If a random variable \(X\) has the following probability distribution :

X	0	1	2	3	4
P(X)	k	2k	3k	\(k^2\)	\(6 k^2\)

then Match List-I with List-II

List-I	List-II
(A) k	(I) 3/7
(B) \(P(x<2)\)	(II) \(6 / 49\)
(C) \(P(X>3)\)	(III) \(1 / 7\)
(D) \(P(2 \leq X \leq 3)\)	(IV) 22/49

Choose the correct answer from the options given below :

Let \(\vec{a}=3 \hat{i}+\hat{j}-4 \hat{k}\) and \(\vec{b}=6 \hat{i}+5 \hat{j}-2 \hat{k}\) be two vectors.
Then a vector perpendicular to both \(\vec{a}\) and \(\vec{b}\) with magnitude 3 units is :

If \(r_{e f f}=\) effective rate of interest, \(r=\) nominal rate of interest and \(m=\) number of conversion periods per year, the relationship between nominal rate and effective rate of interest is :

Rakshita plans to buy a house for Rs. 1,00,00,000 with down payment of 20% of the value of the house paid by her mother. Rest of the amount she wishes to pay in 25 years by equal monthly instalments at an interest of 9% per annum compounded monthly Then the EMI paid by her is \(\left(\right.\) Given \(\left.(1.0075)^{300}=9\right)\) :

Let A be a square matrix of order n, then which of the following are TRUE?
(A) \(|\operatorname{adj} A|=|A|^{n-1}\)
(B) \(|A \cdot \operatorname{adj} A|=|A|^n\)
(C) A. (adj A) = |A|
(D) |KA| = K|A|
(E) \(\left|A^{-1}\right|=\frac{1}{|A|},|A| \neq 0\)
Choose the correct answert from the option given below :

The values of \(a\) for which the function \(f(x)=a^x\) is increasing on \(R\) are given by :

If \(\left[\begin{array}{cc}4 x & 5 x-7 \\ 4 x & 2 x+y\end{array}\right]=\left[\begin{array}{cc}x+6 & y \\ 7 y-13 & 7\end{array}\right]\) then the value of \(2 x+y\) is:

Read the passage carefully and answer the questions
The speed at which a chemical reaction takes place is called the rate of reaction. The rate of reaction depends on various factors like concentration of the reactants, temperature, etc. The relation between the rate of reaction and the concentration of reacting species is represented by the equation r = k[A]^x[B]^y, where x and y are the order of the reaction with respect to the reactants A and B, respectively. The overall order of the reaction is x + y. The rate of reaction can also be increased by the use of a catalyst which provides an alternate pathway of lower activation energy. It increases the rate of forward and backward reaction to an equal extent. It does not alter the Gibbs energy of the reaction.
The rate law of a reaction is given by r = k[CH₃OCH₃]^3/2. If the pressure is measured in bar and time in minutes, then the unit of rate constant will be

The calculated magnetic moment using the 'spin only' formula \(\mu=\sqrt{n(n+2)}\) for \(\mathrm{Cr}^{2+}\) and \(\mathrm{Fe}^{2+}\) respectively is

Arrange the following alcohols in increasing order of their boiling points.
(A) Propan-1-ol
(B) Butan-2-ol
(C) Butan-1-ol
(D) Pentan-1-ol
Choose the correct answer from the options given below:

If some blood cells are placed in a solution containing more than \(0 . 9 \% ( m / v ) N a C l\), then the water inside the cells will flow out of the cells and they will shrink. Such a solution is known as

The IUPAC name of the coordination compound \(\left[ CoCl _2( en )_2\right]^{+}\)is :

Read the following passage given below and answer the question.
Production of electricity by thermal plants is not very efficient method. It is now possible to make cells in which reactants are fed continuously to the electrodes and products are also removed continuously. One of the most successful fuel cells is hydrogen fuel cell.
Which of the following statement is correct regarding hydrogen fuel cells?