If \(A=\left[\begin{array}{cc}2 & 3 \\ 5 & -2\end{array}\right]\) then:

The area (in sq., units) of the region bounded by the parabola \(y^2=4 x\) and the line \(x=1\) is:

The following statements are made on the basis of given graph.
(A) OB represents the cost function.
(B) MA represents the cost function.
(C) Loss occurs at x = 5.
(D) Loss occurs at x = 15.
(E) Profit occurs at x = 10.

In the context of linear programming, Match List I with List II

List - I	List - II
(A) Z = 250x +75y	I. non-trivial constraints
(B) \(5 x+y \leq 100, x-y \leq 4\)	II. feasible solution
(C) \(x, y \geq 0\)	III. objective function
(D) points within and on the boundary of shaded region	IV. Trivial constraints

The interval(s), where the function \(f(x)=\left\{\begin{array}{l}\frac{1-e^x}{e^{2 x}-1}: x \neq 0 \\ -\frac{1}{2}: x=0\end{array}\right.\) is increasing, is/are:

Solution of the differential equation \(\frac{d y}{d x}=\sqrt{1+x^2+y^2+x^2 y^2}\) is : (Here \(C\) is an arbitrary costant)

The linear programming problem : minimise \(z=3 x+2 y\)
subject to the constraints \(x+y \geq 8,3 x+5 y \leq 15, x \geq 0, y \geq 0\)
has

ABO blood group is an example of:

Let \(x\) denote the number of heads in a simultaneous toss of three coins, then \(P(0 < x \leq 3)\)

A field of \( 2 \times 10^{3} \text{ A/m} \) produces a flux of \( 2.4 \times 10^{-5} \text{ Wb} \) in an iron bar having area of cross-section \( 0.2 \text{ cm}^2 \). The relative permeability of medium is:

C and Z in the species-area relationship log S = log C + Z log A represents:

The organism responsible for large holes in 'Swiss cheese' is :

Read the following passage carefully and answer the given questions
The separated DNA fragments can be visualized only after staining the DNA with ethidium bromide followed by exposure to UV radiation. Bright orange colored bands of DNA in ethidium bromide stained gel exposed to UV light can be seen. The separated bands of DNA are cut out from the agarose gel and extracted from the gel piece. This step is known as elution. The DNA fragments purified in this way are used in constructing recombinant DNA by joining them with a cloning vector.
Which one of the following techniques is used to separate DNA fragments?