For the given five values 16, 25, 19, 34, 46, the three years moving averages are:

Cofactor of \(a_{12}\) in \(A=\left[\begin{array}{ccc}1 & 2 & 3 \\ 4 & -5 & 6 \\ 0 & 1 & -1\end{array}\right]\) is:

The feasible region for an LPP is shown by shaded region in the figure. Then the minimum value of Z = 11x + 7y is

The relation \(R\) in the set \(\{1,2,3\}\) given by \(R=\{(1,1),(2,2),(3,3),(1,2),(2,3)\}\) is:

If \(\cos^2 y + \sin(xy) = \lambda\), then \(\frac{dy}{dx} =\)

\(y=a \cos x+b \sin x\) where \(a, b\) are arbitrary constants is a solution of the differential equation:

match List - I with List - II

List - I (Differential Equation)	List - II (Degree)
(A) \(x y \frac{d^2 y}{d x^2}+x\left(\frac{d y}{d x}\right)^2-y \frac{d y}{d x}=0\)	(I) 3
(B) \(\frac{d^2 y}{d x^2}+\log \left(\frac{d y}{d x}\right)=0\)	(II) 1
(C) \(\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)^3+\frac{d y}{d x}+1=0\)	(III) not defined
(D) \(2 x^2\left(\frac{d^2 y}{d x^2}\right)^3-5\left(\frac{d y}{d x}\right)^2+y=0\)	(IV) 2

Choose the correct answert from the option given below :

Answer the question on the basis of passage given below :
Adsorption is a surface phenomenon and it differs from absorption which occurs throughout the body of the substance that absorbs. In physiosorption the attractive forces are mainly van der Waal's forces while in chemisorption ionic/covalent bonds are formed between particles of adsorbent and adsorbate. The catalytic activity of finely divided iron in Haber's process of ammonia manufacture can be explained by adsorption theory. Adsorption being an exothermic process, the heat of adsorption is utilised in enhancing the rate of the reaction. Adsorption has many applications being used in gas masks, control of humidity, chromatograph separation, curing diseases etc.
Chromatography is based on:

Arrange the following substances in the increasing order of magnetic susceptibility.
(A) Paramagnetic substances
(B) Superconductors
(C) Diamagnetic substances
(D) Ferromagnetic substances
Choose the correct answer from the options given below :

There is a solenoid of length 1 m has a radius 1 cm and is made up of 1000 turns, carrying a current of 10 A. The magnitude of the magnetic field inside the solenoid is

Read the Passage carefully and answer the the questions
Insulin consists of two short polypeptide chains : chain A and chain B, that are linked together by disulphide bridges. The first clinical gene therapy was given in 1990 to a 4-year old girl with adenosine deaminase (ADA) deficiency. This enzyme is crucial for the immune system to function. Recombinant DNA technology, Polymerase Chain Reaction (PCR) and Enzyme Linked Immuno-sorbent Assay (ELISA) are some of the techniques that serve the purpose of early diagnosis of diseases. 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 (α-1-antitrypsin) used to treat emphysema. Biopiracy is the term used to refer to the use of bio-resources by multinational companies and other organisations without proper authorisation from the countries and people concerned without compensatory payment.
In 1997, an American company got patent rights on Basmati rice through the US Patent and Trademark Office. This allowed the company to sell a ‘new’ variety of bvasnmati, in the US and abroad. This ‘new’ variety of Basmati had actually been derived from Indian farmer's varieties.. Indiian Basmati was crossed with semi-dwarf varieties and claimed as an invention or a novelty. This is a case of :

Value of \(\int \frac{2}{(x-3) \sqrt{x+1}} d x\) is : (Here \(C\) is an arbitrary constant)

The two possible nuclei to complete the reactions given below are, respectively
(1) \({ }_7 N^{14}+{ }_2 He ^4={ }_8 O ^{17}+\)_______
(2) \({ }_8 O ^{16}+{ }_1 H ^2={ }_7 N^{14}+\)_____