Consider the LPP: Minimize \(Z=x+2 y\) subject to \(2 x+y \geq 3, x+2 y \geq 6, x, y \geq 0\). The optimal feasible solution occurs at:

If \(A = \begin{bmatrix} 2a & 0 & 0 \\ 0 & 2a & 0 \\ 0 & 0 & 2a \end{bmatrix}\), then the value of \(|\text{adj A}|\) is:

Let \(y=\cos \left(\sin x^2\right)\), then the value of \(\frac{d y}{d x}\) at \(x=\frac{\sqrt{\pi}}{2}\) is equal to

If \(e^y=\log x\), then which of the following is true?

The point on the unit circle with center (0, 0); where tangents are equally inclined to the co-ordinate axes are:

If \(m\) and \(n\) are respectively the order and degree of the differential equation :
\(\left(\frac{d^2 y}{d x^2}\right)^5+6 \frac{\left(\frac{d^2 y}{d x^2}\right)^3}{\frac{d^3 y}{d x^3}}+\frac{d^3 y}{d x^3}=x^2+5\), then \(:\)

If R and S are two equivalence relations on a set A, then

Match List-I with List-II

List-I (EM waves)	List-II (Application)
(A) Infrared	(I) diagnostic tool in medicine
(B) X-rays	(II) water purification
(C) UV rays	(III) communication radar
(D) Microwaves	(IV) improving visibility in foggy days

Choose the correct answer from the options given below:

The armature coil of a generator has 20 turns and its area is \( 0.127 \, \text{m}^2 \). How fast approximately should it be rotated in a magnetic field of \( 0.2 \, \text{Wb m}^{-2} \) so that the peak value of induced emf is 160 V?

If the vectors \(\hat{i}-2 x \hat{j}+3 y \hat{k}\) and \(\hat{i}+2 x \hat{j}-3 y \hat{k}\) are perpendicular, then the locus of \((x, y)\) is:

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?

Match List-I and List-II

List-I	List-II
A. Alchohol + water	I. Ideal solution
B. Benzene + Toluene	II. Positive deviation
C. Water + Nitric acid	III. Negative deviation

Choose the correct answer from the options given below :

A substance, when placed in a magnetic field acquires feeble magnetization in a direction opposite to the applied field, is