The total number of compounds from below when treated with hot \(\text{KMnO} _4\) giving benzoic acid is _______.

\(Pt ( s ) H _2( g )(1 bar )\left| H ^{+}( aq )(1 M )\right|\left| M ^{3+}( aq ), M ^{+}( aq )\right| Pt ( s )\) The \(E _{\text {ceil }}\) for the given cell is \(0.1115\,V\) at \(298\,K\) when \(\frac{\left[ M ^{+}( aq )\right]}{\left[ M ^{3+}( aq )\right]}=10^{ a }\) The value of a is Given : \(E _{ M ^{3+} / M ^{+}}=0.2\,V\) \(\frac{2.303 RT }{ F }=0.059\,V\)

\(200\; mL\) of \(0.01\; M\; HCl\) is mixed with \(400 \;mL\) of \(0.01\; M\; H _{2} SO _{4}\). The \(pH\) of the mixture is

Given below are two statements:
Statement I: In the oxalic acid vs \(\mathrm{KMnO}_4\) (in the presence of dil \(\mathrm{H}_2 \mathrm{SO}_4\) ) titration the solution needs to be heated initially to \(60^{\circ} \mathrm{C}\), but no heating is required in Ferrous ammonium sulphate (FAS) vs \(\mathrm{KMnO}_4\) titration (in the presence of dil \(\mathrm{H}_2 \mathrm{SO}_4\) )
Statement II: In oxalic acid vs \(\mathrm{KMnO}_4\) titration, the initial formation of \(\mathrm{MnSO}_4\) takes place at high temperature, which then acts as catalyst for further reaction. In the case of FAS vs \(\mathrm{KMnO}_4\), heating oxidizes \(\mathrm{Fe}^{2+}\) into \(\mathrm{Fe}^{3+}\) by oxygen of air and error may be introduced in the experiment.
In the light of the above statements, choose the correct answer from the options given below

\(IUPAC\) name of following compound \((\mathrm{P})\) is 

A \(100\,mL\) solution of \(CH _{3} CH _{2} MgBr\) on treatment with methanol produces \(2.24\,mL\) of a gas at \(STP\). The weight of gas produced is \(......mg\). [nearest integer]

In Dumas method for estimation of nitrogen, 0.50 g of an organic compound gave 70 mL of nitrogen collected at 300 K and 715 mm pressure. The percentage of nitrogen in the organic compound is ______ \( \% \)
(Aqueous tension at 300 K is 15 mm).

Read the following statements: \(A.\) When small temperature difference between a liquid and its surrounding is doubled the rate of loss of heat of the liquid becomes twice. \(B.\) Two bodies \(P\) and \(Q\) having equal surface areas are maintained at temperature \(10^{\circ}\,C\) and \(20^{\circ}\,C\). The thermal radiation emitted in a given time by \(P\) and \(Q\) are in the ratio \(1: 1.15\) \(C.\) A carnot Engine working between \(100\,K\) and \(400\,K\) has an efficiency of \(75 \%\) \(D.\) When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice. Choose the correct answer from the options given below :

The number of \(3\)-\(digit\) odd numbers, whose sum of digits is a multiple of \(7\) , is

The line \(x =8\) is the directrix of the ellipse \(E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) with the corresponding focus \((2,0)\). If the tangent to \(E\) at the point \(P\) in the first quadrant passes through the point \((0,4 \sqrt{3})\) and intersects the \(x\)-axis at \(Q\), then \((3PQ)^2\) is equal to \(........\)

It is true that :

If electric field intensity of a uniform plane electro magnetic wave is given as \(E =-301.6 \sin ( kz -\omega t ) \hat{a}_{ x }+452.4 \sin ( kz -\omega t )\) \(\hat{a}_{y} \frac{V}{m}\) Then, magnetic intensity \(H\) of this wave in \(Am ^{-1}\) will be [Given: Speed of light in vacuum \(c =3 \times 10^{8} ms ^{-1}\), permeability of vacuum \(\mu_{0}=4 \pi \times 10^{-7} NA ^{-2}\) ]

A wire carrying current \(I\) is bent in the shape \(A\,B\,C\,D\,E\,F\,A\) as shown, where rectangle \(A\,B\,C\,D\,A\) and \(A\,D\,E\,F\,A\) are perpendicular to each other. If the sides of the rectangles are of lengths \(a\) and \(b,\) then the magnitude and direction of magnetic moment of the loop \(A\,B\,C\,D\,E\,F\,A\,\) is