Using the provided information in the following paper chromatogram the calculate \(R _{ f }\) value of \(A\) .......... \(\times 10^{-1}\)

Given below are two statements: one is labelled as Assertion \((A)\) and the other is labelled as Reason \((R)\) : Assertion \((A)\) : \(\mathrm{S}_{\mathrm{N}} 2\) reaction of \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_2 \mathrm{Br}\) occurs more readily than the \(\mathrm{S}_{\mathrm{N}} 2\) reaction of \(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{Br}\). Reason \((R)\) : The partially bonded unhybridized p-orbital that develops in the trigonal bipyramidal transition state is stabilized by conjugation with the phenyl ring. In the light of the above statements, choose the most appropriate answer from the options given below:

In Carius method, halogen containing organic compound is heated with fuming nitric acid in the presence of :

The gas phase reaction \(2 A ( g ) \rightleftharpoons A _{2}( g )\) at \(400\, K\) has \(\Delta G ^{\circ}=+25.2\, kJ mol ^{-1}\). The equilibrium constant \(K _{ C }\) for this reaction is \(...... \times 10^{-2}\). (Round off to the Nearest integ \(\left[\right.\) Use \(: R=8.3\, J mol ^{-1} K ^{-1}, \ln 10=2.3\) \(\left.\log _{10} 2=0.30,1\, atm =1\, bar \right]\) \([\) antilog \((-0.3)=0.501]\)

Identity the incorrect pair from the following:

If \(250\, cm ^{3}\) of an aqueous solution containing \(0.73\, g\) of a protein \(A\) is isotonic with one litre of another aqueous solution containing \(1.65\, g\) of a protein \(B ,\) at \(298\, K ,\) the ratio of the molecular mases of \(A\) and \(B\) is..........\(\times 10^{-2}\) (to the nearest integer).

The pair of metal ions that can give a spin-only magnetic moment of \(3.9\, BM\) for the complex \([M(H_2O)_6]Cl_2\) is

Let \(A\) and \(B\) be two finite sets with \(m\) and \(n\) elements respectively. The total number of subsets of the set \(A\) is 56 more than the total number of subsets of \(B\). Then the distance of the point \(P ( m , n )\) from the point \(Q (-2,-3)\) is

Let \(A=\{1,2,3,4\}\) and \(R\) be a relation on the set \(A \times A\) defined by \(R=\{((a, b),(c, d)): 2 a+3 b=4 c+5 d\}\). Then the number of elements in \(R\) is:

The equations of two sides \(\mathrm{AB}\) and \(\mathrm{AC}\) of a triangle \(\mathrm{ABC}\) are \(4 \mathrm{x}+\mathrm{y}=14\) and \(3 \mathrm{x}-2 \mathrm{y}=5\), respectively. The point \(\left(2,-\frac{4}{3}\right)\) divides the third side \(\mathrm{BC}\) internally in the ratio \(2: 1\). The equation of the side \(\mathrm{BC}\) is :

The number of pairs of the solution having the same value of the osmotic pressure from the following is (Assume \(100\%\)  ionization) \(A.\) \(0.500\,M\,C _2 H _5 OH ( aq )\) and \(0.25\, M\, KBr ( aq )\) \(B.\) \(0.100\,M\,K _4\left[ Fe ( CN )_6\right]\) (aq) and \(0.100\, M\) \(FeSO _4\left( NH _4\right)_2 SO _4\) (aq) \(C.\) \(0.05 \,M\, K _4\left[ Fe ( CN )_6\right]( aq )\) and \(0.25\, M\, NaCl\) (aq) \(D.\) \(0.15\, M\, NaCl ( aq )\) and \(0.1\, M BaCl _2\) (aq) \(E.\) \(0.02\, M\, KCl\, MgCl _{2 .} 6 H _2 O ( aq )\) and \(0.05\, M\) \(KCl ( aq )\)

Let a function \(f: R \rightarrow R\) be defined as \(f(x)=\sin x-e^{x} \,\,\,\, \text { if } x \leq 0\) \(\quad\quad\quad a+[-x] \,\,\,\, \text { if } 0\,<\,x\,<\,1\) \(\quad\quad\quad 2 x-b \,\,\,\,\,\,\,\, \text { if } \geq 1\) where \([\mathrm{x}]\) is the greatest integer less than or equal to \(\mathrm{x}\). If \(\mathrm{f}\) is continuous on \(\mathrm{R}\), then \((\mathrm{a}+\mathrm{b})\) is equal to:

Three identical coils \(C _1, C _2\) and \(C _3\) are closely placed such that they share a common axis.\(C _2\) is exactly midway.\(C _1\) carries current I in anti-clockwise direction while \(C _3\) carries current I in clockwise direction. An induced current flows through \(C _2\), will be in clockwise direction when