Consider the differential equation \(x d y=(x+y) d x\). Which of the following are true?
(A) It is a homogenous differential equation
(B) It is a differential equation of order 2
(C) The general solution of the differential equation contains 2 arbitrary constants
(D) Integrating factor of differential equation is \(\frac{1}{x}\)
(E) Degree of the differential equation is not defined
Choose the correct answer from the options given below:

If the corner points of the bounded feasible region of an LPP are (0,2), (3,0), (6,0), (6,8) and (0,5) then the minimum value of the objective function F = 4x+6y occurs at

If \(x, y\) and \(z\) are real numbers such that \(x+y+z=0\), then the value of \(\left|\begin{array}{ccc} 3 x & -x+y & -x+z \\ x-y & 3 y & z-y \\ x-z & y-z & 3 z \end{array}\right| \) is

Which of the following is NOT correct?

The integrating factor of the linear differential equation \(\frac{d y}{d x}+P(x) y=Q(x)\) is:

For a square matrix \(A\) of order 3, if \(|A|=2\), then \(|\operatorname{adj}(2 A)|=\)

Time reversal test is satisfied by:

A proton is moving in a circular path of radius R in a uniform magnetic field B. It carries a kinetic energy of 2 MeV. What should be the energy of an \(\alpha\)-particle to move in a circle of same radius in the same field ?

List-I (Reaction Name)	List-II (Reaction)
(A) Carbylamine reaction	(I)
(B) Gatterman Rection	(II)
(C) Sandmeyer reaction	(III)
(D) Hoffmann Bromamide reaction	(IV)

Choose the correct answer from the options given below:

Which of the following are not electromagnetic waves?
A. Gamma rays
B. Cathode rays
C. X-rays
D. \(\beta\)-rays
E. Radio waves
Choose the correct answer from the options given below:

How can fringe width increase in Young's double slit experiment?

Read the passage carefully and answer the given questions.
Recombinant DNA Technology Asexual reproduction preserves the genetic information, while sexual reproduction permits variation. Traditional hybridization procedures used in plants and animals breeding very often lead to inclusion and multiplication of undesirable genes along with the desired genes. The techniques of genetic engineering, which include creation of recombinant DNA, use of gene cloning and gene transfer, overcome this limitation and allow us to isolate and introduce only one or a set of desirable genes without introducing genes into the target organism.
Which one of the following options is correct for working of restriction enzymes?

If \(\left|\begin{array}{cc}2 & 3-x \\ x & 1\end{array}\right|=0\), then the values of x are: