Two spheres of silver of same radii, one solid and the other hollow are charged to the same potential, then :

A metallic wire of uniform area of cross section has a resistance R, resistivity \(\rho\) and power rating P at V volts. The wire is uniformly stretched to reduce the radius to half the original radius. The values of resistance, resistivity and power rating at V volts are now denoted by R', and P' respectively. The corresponding values are correctly related as __________ . Fill in the blank with the correct answer from the options given below

Identify the correct statement(s) among the following.
1. Electrical conductivity in an intrinsic semiconductor is due to electrons excited from the conduction band to valence band.
2. In germanium atom electrical conductivity is due to intrinsic charge carriers.
3. In doped atoms, the size of the dopant atom should be almost the same as that of the intrinsic crystal.
4. In n-type semiconductor, the donor atom becomes negatively charged.
Choose correct answer from the options given below:

Choose the correct statments from below:
A. Nuclides with same atomic number but different number of neutrons are called Isotopes.
B. Nuclides with same mass number are known as Isotopes.
C. Nuclides with same number of neutrons are called Isobars.
D. More than 99.9% mass of atom is concentrated in nucleus.
Choose the correct answer from the options given below:

At a place, the horizontal component of earth's magnetic field is \( 4 \times 10^{-4} \text{ T} \) and angle of dip is \( 60^\circ \). The value of horizontal component of earth's magnetic field at the equator is :

Match List-I with List-II:

List-I (Application)	List-II (Electromagnetic Waves)
(A) Used in radiography	(I) UV rays
(B) Detection by stimulating nerve endings of the human retina	(II) Microwaves
(C) Water purification	(III) Visible light
(D) Radar communication	(IV) X rays

Choose the correct answer from the options given below:

What is the power factor of an ac circuit having resistance R and inductance L connected in series? (\( \omega \) is the angular frequency )

Consider the following statements about the physical and chemical characteristics of interstitial compounds and identify the correct statements
(A) They have high melting points.
(B) They are very hard.
(C) They retain metallic conductivity.
(D) They are chemically very reactive.
Choose the correct answer from the options given below:

Let \(A=\{1,2,3\}\) and \(R=\{(1,1),(1,3),(3,1),(2,2),(2,1),(3,3)\}\) be a relation on \(A\). Then, \(R\) is:

The wavelength of the first spectral line of an element is 5893 Å. The first excitation energy is :

An equiconvex lens has a focal length\(\frac{2}{3}\) times the radius of curvature of either surface. The refractive index of the material of the lens is :

Read the passage carefully and answer the following questions
Aldehydes, carboxylic acids and ketones are widespread in the animal and plant kingdoms. They play a pivotal role in various biochemical processes of life. Their presence in nature adds fragrance and flavor. These compounds are widely used in food products, pharmaceuticals, paints, resins and other important product industries. These compounds are prepared by various laboratory methods, which mainly include oxidation, formylation, acylation and reduction. Due to the polar nature of the carbonyl group in aldehydes and ketones, they can exhibit different reactions like nucleophilic addition. They do exhibit redox and various condensation reactions which lead to the formation of various important compounds. On the other hand, the carboxylic acids are mainly prepared by oxidation and hydrolysis of different compounds. The carboxylic acid consists of a carbonyl group and the hydroxy group (attached to the carbonyl carbon atom). This makes it possible for the carboxylic acid to participate in various chemical reactions which involve cleavage of the C-OH bond and the O-H bond along with the reactions involving the complete - COOH group.
Arrange the following in the increasing order of their \(p K_{ a }\) values :
(A) \(CF _3- COOH\)
(B) \(O _2 N- CH _2- COOH\)
(C) \(NC - CH _2- COOH\)
(D) \(H - COOH\)
Choose the correct answer from the options given below :

Match List - I with List - II.

List 1	List 2
(A) Infra red waves	(I) to detect fracture of bones
(B) Radio waves	(II) absorbed by the ozone layer of atmosphere
(C) X-rays	(III) to treat muscular pain
(D) Ultraviolet rays	(IV) for broadcasting

Choose the correct answer from the options given below :