Magnetic moment of a thin bar magnet is 'M'. If it is bent into a semicircular form, its new magnetic moment will be :

In a double slit experiment, the distance between slits is increased 10 times whereas their distance from screen is halved, then what is the fringe width ?

Carbon, silicon and germanium have four valence electrons each. Their valence and conduction bands are separated by energy gap \( E_g \). If we represent \( (E_g)_C, (E_g)_{Si} \) and \( (E_g)_{Ge} \) as their respective energy gaps, then which of the following is true

A moving coil galvanometer has a resistance of 40 \( \Omega \). It gives a full scale deflection with a current of 2 mA. How is to be modified to convert it to a voltmeter of 5 V range?

Match List-I with List-II

List-I (Law/Rule)	List-II (Application)
(A) Faraday's law	(l) Determines direction of force on a current carrying wire in a magnetic field
(B) Lenz's law	(II) Obeys principle of energy conservation
(C) Fleming's right-hand rule	(III) Determines direction of induced current
(D) Fleming's left-hand rule	(IV) Electromagnetic Induction

Choose the correct answer from the options given below :

A proton moves from south to north with a speed of \( 2 \times 10^7 \, \text{m/s} \). When a magnetic field is applied from west to east, the proton gets an acceleration of \( 10^{12} \, \text{m/s}^2 \). The mass of the proton is \( 1.6 \times 10^{-27} \, \text{kg} \). The value of the magnetic field is:

An equiconvex lens has a focal length of 20 cm and its radius of curvature is 30 cm . Its refractive index is

Match List - I with List - II.

List - I	List - II
A. Simple and face centred cubic	I. \(\text{a} = \text{b} = \text{c}\)
B. Cubic and rhombohedral	II. \(\alpha = \beta = \gamma = 90°\)
C. Cubic and tetragonal	III. have only two crystallographic angle of \(90°\)
D. Hexagonal and monoclinic	IV. belong to the same crystalline system

Choose the correct answer from the options given below :

Choose the correct statements from the following :
(A) two different solutions of sucrose of same molality prepared in different solventswill have the same depression in freezing point.
(B) the osmotic pressure of a solution is given by the equation \(II = CRT\) (where C is the molarity of the solution)
(C) decreasing order of osmotic pressure for 0.01 M aqueous solution of \(BaCl _2, KCl , CH _3 COOH\), and sucrose is \(BaCl _2 > KCl > CH _3 COOH >\) sucrose
(D) according to Raoult's law the vapor pressure exerted by a volatile component of asolution is directly proportional to its mole fraction in the solution
Choose the correct answer from the options given below :

If \(P(A)=\frac{6}{11}, P(B)=\frac{5}{11}\) and \(P(A \cup B)=\frac{7}{11}\), then
A. \(P(A \cap B)=\frac{4}{11}\)
B. \(P(A \mid B)=\frac{ 4 }{ 5 }\)
C. \(P(B \mid A)=\frac{2}{5}\)
D. \(A\) and \(B\) are independent events
E. \(P(\) neither \(A\) nor \(B)=\frac{4}{11}\)
Choose the correct answer from the options given below:

Industrial melanism is an observation which supports evolution by:

The interval, on which the function \(f(x)=x^2 e^{-x}\) is increasing, is equal to:

The flocculating power of \(\left[ Fe ( CN )_6\right]^{4-}\) is higher than \(PO _4^{3-}\) ion because :