It is given that mean and variance of a binomial variate X are 2 and 1 respectively. Find the probability that X takes value greater than or equal to 1.

If \(x=e^y+e^y+\cdots\) to \(\infty, x>0\) then \(\frac{d^2 y}{d x^2}\) is:

For the given five values 16, 25, 19, 34, 46, the three years moving averages are:

Match List 1 with List 2.

List 1	List 2
(A) Perpetuity	(I) A person deposits a fixed amount every year in his bank account to renovate his house after \(10\) yrs.
(B) EMI	(II) A person deposits an amount regularly in his bank account and withdraws in case of need.
(C) Sinking Fund	(III) A fixed amount is debited from the bank account of a person, every month, against a personal loan.
(D) Saving Account	(IV) A person purchased a house and rents it out.

Choose the Correct answer from the options given below :

The maximum value of \(z=4 x+3 y\) subject to constraint \(x+y \leq 6, x, y \geq 0\) is:

Assume \(A, B\) and \(C\) are matrices of order \(m \times n, n \times 3\) and \(3 \times q\) respectively. The restrictions on \(m, n\) and \(q\) so that \(A B+B C\) is defined are

The number of all possible matrices of order \(3 \times 4\) with each entry 1, 2 or 3 are:

Read the passage carefully and answer the question
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.
Calculate the order of a reaction whose Rate = k[A]^1/2 [B]^3/2.

The oxidation number of Co in the complex \(\left[ Co \left( H _2 NCH _2 CH _2 NH _2\right)_3\right]_2\left( SO _4\right)_3\) is:

Two slits are made 0.8 mm apart and the screen is placed 1.5 m away. What should be the width of each slit to obtain 8 maxima of the double slit pattern within the central maximum of the single slit pattern?

Primary Alkyl halide \(\text{C}_4\text{H}_9\text{Br}\) (X) reacts with alcoholic \(\text{KOH}\) to give the compound (Y). Compound (Y) is reacted with \(\text{HBr}\)
to give (Z) which is an isomer of (X). When (X) is reacted with \(\text{Na/dry ether}\), it gives a compound (T), \(\text{C}_8\text{H}_{18}\), which is
different from the compound formed when n-butyl bromide is reacted with \(\text{Na/dry ether}\). The correct IUPAC name of (T) is:

Daily life phenomena based on scattering of light are
(A) Blue colour of sky
(B) Clouds appearing white
(C) Twinkling of stars
(D) Danger signals being red
Choose the correct answer from the options given below:

Which of the following represents Ohm's law for a conducting material?