"Choose the reactions given by \(\text{Cr}_2\text{O}_7^{2-}\)
(A)\(\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6\text{Fe}^{2+} \rightarrow 2\text{Cr}^{3+} + 6\text{Fe}^{3+} + 7\text{H}_2\text{O}\)
(B) \(\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 3\text{H}_2\text{S} \rightarrow 2\text{Cr}^{3+} + 3\text{SO}_4^{2-} + 7\text{H}_2\text{O}\)
(C) \(\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 3\text{Sn}^{2+} \rightarrow 2\text{Cr}^{3+} + 3\text{Sn}^{4+} + 7\text{H}_2\text{O}\)
(D) \(\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ \rightarrow 3\text{Cr}^{3+} + 2\text{H}_2\text{O}\)
(E) \(\text{Cr}_2\text{O}_7^{2-} + 2\text{OH}^- \rightarrow 2\text{CrO}_4^{2-} + \text{H}_2\text{O}\)
Choose the correct answer from the options given below:"

In alcohols, C-O-H bond angle 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 half call reaction is the one that

The role of a catalyst is to change :

Which of the following defects are shown by \(\text{KCl}\) Crystal?
(A) Schottky defect
(B) Frenkel defect
(C) Metal excess defect
(D) Metal deficiency defect
Choose the correct answer from the options given below :

Zr and Hf (transition metals) occur together in nature and are difficult to separate. This can be attributed to

Why is HCl not used to make the medium acidic in oxidation reactions of KMnO₄ in acidic medium?

Match List - I with List - II.

List - I (lon)	List - II (Magnetic Moment (BM))
(A) \(V^{2+}\)	(1) 1.73
(A) \(Ni ^{2+}\)	(II) 3.87
(C) \(Cu ^{2+}\)	(III) 4.90
(D) \(Cr ^{2+}\)	(IV) 2.84

Choose the correct answer from the options given below :

Which of the following functions \(f(x)\) are differentiable at \(x=0\) ?
(A) \(|x|\)
(B) \(|x-1|\)
(C) \(|\sin x|\)
(D) \(|\cos x|\)
(E) \(x^2\)
Choose the correct answer from the options given below :

One face of a prism of refractive index 1.5 and angle \(75^{\circ}\) is covered with a liquid of refractive index \(\frac{3 \sqrt{2}}{4}\).
What should be the angle of incidence of light on the clear face of prism for which light is just totally reflected at the liquid covered face?

Match List I with List II

List I (Acronym)	List ll (Description)
(A) ZIFT	(I) Transfer of an ovum from a donor into the fallopian tube of another female.
(B) GIFT	(II) Semen collection from husband/healthy donor is artificially introduced into the uterus of the female.
(C) IUT	(III) Transfer of zygote or embryo of upto 8 blastomeres into fallopian tube.
(D) IUI	(IV) Transfer of embryo with more than 8 blastomeres into uterus.

Choose the correct answer from the options given below:

Let * be a binary operation defined on \(Q ^{+}\)(the set of positive rational numbers) by the rule \(a * b=\frac{a b}{7}\) for all \(a, b \in Q ^{+}\). Then inverse of \(2 * 7\) is:

The value of the integral \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos ^2 x d x\) is: