If \(A=\left[\begin{array}{cc}2 & 3 \\ -1 & 1\end{array}\right]\) and \(A^2-3 A+k I=0\), then the value of \(k\) is:

A coin is tossed 3 times. If \(X\) denotes the number of heads, then Match List I with List II

LIST I	LIST II
A. \(P(X=0)\)	I. \(\frac{1}{8}\)
B. \(P(X=1)\)	ㅍ. \(\frac{7}{8}\)
C. \(P(X \leq 2)\)	III. \(\frac{4}{8}\)
D. \(P(X \geq 2)\)	IV. \(\frac{3}{8}\)

Choose the correct answer from the options given below:

A random variable \(X\) follows Poisson distribution such that P(X = 1) = 2P(X = 2), then P(X = 0) is:

The value of \(\cot ^{-1}\left[2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right]\) is

Match List - I with List - II.

List - I	List - II
(A) \(\left(y^{\prime \prime}\right)^3+\sin \left(y^{\prime}\right)=e^x\)	(I) 2
(B) \(\left(y^{\prime \prime}\right)^2+\left(y^{\prime}\right)^3=\sin x\)	(II) 1
(C) \(y^{\prime \prime \prime}+5 y^{\prime \prime}+6 y^{\prime}+3 y=\cos x\)	(III) Not defined
	(IV) 3

Choose the correct answer from the options given below :

The value of \(\int\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)^2 d x\) is:

If \(P(A)=\frac{2}{5}, P(B)=\frac{3}{10}\) and \(P(A \cap B)=\frac{1}{5}\), then \(P\left(A^{\prime} / B^{\prime}\right) \cdot P\left(B^{\prime} / A^{\prime}\right)\) is equal to :

The magnetic flux \(\Phi\), linked with a coil of resistance 5 \(\Omega\) varies with time as \(\Phi = (5t^2 - 4t + 1)\text{Wb}\). The current induced in the coil at 0.2 s is :

Which of the following is not the saleint feature of Human Genome Project (HGP)?

The thermostable DNA polymerase is isolated from the bacterium:

Read the passage carefully and answer the questions:
Optically active polyhydroxy aldehydes or ketones or molecules which provide such units on hydrolysis are called carbohydrates. They can be broadly classified as monosaccharides, disaccharides and polysaccharides depending on their behavior towards hydrolysis. They are also classified as reducing or non-reducing sugars. Another class of biomolecules is proteins which are polymers of twenty different amino acids linked by peptide bonds. Amino acids can be classified as acidic, basic or neutral depending on the relative number of amino and carboxyl groups in their
molecule. The essential amino acids cannot be synthesized by our body and hence must be provided through diet. Nucleic acids are the polymers of nucleotides which in turn consist of a base, pentose sugar and phosphate. There are two types of nucleic acids namely, DNA and RNA which differ in the composition of sugar and a base
The sugar moiety in DNA and RNA molecules, respectively, are

A network of resistors is connected as shown in the figure. The potential drop across 4\(\Omega\) resistors is

The sum of the order and degree of the differential equation representing the family of curves \(y=m x+m^4\), where \(m\) is arbitrary constant, is