Which of the following will have the smallest radius of first orbit (n = 1)

A bar magnet when suspended horizontally and perpendicular to earth's field experiences a torque of \( 3 \times 10^{-4} \text{ N m} \). The Magnetic moment of the magnet would be: (take horizontal component of Earth's magnetic field at the place \( 0.4 \times 10^{-4} \text{ T} \))

Arrange the following steps \(( A , B , C\) and D \()\) in proper sequence to determine the index correction in the given arrangement.

(A) The difference between the two gives the correction to be applied to the observed distance.
(B) The positions of the uprights are read on the scale. Their difference gives the observed distance between tip of the pin and the pole of the mirror.
(C) A thin straight index needle OP is placed so that its one end O touches the tip of the pin and the other end P touches the pole of the mirror.
(D) Length of the needle OP is measured by placing it on the scale which is the actual distance between the points in question.
Choose the correct answer from the options given below:

A charge of \( Q = 8.0 \times 10^{-9} \text{ C} \) is uniformly distributed on the surface of a spherical shell of radius \( R = 10 \text{ cm} \). The electric field at a distance of 10 cm from the outer surface of the shell is

Light of uniform intensity shines perpendicularly on a totally absorbing surface, fully illuminating the surface. If the area of the surface is decreased, what is the effect on radiation pressure ?

When a dielectric slab is introduced in between the plates of a charged capacitor with battery connected across the plates, following are the observations. Choose which observation is incorrect?

Two concentric circular coils of 10 turns each are situated in the same plane. Their radii are 20 cm and 40 cm and they carry 0.2 A and 0.3 A currents respectively in opposite directions. The magnetic field at the center is:

Match List-I with List-II

List-I	List-II
(A) Degree of this differential equation \(\frac{d^4 y}{d x^4}+2 \log _e\left(\frac{d^3 y}{d x^3}\right)=0\)	(I) 1
(B) Order of this differential equation \(e^{\left(\frac{dy}{dx}\right)^3}+3 y\left(\frac{d^2 y}{d x^2}\right)^3=0\)	(II) 4
(C) Degree of \(\frac{d^4 y}{d x^4}+\left(\frac{d y}{d x}\right)^2=0\)	(III) not defined
(D) Order of the differential equation \(2 \frac{d^4 y}{d x^4}+\left(\frac{d^2 y}{d x^2}\right)^5=0\)	(IV) 2

Choose the Correct answer from the options given below :

If 200 MeV energy is released in the fission of a single nucleus of uranium-235, how many fissions per second will produce a power of 32 kW?

What does 'r' denotes in the given equation?
(dN/dT = rN)

What would be the amount of energy released if 1 g of a substance is converted to energy? (Given, speed of light in vacuum \(=3 \times 10^8 m s ^{-1}\) )

Match List - I with List - II.

LIST I	LIST II
A. Ovulatory phase	I. Proliferative phase
B. Follicular phase	II. Both LH and FSH attain peak level
C. Luteal phase	III. Breakdown of endometrial lining of uterus and its blood vessels
D. Menstrual phase	IV. Secretory phase

Choose the correct answer from the options given below:

A short bar magnet of magnetic moment \( 5.25 \times 10^{-2} \text{ J/T} \) is placed with its axis perpendicular to Earth's magnetic field direction. The distance from the center of the magnet on its perpendicular bisector where the resultant field makes 45° with Earth's field will be : (Earth's magnetic field at that place is 0.42 G.)