \) Statement \(-2\): If the line, \(y = mx + \frac{{\sqrt 5 }}{m}\left( {m \ne 0} \right)\) is their common tangent , then \(m\) satisfies \({m^4} - 3{m^2} + 2 = 0\). 

If \(\overrightarrow {{{\left| c \right|}^2}}  = 60\) and \(\overrightarrow c  \times \left( {\hat i + 2\hat j + 5\hat k} \right) = \overrightarrow 0 \), then a value of \(\overrightarrow c .\left( { - 7\hat i + 2\hat j + 3\hat k} \right)\) is

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

List\(-I\) (Parameter)	List\(-II\) (Unit)
\((a)\) Cell constant	\((i)\) \(\mathrm{S}\, \mathrm{cm}^{2} \,\mathrm{~mol}^{-1}\)
\((b)\) Molar conductivity	\((ii)\) Dimensionless
\((c)\) Conductivity	\((iii)\) \(\mathrm{m}^{-1}\)
\((d)\) Degree of dissociation of electrolyte	\((iv)\) \(\Omega^{-1} \,\mathrm{~m}^{-1}\)

Choose the most appropriate answer from the options given below :

If the range of the function \(f(x)=\frac{5-x}{x^2-3 x+2}\), \(x \neq 1,2\), is \((-\infty, \alpha] \cup[\beta, \infty)\), then \(\alpha^2+\beta^2\) is equal to: