A series combination of two capacitors \( C_1 = 3 \, \mu\text{F} \) and \( C_2 = 6 \, \mu\text{F} \) is connected in parallel with a third capacitor \( C_3 = 4 \, \mu\text{F} \). This system is connected to a 10 V battery. The total energy stored in the system is:

Arrange the following nuclei in the ascending order of their stability.
(A) Oxygen (\( {}^{16}\text{O} \)) with binding energy 127.5 MeV
(B) Uranium (\( {}^{238}\text{U} \)) with binding energy 1808.8 MeV
(C) Helium (\( {}^{4}\text{He} \)) with binding energy 28.3 MeV
(D) Iron (\( {}^{56}\text{Fe} \)) with binding energy 490 MeV
Choose the correct answer from the options given below:

The wavelength of matter wave depends upon:
A. charge
B. velocity
C. momentum
D. mass
E. charge density
Choose the correct answer from the options given below:

Three charges \(+4 q, Q\) and \(q\) are placed along \(x\)-axis at points, \(x=0, I / 2\) and I respectively. The value of Q to make the net force on \(q\) to be zero :

In a coil of self inductance 10 H, the rate of change of current is \( 4 \text{ A s}^{-1} \). The electromotive force (emf) induced in the coil will be

Match List-I with List-II

List - I (Observation)	List - II (Light related phenomenon)
(A) Blue colour of sky	(I) Dispersion
(B) Seven colours obtained from prism	(II) Refraction
(C) Bending of pencil dipped in water	(III) Scattering
(D) Alternate bright and dark bands of equal thickness	(IV) Interference

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A ray of light is incident on an equilateral prism at an angle of 45° and is refracted parallel to the base of the prism. The angle of deviation would be

Match List - I with List - II.

LIST - I	LIST - II
(A) \(x^x\) has a stationary point at \(x\) equal to	(I) \(e\)
(B) For \(x>0\), minimum value of \(x^x\)	(II) \(1 / e\)
(C) The greatest value of \(\left(\frac{1}{x}\right)^x\)	(III) \(e^{1 / e}\)
(D) The stationary point of \(\frac{\log x}{x}\) for \(x\), where \(x>0\), is	(IV) \(e^{-1 / e}\)

Choose the correct answer from the otions given below:

Which one of the following is not an example of narrowly utilitarian reason to conserve biodiversity?

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:

Species -area relationship in South American jungles was studied by -

Australian marsupials show the phenomena of:

RNA polymerase III is responsible for transcription of -