The effective rate that is equivalent to a nominal rate of \(12 \%\) compounded quarterly is :

The value of \(\int \frac{\cos x d x}{(1+\sin x)(2+\sin x)}\) is :

If \(m\) and \(n\) are respectively the order and degree of the differential equation :
\(\left(\frac{d^2 y}{d x^2}\right)^5+6 \frac{\left(\frac{d^2 y}{d x^2}\right)^3}{\frac{d^3 y}{d x^3}}+\frac{d^3 y}{d x^3}=x^2+5\), then \(:\)

Match List I with List II

(List I)	(List II)
A. \(\frac{d}{d x}\left(a^x\right)\)	\(I.\) \(0\)
B. \(\frac{d}{d x}\left(x^a\right)\)	\(II.\) \(x^x\left(1+\log _e x\right)\)
C. \(\frac{d}{d x}\left(a^a\right)\)	\(III.\) \(a x^{a-1}\)
D. \(\frac{d}{d x}\left(x^x\right)\)	\(IV.\) \(a^x \log _e a\)

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\(\int \frac{d x}{\left(1+5 \sin ^2 x\right)}\) is equal to

If \(A^2-A+I=0\), then \(A^{-1}\) is equal to :

The projection of \(\hat{i}-\hat{j}\) on the vector \(\hat{i}+\hat{j}\) is :

Which one of the following guides the entry of the pollen tube into the embryo sac?

The force between two electric charges is expressed by the equation : \( F = \frac{kq_1q_2}{r^2} \).
Which of the following is a correct statement ?

Match List - I with List - II.

List - I (Magnetic Property)	List - II (Substance)
(A) Ferrimagnetic	(I) MnO
(B) Antiferromagnetic	(II) \(H _2 O\)
(C) Ferromagnetic	(III) \(ZnFe _2 O _4\)
(D) Diamagnetic	(IV) \(CrO _2\)

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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.
Deficiency of adenosine deaminase (ADA) can be permanently cured by -

The fringe width in Young's double slit experiment is \( 2.4 \times 10^{-4} \, \text{m} \), when red light of wavelength 6400 \( \text{\AA} \) is used. The decrease in the fringe width, if light of wavelength 4000 \( \text{\AA} \) is used instead of red light, will be:

DNA fingerprinting is used for:
(A) Forensic Laboratories for identification of criminals
(B) To identify paternity of an individual
(C) To identify the dead bodies by comparing the DNA of parents or children
(D) To identify racial groups, to rewrite biological evaluations.
Choose the correct answer from the options given below: