Two identical conducting wires, A and B of different materials, are joined in series across a battery. If the number density of electrons in A is thrice that in B, then the ratio of drift velocity of electrons in the two wires is

Rohit has been given two converging lenses of focal lengths 1.25 cm and 5 cm, respectively to design a compound microscope. If it is desired to have a magnification of 30, what would be the separation between the objective and the eyepiece when the final image is formed at the least distance of distinct vision?

A 200 turns closely wound circular coil of radius 10 cm carries a current of 3.5 A. The magnetic moment of the coil is

Huygen's principle allows us to understand and determine.

Two slits 0.1 mm apart with screen 2 m away produce fringe separation with 500 nm light. The separation is :

Match List-I with List-II

List-I	List-II
(A) The current lags behind the emf by \( \pi/4 \) in phase	(I) A.C. circuit containing only an inductor
(B) The e.m.f. lags behind the current by \( \pi/4 \) in phase	(II) A.C. circuit with resistance and inductances in series
(C) The current lags behind the e.m.f. in phase by \( \pi/2 \)	(III) A.C. circuit containing only as capacitor
(D) The e.m.f. lags behind the current in phase by \( \pi/2 \)	(IV) A.C. circuit with resistance and capacitor in series

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An atom has a positively charged point nucleus of charge Ze surrounded by a uniform density of negative charge up to a radius R. The atom is taken as neutral. The electric field at a distance r < R from the nucleus is given by:

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

Eli Lilly, in 1983, developed human insulin using rDT by combining chain A and chain B with:

Answer the questions on the basis of passage given below :
As aldehydes ketones possess the carbonyl functional group, they show similar reaction They exhibit nucleophilic addition reactions, reduction, oxidations, reactions due to alpha-Hydrogen atom, and many other reactions, like Cannizzaro reaction to electrophilic substitution reactions (in case of aromatic aldehydes ketones).
These reactions help in the preparation of a number of important compounds, like acetic acid, vinyl acetate, polymers and in perfume and dye industries.
Nucleophilic addition reactions form cyanohydrins, acetals, alcohols and
N-substituted derivatives like imine, oxime, semicarbazone, phenylhydrazone Schiff's base. Reactions due to alpha-hydrogen atoms help in formation of aldols and alpha, beta-unsaturated aldehydes ketones.
Identify the final product of the following reaction :

Two point charges, \( q_1 = 3 \, \mu\text{C} \) and \( q_2 = -2 \, \mu\text{C} \), are placed 6 cm apart. The magnitude of the electric force between them is:

Match List-l with List-ll

List-l (Microorganisms)	List-II (Commercial Uses)
(A) Lactobacillus	(I) Use for the production of butyric acid
(B) Saccharomyces cerevisiae	(II) Use for production of swiss cheese
(C) Propionibacterium sharmanii	(III) Use for making bread
(D) Clostridium butylicum	(IV) Improves nutritional quality of milk by increasing vitamin B12

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Match the complexes given in List-I with the number of unpaired electrons given in List-II

List-I (Complexes)	List-II (No. Of unpaired electrons.)
(A) \(\left[ Ti \left( H _2 O \right)_6\right]^{3+}\)	(I) 1
(B) \(\left[ NiF _6\right]^{4-}\)	(II) 5
(C) \(\left[ Fe ( CN )_6\right]^{4-}\)	(III) 2
(D) \(\left[ MnF _6\right]^{4-}\)	(IV) 0

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