The side of an equilateral triangle is increasing at the rate of \(3 cm / sec\).
The rate at which the area of the triangle is increasing, when the side is 4 cm , is:

If the difference between mean and variance of a Binomial distribution is 1 and the difference of their squares is 5 , then the probability of success is

Out of the given statement, choose the correct statement.
(A) The direction ratios of the vector \(\vec{a}=3 \hat{i}-\hat{j}+4 \hat{k}\) is \(3,-1,4\).
(B) If \(\theta\) is the angle between two vectors \(\vec{a}\) and \(\vec{b}\), then their cross product is given as \(\vec{a} \times \vec{b}=|\vec{a}||\vec{b}| \cos \theta\).
(C) The unit vector in the direction of vector \(\vec{a}=\hat{i}+2 \hat{j}-2 \hat{k}\) is \(\hat{a}=\frac{1}{3}(\hat{i}+2 \hat{j}-2 \hat{k})\).
(D) If \(\vec{a}=3 \hat{i}\) and \(\vec{b}=4 \hat{j}\) then \(\vec{a} \cdot \vec{b}=12\).
(E) If \(\vec{a}\) and \(\vec{b}\) represent the adjacent sides of a triangle then its area is given of \(\frac{1}{2}|\vec{a} \times \vec{b}|\).
Choose the correct answer from the options given below :

The interval in which \(f(x)=\sin x-\cos x, 0 \leq x \leq 2 \pi\) is strictly decreasing is:

For a linear programming problem, the feasible region is shown in the figure by shaded portion, then linear constraints are

The slope of the normal to the curve \(y=x^3+3 x-2\) at its point of intersection with y-axis is:

The function \(f(x)=|x-3|, x \in R\) is:

Arrange the halogens in the increasing order of bond dissociation enthalpy :
(A) \(F_2\)
(B) \(Cl_2\)
(C) \(Br_2\)
(D) \(I_2\)
Choose the correct answer from the options given below :

The function \(f(x) = |x - 1|\) is

Match List-I with List-II:

List-I	List-II
(A) Current	(I) Opposition to flow of current
(B) Resistance	(II) Rate of flow of charge
(C) Resistivity	(III) Work done per unit charge
(D) EMF	(IV) Resistance per unit length \( \times \) unit cross sectional area

Choose the correct answer from the options given below:

Match List - I with List - II.

List - I	List - II
(A) The common region determined by all the constraints of LPP is called	(I) objective function
(B) Minimize \(z=c_1 x_1+c_2 x_2+\cdots+c_n x_n\) is	(II) convex set
(C) A solution that also satisfies the non-negative restrictions of a LPP is called	(III) feasible region
(D) The set of all feasible solutions of a LPP is a	(IV) feasible solution

Choose the correct answer from the options given below :

Identify X in the following nuclear reaction:
\( {}_{6}^{12}C + {}_{1}^{1}H \rightarrow X \)

Read the following paragraph carefully and answer the given questions.
In the year 1963 the two enzymes responsible for restricting the growth of bacteriophage in E. coli were isolated. The first restriction endonuclease - Hind II, whose functioning depended on a specific DNA nucleotide sequence was characterized five years later. It was found that Hind II always cut DNA molecules at a particular point by recognizing a specific sequence of six base pairs. This specific base sequence is known as the recognition sequence for Hind II. Besides Hind II, today we know more than 900 restriction enzymes that have been isolated from over 230 strains of bacteria, each of which recognize different recognition sequences.
When DNA from different sources is cut by the same restriction enzymes, the resultant DNA fragments have the :