If \(A=\left[\begin{array}{cc}1 & 0 \\ \frac{1}{25} & 1\end{array}\right]\), then the value of \(A^{125}\) is :

\(\int \frac{\sqrt{\tan x}}{\sin x \cos x} d x\) equals :

For the function \(f(x)=e^x+e^{-x}\)
(A) \(f^{\prime}(x)=e^x-e^{-x}\)
(B) The critical point is \(x=0\)
(C) The minimum value is 1
(D) \(x=0\) is the point of local minimum.
Choose the correct answer from the options given below:

The area of the region bounded by the parabola \(y^2=4 a x\) and its latus rectum is:

Let R be the relation in the set \(\{a, b, c\}\) given by \(R=\{(a, b),(b, b),(a, a),(a, c),(c, c),(c, b)\}\) Choose the correct answer from the options below :

A furniture trader deals in only two items - chairs and tables.
He has Rs. 50, 000 to invest and a space to store at most 35 items.
A chair costs Rs. 1000 and a table costs Rs. 2000.
The trader earns a profit of Rs. 150 on a chair and Rs. 250 on a table.
Choose the correct option that describes the given linear programming problem (LPP) to maximize the profit, where \(x\) and \(y\) are the number of chairs and tables.

The value of \(\cot ^{-1}\left[2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right]\) is

Read the following passage carefully and answer the given questions.
Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans (tobacco budworm, armyworm), coleopterans (beetles) and dipterans (flies, mosquitoes). B. thuringiensis forms protein crystals during a particular phase of their growth. 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 (a-1-antitrypsin) used to treat emphysema. In 1997, the first transgenic cow, Rosie, produced human protein-enriched milk (2.4 grams per litre). The milk contained the human alpha-lactalbumin and was nutritionally a more balanced product for human babies than natural cow-milk. A nematode Meloidegyne incognitia infects the roots of tobacco plants and causes a great reduction in yield. A novel strategy was adopted to prevent this infestation which was based on the process of RNA interference (RNAi). This method involves silencing of a specific mRNA due to a complementary dsRNA molecule that binds to and prevents translation of the mRNA (silencing). 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. ELISA is based on the principle of antigen-antibody interaction. Infection by pathogen can be detected by the presence of antigens (proteins, glycoproteins, etc.) or by detecting the antibodies synthesised against the pathogen.
Biopiracy is the term used to refer:

Select the correct statements from the following:
(A) Mn show the highest oxidation state in first transition series elements.
(B) Titanium (II) is more stable than titanium (III) and titanium (IV).
(C) Scandium does not exhibit variable oxidation states.
(D) Zn form complexes with only (II) oxidation state.
Choose the correct answer from the options given below:

Which is quantised in Bohr's atomic model ?

The mutual inductance of two co-axial coils is 2 H. If the current in one coil changes uniformly from zero to 1.0 A in 100 ms, the emf induced in the other coil is

Increase in population is due to:

A coin is tossed 3 times. If \(X\) denotes the number of heads, then Match List I with List II

LIST I	LIST II
A. \(P(X=0)\)	I. \(\frac{1}{8}\)
B. \(P(X=1)\)	ㅍ. \(\frac{7}{8}\)
C. \(P(X \leq 2)\)	III. \(\frac{4}{8}\)
D. \(P(X \geq 2)\)	IV. \(\frac{3}{8}\)

Choose the correct answer from the options given below: