Using the data given below, the strongest reducing agent is:
\(E^o_{\text{Cr}_2\text{O}_7^{2-}/\text{Cr}^{3+}} = 1.33\) V    \(E^o_{\text{MnO}_4^-/\text{Mn}^{2+}} = 1.51\) V
\(E^o_{\text{Cl}_2/\text{Cl}^-} = 1.36\) V    \(E^o_{\text{Cr}^{3+}/\text{Cr}} = -0.74\) V

An organic compound \([\mathrm{A}]\left(\mathrm{C}_5 \mathrm{H}_{12} \mathrm{O}\right)\), on reaction with conc. \(\mathrm{H}_2 \mathrm{SO}_4\) at \(443 \mathrm{~K}\) gives \([\mathrm{B}]\) as one of the products. Compound [B] undergoes further reaction with \(\mathrm{O}_3\) and \(\mathrm{Zn} / \mathrm{H}_2 \mathrm{O}\) to give Propanone and Ethanal as products. Identify compound [A]

Mesomeric effect involves delocalisation of

Which of the following is correct order of their increasing boiling points?

Match \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) and D with the appropriate functions given.
\(\begin{array}{|l|l|l|l|} \hline & \text { Column I } & & \text { Functions } \\ \hline \text { A } & \text { Oxidoreductase } & \text { P } & \text { Malfunctioning leads to Addison's disease. } \\ \hline \text { B } & \text { Phosphodiester bonds } & \text { Q } & \text { Regulates responses to external stimuli. } \\ \hline \text { C } & \text { Adrenal cortex } & \text { R } & \text { Catalyses glycolysis. } \\ \hline \text { D } & \text { Epinephrine. } & \text { S } & \text { Links nucleotides together. } \\ \hline \end{array}\)

Aqueous \(\mathrm{CuSO}_4\) changes its colour from sky blue to deep blue on addition of \(\mathrm{NH}_3\) because

The reactions taking place with \(\mathrm{2- Phenyl-2-bromopropane}\) as the starting material is shown below. Identify [A] and [B] formed in the reaction.
\(
\mathrm{C}_6 \mathrm{H}_5-\mathrm{C}\left(\mathrm{CH}_3\right)_2^{-} \mathrm{Br} \xrightarrow[\Delta]{\text { KOH Alcoholic }}[\mathrm{A}]
\)
\(
[\mathrm{A}]+\mathrm{HBr} \xrightarrow{\left(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CO})_2 \mathrm{O}\right.}[\mathrm{B}]\)

The conductivity of 0.01 M solution of \(\mathrm{CH}_3 \mathrm{COOH}\) at 298 K is \(1.65 \times 10^{-4} \mathrm{Scm}^{-1}\)
What is the \(\mathrm{pK}_{\mathrm{a}}\) value of the acid if \(\lambda^0\left(\mathrm{H}^{+}\right)\)and \(\lambda^0\left(\mathrm{CH}_3 \mathrm{COO}\right)^{-1}\) are \(349.1 \mathrm{Scm}^2 \mathrm{~mol}^{-1}\) and \(40.9 \mathrm{Scm}^2 \mathrm{~mol}^{-1}\) respectively?

The particular solution of \(e^{\dfrac{d y}{d x}}=2 x+1\) given that \(y=1\) when \(x=0\) is

Identify the property which is not characteristic for a semi-conductor.

Given, two vectors \(\hat{\hat{i}}-\hat{\mathfrak{j}}\) and \(\hat{\hat{i}}-2 \hat{\mathfrak{j}}\). The unit vector, coplanar with the two given vectors and perpendicular to \((\hat{\hat{\mathbf{i}}}-\hat{\hat{\mathfrak{j}}})\) is

Solve the following differential equation \(\cos ^2 x \dfrac{d y}{d x}+y=\tan x\), given that \(y(0)=1\). Hence find \(y\left(\dfrac{\pi}{4}\right)\)

If \(\sin A+\sin B=-\dfrac{21}{65}, \cos A+\cos B=-\dfrac{27}{65}\) and \(\pi < A-B < 3 \pi\), then the value of \(\cos \left(\dfrac{A-B}{2}\right)\) is