If the matrix \(A=\left[\begin{array}{ccc}x & 2 & y \\ -2 & 0 & 3 \\ -1 & z & 0\end{array}\right]\) is skew-symmetric, then the value of \(2 x-3 y+5 z\) is equal to

Match List - I with List - II.

LIST I	LIST II
A. \(\left[1+\left(\frac{d y}{d x}\right)^2\right]=\left(\frac{d^2 y}{d x^2}\right)^2\)	I. order \(=2\), degree \(=2\)
B. \(\frac{d^3 y}{d x^3}-3 \frac{d^2 y}{d x^2}+2\left(\frac{d y}{d x}\right)^4=y^4\)	II. order \(=3\), degree \(=2\)
C. \(\left(1+\frac{d y}{d x}\right)^3=\left(\frac{d^3 y}{d x^3}\right)^2\)	III. order \(=2\), degree \(=1\)
D. \(\left[1+\left(\frac{d y}{d x}\right)^2\right]^?=\frac{d^2 y}{d x^2}\)	IV. order \(=3\), degree \(=1\)

Choose the correct answer from the option given below:

Which of the following functions are increasing on \(x \in\left(0, \frac{\pi}{2}\right)\) ?
(A) \(f(x)=\sin x\)
(B) \(f(x)=\cos x\)
(C) \(f(x)=\tan x\)
(D) \(f(x)=\cos 3 x\)
Choose the correct answer from the options given below :

Under which of the following conditions the Poisson distribution is the limiting case of, binomial distribution :
(A) The number of trials is indefinitely large.
(B) The probability of success for each trial is indefinitely small.
(C) The product of the number of trials and the probability of success for each trial is finite.
(D) The probability of success for each trial is indefinitely large.
Choose the correct answer from the options given below :

\(\int \frac{f^{\prime}(x)}{f(x) \log _e[f(x)]} d x\) is equal to

The refractive index of the material of an equilateral prism is \(\sqrt {2}\). The angle of minimum deviation of that prism is

Let \(A=\left[\begin{array}{cc}\frac{1}{3} & 2 \\ 0 & 2 x-3\end{array}\right]\) and \(B=\left[\begin{array}{cc}3 & 6 \\ 0 & -1\end{array}\right]\).
If AB = I (where I is an identity matrix of order 2), then the value of x is:

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.
Four bases present in RNA molecule are:

Who popularised the term 'Biodiversity'?

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
Which of the following is non-reducing sugar?

Least basic compound among the following would be:

Read the following passage carefully and answer the given questions.
Cancerous cells just continue to divide giving rise to masses of cells called tumors. Benign tumors normally remain confined to their original location and do not spread to other parts of the body and cause little damage. The malignant tumors, on the other hand are a mass of proliferating cells called neoplastic or tumor cells. Transformation of normal cells into cancerous neoplastic cells may be induced by physical, chemical or biological agents. Ionising radiations like X-rays and gamma rays and non-ionizing radiations like UV cause cancer. Cancer-causing viruses are called oncogenic viruses which have viral oncogenes. The substances to which an immune response is produced are called allergens. The antibodies produced to these are of IgE type. Common examples of allergens are mites in dust, pollens, animal dander, etc. The primary lymphoid organs are bone marrow and thymus. The secondary lymphoid organs provide the sites for interaction of lymphocytes with the antigen, which then proliferate to become effector cells.
The tumors that remain confined to their original location and do not spread to other parts of the body are:

If \(A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]\) and \(I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\), then the value of \(A^2-5 A+6 I\) is