Two cards are drawn with replacement from a pack of 52 cards.
The probability distribution of number of aces is:

A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be heart. Then the probability of the missing card to be a heart is:

The function \(f(x)=\left\{\begin{array}{ll}\frac{x^2+2 x-3}{x-1}, & \text { if } x \neq 1 \\ 0, & \text { if } x=1\end{array}\right.\) is

The total cost \(C(x)\) associated with the production of \(x\) units of an item is given by
\(\ C(x)=0.001 x^3+0.06 x^2+20 x+500\).
The marginal cost when 10 units are produced is:

Let \(A=\left[\begin{array}{ccc}1 & -2 & 3 \\ 1 & 2 & 1 \\ \lambda & 2 & -3\end{array}\right]\). If \(A^{-1}\) does not exist, then \(\lambda=\)

In a box containing 100 bulbs, 10 are defective.
The probability that out of a sample of 5 bulbs none is defective is:

For any square matrix \(A ;\left(A-A^{\prime}\right)\) is :

Read the passage carefully and answer the questions based on the passage:
The number of reacting species (atoms, ions or molecules) taking part in an elementary reaction, which must collide simultaneously in order to bring about a chemical reaction is called molecularity of a reaction. In the rate equation Rate \(=k[\mathrm{~A}]^x[\mathrm{~B}]^y\)
\(x\) and \(y\) indicate how sensitive the rate is to the change in concentration of A and B, respectively. Sum of these exponents, i.e., \(x +y\) gives the overall order of a reaction where \(x\) and \(y\) represent the order with respect to the reactants A and B respectively. Hence, the sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction. For a first order reaction, the concentration of the reactant varies as \([\mathrm{R}]=[\mathrm{R}]_0 e^{-k t}\)
Which of the following statements is not true for order of a reaction?

Amines are reactive in nature, mainly due to difference in electronegativity between Nitrogen and Hydrogen and, due to lone pair of electrons on Nitrogen. Amines behave like nucleophiles and as good lewis bases and there are various reactions to support this. Different degree of amines differ in their reactivity due to steric hinderance and electronic effects. Aromatic amines are less basic due to + R effect, hence have higher pkb value than aliphatic amines. Basic strength of amines also depends on stability of corresponding conjugate acid in aqueous medium.
Which of the following will be having lowest \(p K_b\) in gaseous medium?

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 :

Industrial melanism is an observation which supports evolution by:

The steps of PCR (Polymerase Chain Reaction) are given below. Arrange them in a correct sequence.
A. Extension of primers
B. Denaturation of DNA fragments by heating
C. Amplified DNA fragments
D. Annealing of primers
Choose the correct answer from the options given below:

Bacillus thuringiensis produces Bt toxin crystals it does not kill the bacterium itself as the toxin is in the: