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

The area bounded by \(x = 1, x = 2, xy = 1\) and x-axis is :

If the events A and B are independent, then which of the following statements are true?
(A) \(P\left(A^{\prime} \cap B\right)=[1-P(A)] P(B)\)
(B) A and B are mutually exclusive
(C) P(A) = P(B)
(D) \(P\left(A^{\prime} \cap B^{\prime}\right)=[1-P(A)][1-P(B)]\)
Choose the correct answer from the options given below:

\[\int e^x\left(1+x^2\right) d x=\]

\(\int \frac{\log _e x}{\left(1+\log _e x\right)^2} d x\)2 is equal to

Maximum value of the objective function Z = 4x + 3y subject to the constraints \(x+y \geq 4, x \geq 4, y \geq 0\) exists at

The probability distribution of a random variable X is given below:

x	-5	-4	-3	-2	-1	0	1	2	3	4	5
P(X)	p	2p	3p	4p	5p	7p	8p	9p	10p	11p	12p

Let \(\vec{a}=2 \hat{i}+3 \hat{j}+2 \hat{k}\) and \(\vec{b}=2 \hat{i}+\hat{j}-2 \hat{k}\). Then a vector of magnitude 24 , which is perpendicular to the vectors \(\vec{a}+\vec{b}\) and \(\vec{a}-\vec{b}\), is:

The local minimum value of the function \(f(x)=|x|+2\), where \(x\) is a real number is :

Identify the most stable complex.

For a non ideal solution exhibiting positive deviation:
A. The vapour pressure is lower than that predicted by Raoult's law
B. The vapour pressure is higher than that predicted by Raoult's law.
C. The interaction at the molecular level are weaker than in the pure state.
D. The interaction at the molecular level are stronger than in the pure state.
E. Mixture of chloroform and acetone is a suitable example.
Choose the correct answer from the options given below:

Read the given passage and answer the question.
ABO blood groups in human beings are controlled by the gene I. The plasma membrane of the red blood cells has sugar polymers that protrude from its surfaces and the kind of sugar is controlled by the gene. The gene (I) has three alleles IA, IB and I. The alleles IA and IB produce a slightly different form of the sugar while allele i does not produce any sugar. Because humans are diploid organisms, each person possesses any two of the three I gene alleles, IA and IB are completely dominant over I.
Match List - I with List - II.

List - I (Phenotype)	List - II (Genotype)
(A) Blood group A	(I) IB IB, IBi
(B) Blood group B	(II) IA, IA IA
(C) Blood group O	(III) IA IB
(D) Blood group AB	(IV) ii

Choose the correct answer from the options given below :

The point on the curve \(y^2=8 x\) for which the abscissa and ordinate change at the same rate, is