Area (in sq. units) of the region bounded by the curve \(y^2=4 x, y\)-axis and the line \(y=3\) is

A bond of face value ₹1000 has a coupon rate 10% per annum paid semi-annually and matures in 4 years. If present value of the bond is ₹1100, then yield to maturity is:

The probability distribution of a random variable \(x\) is, \(P(x)=\frac{k}{2^x}, x=0,1,2,3\). Then
Match List-I with List-II

List-I	List-II
(A) k	(I) \(\frac{2}{15}\)
(B) \(P ( x =1)\)	(II) \(\frac{1}{5}\)
(C) \(P (1<x<3)\)	(III) \(\frac{8}{15}\)
(D) \(P(x \geq 2)\)	(IV) \(\frac{4}{15}\)

Choose the correct answer from the options given below :

The solution set of the inequation \(|2 x-3| \leq 4\) is

If \(\vec{a}+\lambda \vec{b}\) is perpendicular to \(\vec{c}\), where
\(\vec{a}=-\hat{i}+2 \hat{j}+\hat{k}, \vec{b}=3 \hat{i}+2 \hat{j}+\hat{k}\), and \(\vec{c}=\hat{i}-\hat{j}\),
then :

The system of linear equations \(k x+5 y=5,2 x+3 y=5\) will be consistent if

The demand function for a commodity is \(p=35-2 x-x^2\), then the consumer's surplus at equilibrium price \(p_0=20\) is

Read the following passage carefully and answer the given questions.
Insulin consists of two short polypeptide chains- chain A and chain B, that are linked together by disulphide bridges. Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans, coleopterans and dipterans. Bt toxin protein is converted into an active form of toxin due to the alkaline pH of the gut which solubilise the crystals. Transgenic animals that produce useful biological products can be created by the introduction of the portion of DNA (or genes) which codes for a particular product such as human protein (alpha-1-antitrypsin) used to treat emphysema. Plants, bacteria, fungi and animals whose genes have been altered by manipulation are called Genetically Modified Organisms (GMO). GM plants have been useful in many ways. Genetic modification has: (i) made crops more tolerant to abiotic stresses. (ii) reduced reliance on chemical pesticides (pest-resistant crops). (iii) helped to reduce post harvest losses. (iv) increased efficiency of mineral usage by plants (this prevents early exhaustion of fertility of soil). (v) enhanced nutritional value of food.
Transgenic animals that produce useful biological products such as human protein (alpha-1-antitrypsin) used to treat the disorder:

The function \(f: Z \rightarrow Z\) defined by \(f(x)=x^2+x\), where \(Z\) is the set of integers, is:

The angle between two vectors \(\vec{a}\) and \(\vec{b}\) with magnitudes \(\sqrt{3}\) and 4 respectively and \(\vec{a} \cdot \vec{b}=2 \sqrt{3}\) is :

If \(y=\sin ^{-1} x\), then \(\left(1-x^2\right) \frac{d^2 y}{d x^2}\) is equal to

A system of three charges -q, + Q and -q are placed at three points at equal distances on a straight line in the same order. If the potential energy of the system is found to be zero, find the ratio Q/q.

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