The region represented by the system of inequalities \(x \geq 0 ; y \geq 0\),
\(2 x+y \geq 8\) and \(x+2 y \geq 10\) is :

In a kilometer race \(P\) runs at \(10 m / sec , Q\) runs at \(5 m / sec\) then which of the following statement \(( s )\) is \(/\) are correct?
(A) \(P\) wins the race in 100 sec
(B) Q wins the race in 100 sec
(C) P defeats Q by 500 m
(D) Q defeats P by 500 m
Choose the correct answer from the options given below :

If a matrix P is both symmetric and skew-symmetric, then

The current through a \(4 / 3 \Omega\) external resistance connected to a parallel combination of two cells with emfs of 2 V and 1 V , internal resistances \(1 \Omega\) and \(2 \Omega\) respectively, is :

The area of the parallelogram determined by the vectors \(\hat{i}+2 \hat{j}+3 \hat{k}\) and \(3 \hat{i}-2 \hat{j}+\hat{k}\) is

If \(\left|\begin{array}{cc}2 x & 5 \\ 8 & x\end{array}\right|=\left|\begin{array}{cc}3 & 0 \\ 4 & -8\end{array}\right|\), then value(s) of \(x\) is/are

The value of \(x\) for which the matrix \(A = \begin{bmatrix} 1 & -2 & 3 \\ 1 & 2 & 1 \\ x & 2 & -3 \end{bmatrix}\) is singular is:

The number of all possible matrices of order \(3 \times 4\) with each entry 1, 2 or 3 are:

Benzene and naphthalene form an ideal solution at room temperature.
The true statements for this solution are :
A. \(\Delta\text{G}\) is positive.
B. \(\Delta\text{S}_{\text{system}}\) is positive.
C. \(\Delta\text{S}_{\text{surroundings}} = 0\).
D. \(\Delta\text{H}_{\text{mix}} = 0\).
E. \(\Delta\text{V}_{\text{mix}} = 0\).
Choose the correct answer from the options given below :

Arrange the following processes of recombinant DNA technology in a correct sequence:
(A). Amplification of gene by using PCR
(B). Isolation of DNA and cutting of DNA at specific location
(C). Obtaining the desired foreign gene product
(D). Insertion of recombinant DNA into the host
Choose the correct answer from the options given below:

Match List-I with List-II

List -I Physical Quantity	List II Dimensional Formula
(A) Capacitance	(I) \( [M L^3 T^{-3} A^{-1}] \)
(B) Electric Flux	(II) \( [M L^2 T^{-3} A^{-1}] \)
(C) Potential	(III) \( [L^{-2} A T] \)
(D) Polarisation	(IV) \( [M^{-1} L^{-2} T^4 A^2] \)

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:

Read the Passage carefully and answer the the questions
The DNA fragments can be separated by a technique known as gel electrophoresis. Since DNA fragments are negatively charged molecules, they can be separated by forcing them to move towards the anode under an electric field through a medium/matrix. The separated DNA fragments can be visualised only after staining the DNA with a compound known as ethidium bromide followed by exposure to UV radiation. The repeated amplification of DNA is achieved by the use of a thermostable DNA polymerase (isolated from a bacterium, Thermus aquaticus). After completion of the biosynthetic stage, the product has to be subjected through a series of processes before it is ready for marketing as a finished product. The downstream processing and quality control testing vary from product to product. The convention for naming restriction enzymes is the first letter of the name comes from the genus and the second two letters come from the species of the prokaryotic cell from which they were isolated.
In agarose gel electrophoresis, the DNA fragments can be visualised only after staining the DNA with a compound known as