The following results were obtained during kinetic studies of the reaction \(2A+B\) \(\to\) products

Experiment	\([A]\) (in \(mol\, L^{-1})\)	\([B]\) (in \(mol\, L^{-1})\)	Initial rate of reaction (in \(mol\, L^{-1}\,min^{-1})\)
\(I\)	\(0.10\)	\(0.20\)	\(6.93 \times {10^{ - 3}}\)
\(II\)	\(0.10\)	\(0.25\)	\(6.93 \times {10^{ - 3}}\)
\(III\)	\(0.20\)	\(0.30\)	\(1.386 \times {10^{ - 2}}\)

The time(in minutes) required to consume half of \(A\) is

The quantum number of four electrons are given below \(I.  n = 4,l = 2,m_l = -2, m_s =  -1/ 2\)
\(II.  n = 3,l = 2, m_l = 1,m_s = +1/ 2\)
\(III. n = 4,l = 1, m_l = 0, m_s = +1/ 2\)
\(IV. n = 3,l = 1, m_l = 1; m_s = -1/ 2\)
The correct order of their increasing energies will be

The primary and secondary valencies of cobalt respectively in \(\left[ Co \left( NH _3\right)_5 Cl \right] Cl _2\) are :

Which of the following statements are correct, if the threshold frequency of caesium is \(5.16 \times 10^{14} \mathrm{~Hz}\) ?
A. When Cs is placed inside a vacuum chamber with an ammeter connected to it and yellow light is focused on Cs the ammeter shows the presence of current.
B. When the brightness of the yellow light is dimmed, the value of the current in the ammeter is reduced.
C. When a red light is used instead to the yellow light, the current produced is higher with respect to the yellow light.
D. When a blue light is used, the ammeter shows the formation of current.
E. When a white light is used, the ammeter shows formation of current.
Choose the correct answer from the options given below :

Which of the following cannot be explained by crystal field theory?

Number of complexes which show optical isomerism among the following is _______. \(\operatorname{cis}-\left[\mathrm{Cr}(\mathrm{ox})_2 \mathrm{Cl}_2\right]^{3-},\left[\mathrm{Co}(\mathrm{en})_3\right]^{3+}\) \(\operatorname{cis}-\left[\mathrm{Pt}(\mathrm{en})_2 \mathrm{Cl}_2\right]^{2+}, \text { cis }-\left[\mathrm{Co}(\mathrm{en})_2 \mathrm{Cl}_2\right]^{+}\) \(\text {trans }-\left[\mathrm{Pt}(\mathrm{en})_2 \mathrm{Cl}_2\right]^{2+}, \text { trans }-\left[\mathrm{Cr}(\mathrm{ox})_2 \mathrm{Cl}_2\right]^{3-}\)

The correct match between Item \(I\) and Item \(II\) is

Item \(I\)	Item \(II\)
\(A\) Ester test	\(P\) Tyr
\(B\) Carbylamine test	\(Q\) Asp
\(C\) Phthalein dye test	\(R\) Ser
	\(S\) Lys

 

\(10.0 \,\mathrm{~mL}\) of \(0.05\, \mathrm{M}\, \mathrm{KMnO}_{4}\) solution was consumed in a titration with \(10.0\, \mathrm{~mL}\) of given oxalic acid dihydrate solution. The strength of given oxalic acid solution is \(.....\,\times 10^{-2} \,\mathrm{~g} / \mathrm{L}\) (Round off to the nearest integer)

Let \(f\) be a real valued continuous function on \([0,1]\) and \(f(x)=x+\int\limits_{0}^{1}(x-t) f(t) d t\). Then which of the following points \(( x , y )\) lies on the curve \(y =f( x )\) ?

Molecules of benzoic acid \((C_6H_5COOH)\) dimerise in benzene. \(‘w’\,g\) of the acid dissolved in \(30\,g\) of benzene shows a depression in freezing point equal to \(2\,K.\) If the percentage association of the acid to form dimer in the solution is \(80,\) then \(w\) is : ............. \(\mathrm{g}\) (Given that \(K_f = 5\,K\, kg\,mol^{-1},\) Molar mass of benzoic acid \(= 122\,g\,mol^{-1}\) )

Let \(L\) be the line of intersection of planes \(\vec{r} \cdot(\hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}})=2\) and \(\vec{r} \cdot(2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}})=2\). If \(\mathrm{P}(\alpha, \beta, \gamma)\) is the foot of perpendicular on \(L\) from the point \((1,2,0)\), then the value of \(35(\alpha+\beta+\gamma)\) is equal to :

If \(15 \sin ^{4} \alpha+10 \cos ^{4} \alpha=6,\) for some \(\alpha \in R ,\) then the value of \(27 \sec ^{6} \alpha+8 \operatorname{cosec}^{6} \alpha\) is equal to ....... .

The isomeric deuterated bromide with molecular formula \(C _4 H _8 DBr\) having two chiral carbon atoms is