The number of all possible matrices of order \(2 \times 3\) with each entry 0 or 1 is

If a line makes angles \(\alpha, \beta, \gamma\) with the positive directions of the coordinate axes, then the value of \(\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma\) is

\(\cos \left(\frac{\pi}{6}-\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right)\) is equal to:

Three varieties A, B and C of rice are mixed together in the ratio 1:1:3 respectively. The price of rice A is Rs 127 per kg and that of rice B is Rs 135 per kg. If the price of the mixture is Rs. 152 per kg, then the price per kg of rice of type C is :

The area of region bounded by two curves \(y^2=x\) and \(x^2=y\) is:

List-1	List-2
(A) \(y=\sqrt{x^3}\)	(I) \(-1\)
(B) \(y=\sqrt{x}\)	(II) 1
(C) \(y=x^3-47 x\)	(III) 1/4
(D) \(x y=16\)	(IV) 3

Choose the correct answer from the options given below :

Let \(e^y(x+1)=1\). Then which of the following are TRUE
(A) \(\frac{d^2 y}{d x^2}=-\frac{1}{(x+1)^2}\)
(B) \(\frac{d^2 y}{d x^2}=\left(\frac{d y}{d x}\right)^2\)
(C) \(\left.\frac{d^2 y}{d x^2}\right|_{x=0}=-1\)
(D) \(\left.\frac{d^2 y}{d x^2}\right|_{x=0}=1\)
(E) \(\left.\frac{d^2 y}{d x^2}\right|_{x=1}=\frac{1}{4}\)
Choose the correct answer from the options given below :

Maximize \(z=2 x-y\)
Subject to constraints
\(x+y \leq 4, \quad x+3 y \leq 6, \quad x \geq 0, \quad y \geq 0 .\)
The corner points of the feasible region are:

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

If A and B are two events such that \(P(B) = \frac{3}{5}\), \(P(A|B) = \frac{1}{2}\) and \(P(A \cup B) = \frac{4}{5}\), then P(A) is equal to:

What physical quantity is the same for X-rays of wavelength \( 10^{-10} \) m, red light of wavelength 680 nm and radiowaves of wavelength 50 m?

The brain capacity of Homo habilis was around ______ cc.

Which of the following is an essential amino acid?