The de Broglie wavelength of a particle of mass 6.63 g moving with a velocity of \(100 \mathrm{~m} \mathrm{~s}^{-1}\) is:

Which of the following pairs has the same size?

If 2 moles of \(\mathrm{C}_6 \mathrm{H}_6(\mathrm{~g})\) are completely burnt \(4100 \mathrm{~kJ}\) of heat is liberated. If \(\Delta H^{\circ}\) for \(\mathrm{CO}_2(\mathrm{~g})\) and \(\mathrm{H}_2 \mathrm{O}(l)\) are -410 and \(-285 \mathrm{~kJ}\) per mole respectively then the heat of formation of \(\mathrm{C}_2 \mathrm{H}_6(\mathrm{~g})\) is

In a galvanic cell, the electrons flow from

A transition metal ion exists in its highest oxidation state. It is expected to behave as

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

In the detection of III group basic radicals \(\mathrm{NH}_{4} \mathrm{OH}\) is added after \(\mathrm{NH}_{4} \mathrm{Cl}\) to

-The solution of the differential equation \(\frac{d y}{d x}=(x+y)^{2}\) is

A motor bike is moving with a speed of \(36 \mathrm{~km} / \mathrm{h}\) along a straight road. The radius of its wheel and its moment of inertia about the axis of rotation are 40 cm and \(5 \mathrm{~kg} \mathrm{~m}^2\) respectively. What is the magnitude of the torque applied by the brake to the wheel so as to stop the bike in 10 s?

The value of \(c\) in Lagrange's mean value theorem for the function \(f(x)=\log (\sin x)\) in the interval \(\left[\frac{\pi}{6}, \frac{5 \pi}{6}\right]\) is

In the energy band diagram of a material shown below, open circles and filled circles denote holes and electrons respectively. The material is a

Let \(\alpha, \beta\) be the roots of the equation \(a x^{2}+b x+c=0\). A root of the equation \(a^{3} x^{2}+a b c x+c^{3}=0\) is

Let the line \(L_1\) be a line passing through the point \((0, -6)\) and making an angle of \(150^\circ\) with the positive \(x\)–axis. Then the equation of a line \(L_2\) parallel to \(L_1\) and crossing the \(y\)–axis 2 units below the origin is: