Sodium fusion extract of an organic compound \(( Y )\) with \(CHCl _3\) and chlorine water gives violet color to the \(CHCl _3\) layer. 0.15 g of \(( Y )\) gave 0.12 g of the silver halide precipitate in Carius method. Percentage of halogen in the compound \(( Y )\) is _______. (Nearest integer).
(Given : molar mass \(g ~ mol ^{-1} C : 12, H : 1, Cl : 35.5\), \(\operatorname{Br}: 80, I : 127\) )

The compound A, \(C_{8}H_{8}O_{2}\) reacts with acetophenone to form a single product via cross-Aldol condensation. The compound A on reaction with conc. NaOH forms a substituted benzyl alcohol as

Given below are two statements:
Statement I: Each electron in \(e_g\) orbitals destabilizes the orbitals by \(+0.6\Delta_o\) and each electron in the \(t_{2g}\) orbitals stabilizes the orbitals by \(-0.4\Delta_o\) in an octahedral field on the basis of crystal field theory.
Statement II: All the d-orbitals of the transition metals have the same energy in their free atomic state but when a complex is formed the ligands destroy the degeneracy of these orbitals on the basis of crystal field theory.
In the light of the above statements, choose the correct answer from the options given below

Consider the reaction \(N _{2} O _{4}( g ) \rightleftharpoons 2 NO _{2}( g )\) The temperature at which \(K _{ C }=20.4\) and \(K _{ P }=600.1,\) is ....... \(K\). (Round off to the Nearest Integer). [Assume all gases are ideal and \(R =0.0831\, L\,bar \, K ^{-1} mol ^{-1}]\)

Consider the following half cell reaction
\(\mathrm{Cr}_2 \mathrm{O}_7^{2-}(\mathrm{aq})+6 \mathrm{e}^{-}+14 \mathrm{H}^{+}(\mathrm{aq})\) \(\rightarrow 2 \mathrm{Cr}^{3+}(\mathrm{aq})+7 \mathrm{H}_2 \mathrm{O}(\mathrm{l})\)
The reaction was conducted with the ratio of \(\frac{\left[\mathrm{Cr}^{3+}\right]^2}{\left[\mathrm{Cr}_2 \mathrm{O}_7^{2-}\right]}=10^{-6}\). The pH value at which the EMF of the half cell will become zero is ________. (nearest integer value)
[Given : standard half cell reduction potential
\(\left.\mathrm{E}_{\mathrm{Cr}_2 \mathrm{O}_7^{2-}, \mathrm{H}^{+} / \mathrm{Cr}^{3+}}^{\mathrm{o}}=1.33 \mathrm{~V}, \frac{2.303 \mathrm{RT}}{\mathrm{~F}}=0.059 \mathrm{~V}\right]\)

Arrange the following compounds in increasing order of rate of aromatic electrophilic substitution reaction

The total change in the oxidation state of manganese involved in the reaction of \(KMnO _4\) and potassium iodide in the acidic medium is \(..........\).

Let \(A\) be a \(3 \times 3\) matrix with \(\operatorname{det}( A )=4\). Let \(R _{ i }\) denote the \(i ^{\text {th }}\) row of \(A\). If a matrix \(B\) is obtained by performing the operation \(R _{2} \rightarrow 2 R _{2}+5 R _{3}\) on \(2 A ,\) then \(\operatorname{det}( B )\) is equal to ...... .

Let \(y=y(x)\) be the solution of the differential equation, \(x y^{\prime}-y=x^{2}(x \cos x+\sin x), x>0\) If \(y (\pi)=\pi,\) then \(y ^{\prime \prime}\left(\frac{\pi}{2}\right)+ y \left(\frac{\pi}{2}\right)\) is equal to

If \(P = \left[ {\begin{array}{*{20}{c}}1&\alpha &3\\1&3&3\\2&4&4\end{array}} \right]\) is the adjoint of  \(3×3 \) matrix \(A\)  and \( |A|=4\)  then \(\alpha \) is equal to 

A wire of resistance \(9 \Omega\) is bent to form an equilateral triangle. Then the equivalent resistance across any two vertices will be _____ ohm.

Match the List \(I\) with List \(II\)

LIST \(I\)	LIST \(II\)
\(A\) Intrinsic Semiconductor	\(I\) Fermi-level near conduction band
\(B\) \(n-\)type semiconductor	\(II\) Fermi-level at middle
\(C\) \(p-\) type semiconductor	\(III\) Fermi-level near valence band
\(D\) Metals	\(IV\) Fermi-level inside conduction band

Choose the correct answer from the options given below:

Two capacitors of capacitances \(C\) and \(2\, C\) are charged to potential differences \(V\) and \(2\, V\), respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is\(.....CV^2\)