A cell of emf E is connected across an external resistance R. When a current I is drawn, the potential difference across the electrodes drops to V. The internal resistance r of the cell is :

A galvanometer having a resistance of \( 8 \, \Omega \) is shunted by a wire of resistance \( 2 \, \Omega \). If the current is 1 A, the part of it passing through the shunt will be:

Choose the correct statements from the following.
A. Like light waves, thermal radiations are also electromagnetic radiation.
B. Electromagnetic waves can travel in vacuum but mechanical waves cannot do so.
C. Gamma rays are more energetic than X-rays.
D. Microwaves are heat waves so they always produce heating.
E. Displacement current is a fictious current and has nothing in common with conduction current.
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A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to \( \left(\frac{3}{4}\right) \)th of the angle of prism. The angle of deviation is :

In the depletion region of an unbiased p-n junction diode there are

For an astronomical telescope with 10 m focal length objective and 10 cm eyepiece, tube length and magnification are:

When a steady current flows in a metalic conductor of non-uniform cross section. Which of these quantities is constant along the conductor?
A. Current
B. Electric field
C. Drift speed
D. Current density
E. Potential gradient
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The function \(f(x)=\frac{x^2-25}{(x+5)}, x \neq-5\) is:

Read the passage carefully and answer the Questions
\(KMnO _4\) is prepared by the fusion of \(MnO _2\) with an alkali metal hydroxide and an oxidizing agent like \(KNO _3\) to give a dark-green manganate ion which disproportionate to give permanganate as follows.
\(\begin{array}{l}2 MnO _2+4 KOH + O _2 \rightarrow 2 K_2 MnO _4+2 H _2 O \\ 3 K_2 MnO _4+4 H ^{+} \rightarrow 2 KMnO _4+ MnO _2+2 H _2 O \end{array}\)
On heating \(K _2 MnO _4\) decomposes at 513 K to give \(K _2 MnO _4\). Permanganate ion is tetrahedral and diamagnetic
Acidified \(KMnO _4\) acts a strong oxidizing agent which oxidizes oxalic acid, ferrous ions, nitrite ion and iodides.
HCl is not used to make the medium acidic in oxidation reaction of \(KMnO _4\) in acidic medium, because....

Read the following passage carefully and answer the given questions.
Bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. Baculoviruses are pathogens that attack insects and other arthropods. The majority of baculoviruses used as biological control agents are in the genus Nucleopolyhedrovirus. These viruses are excellent candidates for species-specific, narrow spectrum insecticidal applications. They have been shown to have no negative impacts on plants, mammals, birds, fish or even on non-target insects. BOD refers to the amount of the oxygen that would be consumed if all the organic matter in one liter of water were oxidised by bacteria. The sewage water is treated till the BOD is reduced. Cheese, is one of the oldest food items in which microbes were used. Different varieties of cheese are known by their characteristic texture, flavour and taste. For example, the large holes in 'Swiss cheese' are due to production of a large amount of CO₂ by a bacterium named Propionibacterium sharmanii.
The greater the BOD of waste water-

Arrange the given steps of DNA fingerprinting in sequence.
(A) Transferring of separated DNA fragments on nitrocellulose membrane
(B) Isolation of DNA and digestion by restriction endonuclease
(C) Hybridisation using VNTR Probe
(D) Separation of isolated DNA fragments by Gel Electrophoresis
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Match List - I with List - II.

List - I	List - II
(A) RNA	(I) Adenosine
(B) Nucleoside	(II) Adenosine monophosphate
(C) Nucleotide	(III) Deoxyribose
(D) Sugar	(IV) Uracil

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Transition metals form a large number of complexes or coordination compounds in which the metal atoms are bound to a number of anions or neutral molecules. The valence bond theory explain the formation, magnetic behaviour and geometrical shapes while the crystal field theory explains the effect of different crystal fields on the degeneracy of d-orbitals energies of the central metal atom/ion. This provides for the quantitative estimation of orbital separation energies, magnetic moments and spectral and stability parameters.
Two complexes of nickel have same geometry but different magnetic behaviour are:
(A) \(\text{[Ni(CN)}_4]^{2-}\)
(B) \(\text{[Ni(CO)}_4]\)
(C) \(\text{[NiCl}_4]^{2-}\)
(D) \(\text{[Ni(NH}_3)_6]^{2+}\)
Choose the correct answer from the options given below :