Two parallel plate capacitors of capacitances \(2 \, \mu\text{F}\) and \(3 \, \mu\text{F}\) are joined in series and connected to a battery of V volts. The values of potential across the two capacitors \(V_1\) and \(V_2\) and energy stored in them \(U_1\) and \(U_2\) are related as :

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:

Match List - I with List - II.

List - I	List - II
(A) Orbital radius of electron	(I) \( \propto \frac{1}{n} \)
(B) Orbital velocity of electron	(II) \( \propto n \)
(C) Orbital frequency of electron	(III) \( \propto \frac{1}{n^3} \)
(D) Angular momentum of electron List	(IV) \( \propto n^2 \)

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The mutual inductance of a pair of solenoid depends :
(A) on their separation
(B) on their relative orientation
(C) on the current flowing
(D) on the number of turns in the solenoids
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In Young's double slit experiment, two slits \( d = 0.12 \text{ mm} \) apart are illuminated by monochromatic light of wavelength \( 480 \text{ nm} \). The screen is \( 1.0 \text{ m} \) away from the slits. The distance of the second bright fringe from the central maximum will be

A parallel plate capacitor having plate area 200 \( cm^2 \) and separation 2.0 mm holds a charge of \( 0.06\mu C \) on applying a potential difference of 60 V. The dielectric constant of the material filled in between the plates is.
Given permittivity of the vaccum \(\epsilon_0=8.85 \times 10^{-12} F / m \))

An electrical circuit contains a battery of V = 4 V, and a resistance of R = 2 \( \Omega \). A galvanometer of resistance G = 40 \( \Omega \) shunted by S = 10 \( \Omega \) is used to measure current in the circuit. The reading of ammeter is

A series AC circuit has a resistance \( 8 \, \Omega \) and a reactance of \( 6 \, \Omega \). The impedance of the circuit is :

Two point charges of 1 C each are separated from each other by a distance of 1 m in vacuum.
The force of interaction between them is:

Match List-I with List-II

List-I (Drugs)	List-II (Sources/features)
(A) Alcohol	(I) Sedative and painkiller
(B) Crack	(II) Diacetylmorphine
(C) Morphine	(III) Liver cirrhosis
(D) Smack	(IV) Erythroxylum coca

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Read the passage carefully and answer the questions
Carboxylic acids are the organic compounds which comprise of carboxyl functional group, -COOH. These are generally found in nature, some higher members are known as fatty acids as they occur in natural fats as esters of glycerol. They can be prepared from oxidation of alcohols and aldehydes, hydrolysis of nitriles and amides and Grignard reagents. They are stronger acids than simple phenols and alcohols. but weaker than mineral acids. Substituents affect the acidity of aliphatic and aromatic carboxylic acids. They undergo reactions involving cleavage of -OH and C-OH bond. Carboxylic acids having an alpha hydrogen get halogenated in the presence of red phosphorus to form alpha halo carboxylic acids. The reaction is known as Hell Volhard Zelinsky reaction. Besides these aromatic carboxylic acids undergo electrophilic substitution reactions. They are versatile and are employed in the manufacture of various useful compounds. For example, methanoic acid is used in rubber, textile, dyeing, leather and electroplating industries. Higher fatty acids are used in the manufacture of soaps and detergents. Esters of Benzoic acid are used in perfumery.
The reagents needed for the preparation of Benzoic acid from ethyl benzene is :

Maxwell's displacement current is

Match List I with List II

List I	List II
A. The triplet nature of genetic code	I. George Gamow
B. The technique of DNA fingerprinting	III. Alec Jefferys
C. lac operon	IV. Jacob and Monod
D. Central dogma	II. Francis Crick

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