A swimmer whose speed in swimming pool is 5 km/h, swims between two points in a river and returns back to starting point. He took 20 minutes more to cover the distance upstream than to cover downstream. If the speed of stream is 2 km/h, then the distance between two points is

If \(A=\left[\begin{array}{cc}1 & 5 \\ 7 & 12\end{array}\right], B=\left[\begin{array}{ll}9 & 1 \\ 7 & 8\end{array}\right]\) and \(C\) are three matrices such that \(3 A+5 B+2 C=0\), then the matrix \(C\) is equal to

Let \(P\) and \(Q\) be any two invertible matrices of the same order. Then Match List-I with List-II

List - I (Matrix)	List - II (Equivalent matrix)
(A) \((P Q)^{-1}\)	(I) \(Q^{-1} P\)
(B) \(\left(P^{-1} Q\right)^{-1}\)	(II) \(Q P^{-1}\)
(C) \(\left(P Q^{-1}\right)^{-1}\)	(III) \(Q^{-1} P^{-1}\)
(D) \(\left(P^{-1} Q^{-1}\right)^{-1}\)	(IV) \(Q P\)

Choose the Correct answer from the options given below :

The effective rate that is equivalent to a nominal rate of 16 % compounded semi-annually is :

Which of the following statements are correct?
(A) If \(\vec{a}\) and \(\vec{b}\) represent the adjacent sides of a triangle, then its area is \(\frac{1}{2}|\vec{a} \times \vec{b}|\)
(B) If \(\vec{a}\) and \(\vec{b}\) represent the adjacent sides of a parallelogram, then its area is \(|\vec{a} \times \vec{b}|\)
(C) \(|\vec{a} \times \vec{b}|=|\vec{a}||\vec{b}| \cos \theta\)
(D) If \(\vec{a}\) and \(\vec{b}\) represent the 'diagonals' of a parallelogram, then its area is \(\frac{1}{2}|\vec{a} \times \vec{b}|\)
Choose the correct answer from the options given below :

\(f(x)=x^3+p x^2+q x+10\) has a maximum at \(x=-3\) and a minimum at \(x=1\). The values of \(p\) and \(q\) are:

The distance of the plane \(\vec{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=3\) from the origin is :

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.
Prions are made up of :

A light with an energy flux of 25 \( W/cm^2 \) falls on a non-reflecting surface at normal incidence. If the surface has an area of 50 \( cm^2 \) and the total energy falling on the surface is \( 10 \times 10^5 \) J. The total duration of time of the incidence of light 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 :

List-I	List-II
(A) Swarts Reaction	(I) \(C _6 H _5 NH _2+ NaNO _2+ HX + Cu _2 X _2 \rightarrow C _6 H _5 X + N _2\)
(B) Finkelstein Reaction	(II) \(2 R X + 2 N a \rightarrow R - R + 2 N a X\)
(C) Sandmeyer Reaction	(III) \(RX + AgF \rightarrow R - F + AgX\)
(D) Wurtz Reaction	(IV) \(R X + N a I \rightarrow R - I + N a X\)

Choose the correct match:

Which of the following is not an essential amino acid ?

Read the passage given below and answer the question.
The transition elements which give the greatest number of oxidation states occur in or near the middle of the series. Manganese, for example, exhibits all the oxidation states from +2 to +7. The lesser number of oxidation states at extreme ends stems from either too few electrons to lose or share (Sc, Ti) on too many d-electrons (hence fewer orbitals available in which to share electrons with others) for higher valence (Cu, Zn). Thus early in the series scandium (II) is virtually unknown and titanium (IV) is more stable than Ti (III) or Ti (II). At the other end, the only oxidation state of zinc is +2 (no d electrons are involved). The maximum oxidation states of reasonable stability correspond in value to the sum of the s- and d-electrons upto manganese (\(TiO_2, VVO^+, CrVIO_4^{2-}, MnVIIO_4\)) followed by a rather abrupt decrease in stability of higher oxidation states, so that the typical species to follow are \(Fe^{II,III}, Co^{II,III}, Ni^{II}, Cu^{I,II}, Zn^{II}\).
The variability of oxidation states, a characteristic of transition elements, arises out of incomplete filling of d-orbitals in such a way that their oxidation states differ from each other by unity, e.g. \(V^{II}, V^{III}, V^{IV}, V^{V}\). This is in contrast with the variability of oxidation states of non transition elements where oxidation states normally differ by a unit of two.
An interesting feature in the variability of oxidation states of the d-block elements is noticed among the groups (groups 4 through 10). Although in the p-block, the lower oxidation states are favoured by the heavier members (due to inert pair effect), the opposite is true in the groups of d-block. For example, in group 6, Mo(VI) and W(VI) are found to be more stable than Cr(VI). The Cr(VI) in the form of dichromate in acidic medium is a strong oxidising agent, whereas \(MoO_3\) and \(WO_3\) are not.
Low oxidation states are found when a complex compound has ligands capable of \(\pi\)-acceptor character in addition to the \(\sigma\)-bonding. For example, in \(Ni(CO)_4\) and \(Fe(CO)_5\), the oxidation state of nickel and iron is zero.
The elements giving minimum number of oxidation states are in extreme left and right in 3d series.
This is because :