The area (in sq. units) of the region bounded by the curve \(y=\sin x,-2 \pi \leq x \leq 2 \pi\) and the \(x\)-axis is :

The angle between the two planes \(x+y-z=3\) and \(3 x+2 y+z=5\) is:

The solution of the differential equation \(\frac{d y}{d x}=\frac{a x+c}{b y+d}\) represents a circle when

A random variable X has the following probability distribution :

X	0	1	2	3
P(X)	0.1	0.2	0.3	0.4

The variance of the X will be :

The value of \(\int_{-1}^1\left|x^3-x\right| d x\) is

Relation \(R\) on the set \(A=\{1,2,\)...,\(15\}\) defined as \(R=\{(x, y): y-4 x=0\}\) is

The points of discontinuity of the function \(f\) defined by \(f(x)=\begin{cases} x + 2 & x \leq 1 \\x - 2 & 1 < x < 2\text { are: } \\0 & x \geq 2 \end{cases}\)

Read the following passage carefully and answer the given questions.
Theory of Evolution
The evolution of life is a gradual process through which simple organisms are transformed into complex life forms over billions of years. It involves genetic changes, adaptation to the environment, and the emergence of diversity in species. Fossil records provide evidence of extinct life forms and transitional stages. Evolution is influenced by factors such as mutation, genetic recombination, and environmental pressure, shaping the biodiversity we see today. Charles Darwin and Alfred Russel Wallace were pioneering naturalists who developed the theory of evolution by natural selection.
According to Darwin, the term 'Fitness' in the context of natural selection refers to:

Arrange the following nuclei in the increasing order of their binding energy per nucleon: \( ^4\text{He}, ^6_3\text{Li}, ^{56}_{26}\text{Fe}, ^{238}_{92}\text{U} \)

The number of all possible matrices of order 3 with each entry either 0 or 1 is :

First meiotic division of primary follicles completes in the

Match List I with List II.

LIST I	LIST II
A. Agarose	I. Polymerase chain reaction
B. Thermostable DNA polymerase	II. Electrophoresis
C. Micro injection	III. Ampicillin resistance gene
D. Selectable marker	IV. Introduction of alien DNA in animal cell

Choose the correct answer from the options given below:

\( P_1, P_2, P_3 \) are three Polaroid sheets; \( P_1 \) and \( P_3 \) are two crossed polaroids. What should be the angle between Polaroids \( P_1 \) and \( P_2 \), so that the value of \( I' = I_0/4 \)? (Where \( I' \) is intensity after \( P_2 \))