In the decay chain given below the sequential order in which the radioactive radiations are emitted will be :
\(^{A}_{Z}X \to ^{A}_{Z+1}Y \to ^{A-4}_{Z-1}P^* \to ^{A-4}_{Z-1}P\)

A p-type semiconductor can be obtained by doping of:

Arrange these in ascending order of wavelength while propagating through different medium.
(A) Light propagating in air
(B) Light propagating in water
(C) Light propagating in diamond
(D) Light propagating in glass
Choose the correct answer from the options given below :

Which of the following is NOT em wave ?

Two sources are producing waves as given in the options below. Which two sources are called coherent ?

A capacitor of \( 25 \mu \text{F} \) is connected in series with d.c Voltage of 5 V. The value of current in the circuit will be:

In a Hydrogen atom there is transition of electron from one orbit to another. Choose the correct option given below in which the emitted photon will have the highest frequency?

The maximum value of \((\sin x)(\cos x)\) is :

If \(c_{i j}\) denotes the cofactor of element \(c_{i j}\) of the matrix \(A=\left[\begin{array}{ccc}1 & 2 & -1 \\ 0 & -3 & 2 \\ 4 & 2 & 3\end{array}\right]\), then the value of \(c_{21} \cdot c_{33}\) is

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

Match List - I with List - II.

List - I	List - II
(A) Leydig cells	(I) Release of sperm from seminiferous tubules
(B) Sertoli cells	(II) Transformation of spermatids to spermatozoa.
(C) Spermiogenesis	(III) Nutrition to growing sperms
(D) Spermiation	(IV) Androgens

Choose the correct answer from the options given below:

Match List - I with List - II

List - I	List - II
(A) \(\int \frac{d x}{a^2-x^2}\)	(I) \(\frac{1}{2 a} \log \left|\frac{x-a}{x+a}\right|+C\)
(B) \(\int \frac{d x}{x^2-a^2}\)	(II) \(\frac{1}{2 a} \log \left|\frac{a+x}{a-x}\right|+C\)
(C) \(\int \frac{d x}{x^2+a^2}\)	(III) \(\sin ^{-1}\left(\frac{x}{a}\right)+C\)
(D) \(\int \frac{d x}{\sqrt{a^2-x^2}}\)	(IV) \(\frac{1}{a} \tan ^{-1} \frac{x}{a}+C\)

Choose the correct answer from the options given below:

What is the correct order of following steps in the preparation of potassiu Solutionm permanganate?
(A) disproportionation in a neutral or acidic solution
(B) production of dark green \(K _2 MnO _4\)
(C) \(MnO _2\)
(D) fusion with alkali metal hydroxide and \(KNO _3\)
Choose the correct answer from the options given below: