The maximum value of \(Z\) for the linear programing problem maximize \(Z=x+y\) subject to the constraints \(x+4 y \leq 8,2 x+3 y \leq 12,3 x+y \leq 9, x \geq 0, y \geq 0\) is :

\(\int_2^5|x-3| d x\) equals

The value of the determinant \(\left|\begin{array}{cc}a \cos \theta & a \sin \theta \\ -a \sin \theta & a \cos \theta\end{array}\right|\) is:

If \(f(x)=3 x^2+10 x-5\), then by using the concept of differentials, the approximate value of \(f(2.03)\) is :

\(A\) runs \(3\) times as fast as \(B\) . If A gives \(B\) a start of \(30\) meters, how far must the goal on the race course be so that \(A\) and \(B\) reach it at the same time?

A person has purchased a home for Rs. 10,00,000 with a down payment of Rs. 2,00,000. He amortizes the balance at 9% per annum compounded monthly for 25 years.
Then the equal monthly instalment (EMI) is :
[Given that \(\frac{(1.0075)^{300}-1}{(0.0075)(1.0075)^{300}}=119.1616\) ]

If \(y=\sqrt{a x+b}\), then \(y \frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2=\)

Observe the given figures and answer the question

Match List - I with List - II.

List - I	List - II
(A) Part/Compound/Gases	(I) C
(B) Electrodes	(II) B
(C) Water which contains organic compounds	(III) D
(D) Gases	(IV) E

Choose the correct answer from the options given below:

A plane electromagnetic wave travels in vacuum along z-direction. What will be the directions of its electric field (\(\vec{E}\)) and magnetic field (\(\vec{B}\)) vectors?

Read the following passage carefully and answer the given questions.
Insulin consists of two short polypeptide chains- chain A and chain B, that are linked together by disulphide bridges. Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans, coleopterans and dipterans. Bt toxin protein is converted into an active form of toxin due to the alkaline pH of the gut which solubilise the crystals. Transgenic animals that produce useful biological products can be created by the introduction of the portion of DNA (or genes) which codes for a particular product such as human protein (alpha-1-antitrypsin) used to treat emphysema. Plants, bacteria, fungi and animals whose genes have been altered by manipulation are called Genetically Modified Organisms (GMO). GM plants have been useful in many ways. Genetic modification has: (i) made crops more tolerant to abiotic stresses. (ii) reduced reliance on chemical pesticides (pest-resistant crops). (iii) helped to reduce post harvest losses. (iv) increased efficiency of mineral usage by plants (this prevents early exhaustion of fertility of soil). (v) enhanced nutritional value of food.
Which one of the followings is not true about insulin?

The correct interpretation of Ohm's law is : (Here, \( \vec{J} \) is current density, '\( \sigma \)' is conductivity, \( \vec{E} \) is electric field and '\( \rho \)' is resistivity)

If A is a square matrix such that \(A^2=A\), then \(|A|\) equals :

Methanogens do not produce: