The temperature \((\mathrm{T})\) and rate constant \((\mathrm{k})\) for a first order reaction \(\mathrm{R} \rightarrow \mathrm{P}\), was found to follow the equation \(\log \mathrm{k}=-(2000) \dfrac{1}{\mathrm{~T}}+8.0\). The pre-exponential factor '\(\mathrm{A}\)' and activation energy \(\mathrm{E}_{\mathrm{a}}\), respectively are: [Given: \(\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\)]

The total number of nodes are given by

In which one of the following pairs does the stability of the monovalent ion increase with respect to the molecule, while the magnetic character remains the same for both?

The correct decreasing order of negative electron gain enthalpy for \(\mathrm{C}, \mathrm{Ca}, \mathrm{Al}, \mathrm{F}\) and \(\mathrm{O}\) is

Match the reactions in Column I with the correct products given in Column II:
\(\begin{array}{|l|l|l|l|} \hline \text{S.N.} & \text{Column I} & \text{S.No.} & \text{Column II} \\ \hline \text{A} & 1- \text{Chloropropane} + (\mathrm{Zn} / \mathrm{HCl}) \rightarrow & \text{P} & \text{Propanone + Methanal} \\ \hline \text{B} & n- \text{Hexane + (anh.} \left.\mathrm{AlCl}_3 / \mathrm{HCl}_{(\mathrm{g})}\right) \rightarrow & \text{Q} & \text{Propanone} \\ \hline \text{C} & 2- \text{Methylpropene} + ( \left.\mathrm{O}_3 ~\&~ \mathrm{Zn} / \mathrm{H}_2 \mathrm{O}\right) \rightarrow & \text{R} & \text{Propane} \\ \hline \text{D} & \text{Propyne} +\left(\mathrm{HgSO}_4 / \mathrm{H}_2 \mathrm{SO}_4\right. at 333 K) \rightarrow & \text{S} & \text{2-Methylpentane + 3-Methylpentane} \\ \hline \end{array}\)

On treatment of glucose with bromine water the product formed is

At Constant volume, the heat required to raise the temperature of \(4.48 \mathrm{~L}\) of an ideal gas at STP by \(15^{\circ} \mathrm{C}\) is 12.0 calories.
The \(\mathrm{C_p}\) of the gas is _____________
\((\mathrm{R}=2 \mathrm{~Cal} \mathrm{~kg}^{-1} \mathrm{~mol}^{-1})\)

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

The maximum current that can be measured by a galvanometer of resistance \(40 ~\Omega\), is \(10 \mathrm{~mA}\). It is converted into a voltmeter that can read upto \(50 \mathrm{~V}\). The resistance to be connected in series with the galvanometer (in \(\Omega\) ) is

A ball falls under gravity from a height of 10m with an initial downward velocity \(u\). It loses three-fifths (or 60%) of its energy in collision and then rises back to 5m. The initial velocity \(u\) is (\(g = 10 \text{ ms}^{-2}\))

What is the minimum band-gap of the LED diode?

The resistance of mercury at \(4.2 \mathrm{~K}\) is

If \(f(x)\) is defined in \([-2,2]\) by \(f(x)=4 x^{2}-3 x+1\) and \(g(x)=\frac{f(-x)-f(x)}{\left(x^{2}+3\right)}\), then \(\int_{-2}^{2} g(x) d x=\)