\(20\,mL\) of \(0.02\,M\,K _{2} Cr _{2} O _{7}\) solution is used for the titration of \(10 \,mL\) of \(Fe ^{2+}\) solution in the acidic medium.The molarity of \(Fe ^{2+}\) solution is ........... \(\times 10^{-2}\,M\) (Nearest Integer)

Given below are two statements: Statement \(I\): Fluorine has most negative electron gain enthalpy in its group. Statement \(II\): Oxygen has least negative electron gain enthalpy in its group. In the light of the above statements, choose the most appropriate from the options given below.

The correct sequential addition of reagents in the preparation of \(3 -\)nitrobenzoic acid from benzene is:

The bond order and the magnetic characteristics of \(CN^-\) are

Number of compounds from the following which will not produce orange red precipitate with Benedict solution is \(..............\).  Glucose, maltose, sucrose, ribose,\(2-\)deoxyribose, amylose, lactose.

\(Pt ( s ) H _2( g )(1 bar )\left| H ^{+}( aq )(1 M )\right|\left| M ^{3+}( aq ), M ^{+}( aq )\right| Pt ( s )\) 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 : \(E _{ M ^{3+} / M ^{+}}=0.2\,V\) \(\frac{2.303 RT }{ F }=0.059\,V\)

The results given in the below table were obtained during kinetic studies of the following reaction: \(2 A + B \longrightarrow C + D\)

Experiment	\([ A ] / molL ^{-1}\)	\([ B ] / molL ^{-1}\)	Initial \(rate/molL\) \(^{-1}\) \(\min ^{-1}\)
\(I\)	\(0.1\)	\(0.1\)	\(6.00 \times 10^{-3}\)
\(II\)	\(0.1\)	\(0.2\)	\(2.40 \times 10^{-2}\)
\(III\)	\(0.2\)	\(0.1\)	\(1.20 \times 10^{-2}\)
\(IV\)	\(X\)	\(0.2\)	\(7.20 \times 10^{-2}\)
\(V\)	\(0.3\)	\(Y\)	\(2.88 \times 10^{-1}\)

\(X\) and \(Y\) in the given table are respectively :  

Statement \(I :\)Two forces \((\overrightarrow{{P}}+\overrightarrow{{Q}})\) and \((\overrightarrow{{P}}-\overrightarrow{{Q}})\) where \(\overrightarrow{{P}} \perp \overrightarrow{{Q}}\), when act at an angle \(\theta_{1}\) to each other, the magnitude of their resultant is \(\sqrt{3\left({P}^{2}+{Q}^{2}\right)}\), when they act at an angle \(\theta_{2}\), the magnitude of their resultant becomes \(\sqrt{2\left({P}^{2}+{Q}^{2}\right)}\). This is possible only when \(\theta_{1}<\theta_{2}\). Statement \(II :\) In the situation given above. \(\theta_{1}=60^{\circ} \text { and } \theta_{2}=90^{\circ}\) In the light of the above statements, choose the most appropriate answer from the options given below

If \(50\%\)  of a reaction occurs in \(100\) seconds and \(75\%\) of the reaction occurs in \(200\) seconds, the order of this reaction is

An electric field is given by \((6 \hat{i}+5 \hat{j}+3 \hat{k}) \ N / C\). The electric flux through a surface area \(30 \hat{\mathrm{i}}\; m^2\) lying in \(YZ-\)plane (in SI unit) is _______.

Let \(L\) be the line passing through the point \(P( 1, 2)\) such that its intercepted segment between the co-ordinate axes is bisected at \(P\). If \(L_1\) is the line perpendicular to \(L\) and passing through the point \((-2 , 1),\) then the point of intersection of \(L\) and \(L_1\) is

Three identical particle \(A , B\) and \(C\) of mass \(100\, kg\) each are placed in a straight line with \(AB = BC =13 \,m\). The gravitational force on a fourth particle \(P\) of the same mass is \(F\), when placed at a distance \(13 \,m\) from the particle \(B\) on the perpendicular bisector of the line \(AC\). The value of \(F\) will be approximately\(....G\)

The decreasing order of electrical conductivity of the following aqueous solutions is
\(0.1\, M\) Formic acid \((a)\)
\(0.1\, M\) Acetic acid \((b)\)
\(0.1\, M\) Benzoic acid \((c)\)