For a random variable z, probability distribution P(x) is given by \(P(x)=\frac{k}{6}(3-x), x=0,1,2\) then Match List-I with List-II

List-I	List-II
(A) \(k\) is equal to	(I)\(\frac{1}{2}\)
(B) \(P(x=0)\)	(II) 1
(C) \(P(x<2)\)	(III) \(\frac{1}{6}\)
(D) \(P(1<x \leq 2)\)	(IV) \(\frac{5}{6}\)

Choose the correct answer from the options given below:

\(\int \frac{\cos x-\sin x}{1+\sin 2 x} d x\) is equal to

For \(x \in[-2,2]\), let \(f(x)=x^2+2\).
A. \(f(x)\) is continuous in \([-2,2]\)
B. \(f(x)\) is differentiable in \((-2,2)\)
C. \(f(-2)=f(2)=6\)
D. \(f^{\prime}(1)=0\)
Choose the correct answer from the options given below:

Corner points of the feasible region for a linear programming problem are \((0,2),(3,0),(6,0),(6,8)\) and \((0,5)\). Let \(F=4 x+6 y\) be the objective function. Then the minimum value of \(F\) occurs at :

\(\int \frac{\cos x - \sin x}{1 + \sin 2x} dx\) is equal to:

The area of the region bounded by the curves \(y=x^2+2, y=x, x=0\) and \(x=2\) is

The variance of the Binomial Distribution \(B\left(5, \frac{1}{4}\right)\) is:

The role of a catalyst is to change :

Molar mass of a non-volatile solute (in g/mol) in its \(10\%\) by mass aqueous solution showing \(2\%\) decrease in its vapour pressure is :

Choose the correct statements from the following :
(A) two different solutions of sucrose of same molality prepared in different solventswill have the same depression in freezing point.
(B) the osmotic pressure of a solution is given by the equation \(II = CRT\) (where C is the molarity of the solution)
(C) decreasing order of osmotic pressure for 0.01 M aqueous solution of \(BaCl _2, KCl , CH _3 COOH\), and sucrose is \(BaCl _2 > KCl > CH _3 COOH >\) sucrose
(D) according to Raoult's law the vapor pressure exerted by a volatile component of asolution is directly proportional to its mole fraction in the solution
Choose the correct answer from the options given below :

Which one of the following is a correct statement about dormancy?

If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three unit vectors such that \(\vec{a}+2 \vec{b}-3 \vec{c}=\overrightarrow{0}\), then the value of \(2 \vec{a} \cdot \vec{b}-6 \vec{b} \cdot \vec{c}-3 \vec{c} \cdot \vec{a}\) is

When an n-p-n transistor is used as an amplifier, then :