The integrating factor of differential equation \(\left[y(1-x \tan x)+x^2 \cos x\right] d x-x d y=0\) is :

The matrix \(\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]\) is a

A person can row a boat in still water at the rate of \(5 km / hr\). It takes him \(4\) times as long to row upstream of a river as to row downstream to cover same distance in the same river. The speed of flow of the stream is:

If \(\vec{a}=3 \hat{i}-6 \hat{j}+\hat{k}\) and \(\vec{b}=2 \hat{i}-4 \hat{j}+\lambda \hat{k}\) are such that \(\vec{a} \| \vec{b}\), then \(3 \lambda+2=\)

For real numbers x and y, the relation R is defined as R = {(x, y) : x + y - \(\pi\) is an irrational number}, then the relation R is:

The edge of a cube is increasing at a rate of 7 cm/s. The rate of change of area of the cube when its side is 3 cm is:

On differentiating \(e^{x^2}\) with respect to x, we get

Answer the question on the basis of passage given below :
Strong oxidising agents oxidise toluene and its derivatives to benzoic acid. However, it is possible to stop the oxidation at the aldehyde stage with suitable reagents that convert the methyl group to an intermediate that is difficult to oxidise further.
Conversions that can be done by same reagent are:
(A) Benzaldehyde to 2-nitrobenzaldehyde
(B) Propan-1-ol to propanal
(C) Pent-3-en-2-ol to pent-3en-2-one
(D) Butanal to Butan-1-ol
(E) Methanal to Ethanol
Choose the correct answer from the options given below :

Chronologically arrange the names of scientists who contributed to the study of genetics.
(A) Alfred Sturtevent
(B) Gregor Mendel
(C) Thomas Hunt Morgan
(D) Sutton and Boveri
Choose the correct answer from the options given below:

Read the given passage carefully and answer the questions
Antibiotics have greatly improved our capacity to treat deadly diseases such as plague, whooping cough (kali khansi), diphtheria (gal ghotu) and leprosy (kusht rog), which used to kill millions all over the globe.
Streptokinase produced by the bacterium Streptococcus and modified by genetic engineering is used as a 'clot buster' for removing clots from the blood vessels of patients who have undergone myocardial infarction leading to heart attack. Microbes are diverse-protozoa, bacteria, fungi and microscopic animal and plant viruses, viroids and also prions that are proteinacious infectious agents. The puffed-up appearance of dough is due to the production of CO₂ gas. Similarly the dough, which is used for making bread, is fermented using baker's yeast (Saccharomyces cerevisiae). Primary sewage treatment basically involve physical removal of particles - large and small from the sewage through filtration and sedimentation. These are removed in stages; initially, floating debris is removed by sequential filtration. Then the grit (soil and small pebbles) are removed by sedimentation. All solids that settle form the primary sludge, and the supernatant forms the effluent. The effluent from the primary settling tank is taken for secondary treatment. The primary effluent is passed into large aeration tanks, where it is constantly agitated mechanically and air is pumped into it. This allows vigorous growth of useful aerobic microbes into flocs. While growing, these microbes consume the major part of the organic matter in the effluent.
Primary sludge treatment involves -

Darwin's finches of Galapagos Islands are the examples of:

The decomposition of \(NH_3\) on platinum surface is a zero order reaction. The rates of production of \(N_2\) and \(H_2\) respectively are : (in \(mol^{-1}Ls^{-1}\)) Given that \(2.5 \times 10^{-4}\text{ mol}^{-1}\text{L s}^{-1}\) is the rate of reaction.

What will happen during the electrolysis of aqueous solution of \(\text{CuSO}_4\) using platinum electrodes?
A. Copper will deposit at cathode.
B. Copper will deposit at anode.
C. Oxygen will be released at anode.
D. Oxygen will be released at cathode.
Choose the correct answer from the options given below: