Two cells of emf \( E \) and \( 2E \) with internal resistances \( r \) and \( 3r \), respectively are connected in parallel. The emf and internal resistance of the combination is:

A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be

The average emf induced in a coil in which current changes from 2 A to 4 A in 0.05 sec is 8 V. The self - inductance of coil is :

If the protons and electrons are the only basic charges in the universe, all the observable charges have to be integral multiples of e. Thus, if an object contains x electrons and y protons, the net charge on the object will be

When a light of wavelength 150 nm is incident on silver surface a potential of 3.58 V is required to stop the photoelectrons from reaching the collector plate. Find the potential required to stop photoelectrons when a light of wavelength 200 nm is incident on it ?
(Work function of silver is 4.7 eV)

Two charges of -2 \(\mu C\) and +2 \(\mu C\) are placed at the point A (0, 2, 0) m and B (0, -2, 0) m located in an electric field \(E = 0.5i\) V/cm. The magnitude of torque acting on the dipole is:

Match List-I with List-II

List-I	List-II
(A) AC generator	(I) Michael Faraday
(B) Polarity of induced emf	(II) Foucault
(C) Electromagnetic Induction	(III) Nicola Tesla
(D) Eddy Current	(IV) Heinrich Friedrich Lenz

Choose the correct answer from the options given below:

Match List I with List II:

List-I	List-ll
A. \(Fe ^{2+}\)	I. 2.84 BM
B. \(Ni ^{2+}\)	II. 0.00 BM
C. \(Mn ^{2+}\)	III. 4.90 BM
D. \(Zn ^{2+}\)	IV. 5.92 BM

Choose the correct answer from the options given below :

The current in a solenoid changes from 0.0A to 10.0A in 0.1 sec. If an average emf of 2V is induced in the circuit, the value of self-inductance is:

A series LCR circuit is connected to a 220 V variable frequency (a.c) supply. If L = 20 mH, \( C = 800/\pi^2 \, \mu \text{F} \) and R = 110 \( \Omega \). The frequency of the source, for which the average power absorbed by the circuit is maximum will be:

If A and B are events such that \(P(A \mid B)=P(B \mid A)\), then :

Read the passage carefully and answer the Questions
Haloalkanes undergo nucelophilic substitution reactions owing to the polarity of CX bond. The nucleophile reacts with the haloalkane on the carbon possessing a partial positive charge holding the halogen atom. The halogen atom X is replaced by a nucleophile. Depending on the kinetics and mode of bond breaking, the mechanism can be either SN1 or SN2 reaction. The rate of SN1 reaction is governed by the stability of carbocation and in SN2 reaction, the rate of reaction is governed by steric factor. Chirality is the main factor in both SN1and SN2. In SN1 reaction, the chirality of alkyl halide is accompanied by racemization of the product, while in SN2 reaction, the product is characterized by inversion of configuration. The structure of alkyl halide and the nature of the solvent also governs the mechanism of the substitution.
What is meant by the term racemic mixture?

In class XII, suppose \(5 \% \) of boys and \(0.25\%\) of girls are physically fit for a game.
A fit student is selected at random from this class having same number of boys and girls.
If the probability that the selected student is a girl is \(\frac{m}{n}\), \(\operatorname{gcd}(m, n)=1\), then \(m+n\) is equal to