Consider the following statements with respect to Probability distribution:
(A) In a given sample space not more than four random variables can be defined
(B) Mean expectation value is a parameter and not a statistic
(C) In a Gaussain distribution if only mean and mode are same it is said to be normally distributed
(D) Probability of 'r' success in 'n' Bernoulli is P(r) = \({ }^n C_r q^r p^{n-r}\)
(E) Variance enables us to study the variability of a random variable from the mean expectation

Choose the correct answer from the options given below:

In a binomial distribution, the probability of getting success is \(1 / 4\) and standard deviation is 3 . Then it's mean is:

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

For the L.P.P. Maximize \(z=10 x+6 y\) subjected to
\(3 x+y \leq 12\)
\(2 x+5 y \leq 34\)
\(x, y \geq 0\)
Then the feasible region represented by system of inequalities is

The value of \(\int_{-\pi / 6}^{\pi / 6}\left(4 x^5+x \sin ^2 x+\tan ^3 x+2\right) d x\) is :

Particular solution of the differential equation \(x\left(1+y^2\right) d x-y\left(1+x^2\right) d y=0\), given that \(y=0\) when \(x=1\), is:

The linear programming problem : minimise \(z=3 x+2 y\)
subject to the constraints \(x+y \geq 8,3 x+5 y \leq 15, x \geq 0, y \geq 0\)
has

Read the passage carefully and answer the questions
Many halogen containing organic compounds are present in nature and some of them are clinically useful. These classes of organic compounds find a wide range of applications in our daily life as well as in industries. Many of the polyhalogen compounds are useful too in agriculture. However, some of these compounds cannot be easily decomposed and are thus considered to be environmental hazards. These halo compounds are prepared via different synthetic routes where a variety of organic compounds can be used as substrates such as amines, hydrocarbons etc. They are used as solvents for relatively non-polar compounds. These compounds exhibit substitution and elimination reactions, in addition to their reactions with different metals, which leads to the formation of a versatile starting material for others organic compounds.
Alkyl halides react with sodium in dry ether and give hydrocarbon containing double the number of carbon atom present in the halides. The reaction is known as:

Read the given paragraph and answer the question:
Humans have 23 pairs of chromosomes. 22 pairs are exactly same in both males and females; these are the autosomes. A pair of X-chromosome are present in the female, whereas the presence of an X and Y chromosome are determinant of the male characteristic.
A number of disorders in human beings have been found to be associated with the inheritance of changed or altered genes or chromosomes. Broadly, genetic disorder may be grouped into two categories-Mendelian disorders and Chromosomal disorders
Which of the following is an example of a sex linked disease?

Four identical bulbs are connected in series with a source. These together dissipate a power P. The power dissipated, if the four bulbs are connected in parallel with the same source, will be

What do you understand by termolecular reactions:

Arrange the following acids in increasing order of their acidic strengths: \(HCOOH , FCH _2 COOH , NO _2 CH _2 COOH , ClCH _2 COOH\)

Rusting occurs in the presence of water and air.