Equation of a plane with intercept \(\sqrt{3}\) on z -axis and parallel to XOY plane is :

The value of integral \(\int \frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha} d x\), where \(\alpha\) is a constant is :

If it is 7:00 pm currently in the clock, what will the clock show (in am or pm) after 674 hours?

If X is a normal variate with mean 16 and standard deviation 4, then the value of the standard normal variate Z corresponding to X = 17 is :

The value of \(\int_{-3}^2 x^2|2 x| d x\) is :

The order and degree of the differential equation \(\frac{d^2 y}{d x^2}+3\left(\frac{d y}{d x}\right)^3+4 y=0\) are :

If X is a random variable with probability distribution as given below:

X	0	1	2	3
P(X)	K	2K	K	3K

Then, the variance of the distribution is:

The external diameter of a 5 m long hollow copper tube is 10 cm and the wall thickness is 5 mm. If the specific resistance of copper is \( 1.7 \times 10^{-8} \text{ }\Omega\text{m} \), the resistance of the tube will be:

The solution of the differential equation \(\frac{d r}{d t}=-r t, r(0)=r_0\) is

The magnetic field at the centre of a closely wound circular coil of 100 turns, radius 22 cm, carrying a current of 3.5 A will be

Read the passage carefully and answer
When a metal is placed in a solution of its ions, the metal can lose electron and can go in the solution as ion or the metal ion in the solution can take electron from the electrode and get deposited as metal. Thus, the electrode acquires either positive or negative charge with respect to the solution leading to the development of a potential difference between the metal electrode and the solution. This potential difference is called the electrode potential of the metal. The electrode potential of a metal is a measure of relative tendency to undergo oxidation (loss of electron) or reduction (gain of electron). When the concentration of the ions in the solution is unity, the electrode potential is called standard electrode potential. The magni of potential depends upon the nature of electrode, concentration of ions in solution and the temperature. In a galvanic cell, the electrode at which oxidation occurs is known as anodic half-cell and the electrode at which reduction occurs is known as cathodic half cell. The emf of the cell in terms of standard reduction potential is given by \(E_{\text {cell }}^{\circ}=E_{\text {cathode }}^{\circ}-E_{\text {anode. }}^{\circ}\).The standard free energy change of the redox reaction taking place in the cell is related to \(E_{\text {cell }}^{\circ}\) by \(\Delta G^{\circ}=-n F E^{\circ}\). A redox reaction would occur spontaneously if the free energy change is negative. The equilibrium constant of the reaction is related to the standard free energy change by \(\Delta G^{\circ}=-R T \ln K\).
The standard reduction potential of Zinc is represented by the reaction

Some heat is developed in a uniform metallic wire across the ends of which a constant voltage V is applied. The heat developed will be tripled if

The amine which will not undergo benzoylation in alkaline medium is