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It is a temperature at which both the allotropes of sulphur are stable ; 369 K is called transition temperature.

The angle (in radian) subtended by an are of a circle at its centre is defined as the ration of the length of the are to its radius,i.e.,

θ (in radian) = length of are/radius = no dimension.

Hence, the measure of an angle is independent of the unit of length used to measure the angle.

The tip of nib of a fountain pen is split to make a narrow capillary so that the ink rises to the tip of the nib continuously. This helps us to write smoothly with ink.

1. (a) (✓)

2. (b) (✓)

3. (b) (✓)

The grandchild in this poem symbolizes the future generation of humans.

The poem foreshadowed the hazards faced by the fauna of four different habitats like terrestrial, water, air, and polar regions due to humans’ indisciriminate activities in degrading the environment and how some species had come into endangered zone.

Due to surface tension, the free surface of liquid at rest behaves like a stretched membrane. When an iron needle floats on the surface of clean water, its weight is supported by the stretched membrane. When some detergent is added to this water, its surface tension decreases.

As a result of it, the stretched membrane on the surface of water is weakened and is not able to support the weight of needle. Hence, needle sinks in such water.

Dimensional formula- of modulus of rigidity is M¹ L^-1 T^-2.

According to Hooke’s law, within the limit of elasticity, the stress is proportional to strain.
Stress ∝ Strain
or Stress = E × Strain.
Here E is a constant known as modulus of rigidity. Its unit is same as that of stress.

“Elasticity is the ability of a body to resist the change in shape or size caused by a deforming force and to return to its original size and shape when the deforming force is removed.” Those bodies which regain its original configuration immediately and completely after the removal of deforming force are called perfectly elastic bodies. And those bodies which does not regain its original configuration at all on the removal of deforming force are called perfectly plastic bodies.

It is the maximum value to deforming force under which an object acts as an elastic body i. e. , when the applied force is removed, the body regains its original position. If force beyond this value is applied on an object, it undergoes permanent deformation.

When deforming force is applied an any object then there is change in its length or volume or shape. The proportional change produced in the shape and size of an object due to the deforming force is called strain. It is a dimensionless quantity. 

According to deformation strain have a three types:

(a) Longitudinal strain
(b) Volume strain
(c) Shearing strain

The force that changes the shape and size of the body is called the Deforming force.

∵ Modulus of elasticity = \(\frac { Stress }{ Strain } \)
Since, strain is a dimensionless quantity
∴ Unit of modulus of elasticity is same as that of stress i.e., Nm^-2

Perfectly elastic bodies: Those bodies which regain their original configuration immediately and completely after the removal of deforming force are called perfectly elastic bodies.

Perfectly plastic bodies: Bodies which do not regain their original configuration at all on the removal of deforming forces are called perfectly plastic bodies. Generally no body is perfectly elastic and perfectly plastic; but they are between these two extremes. Normally, quartz is perfectly elastic body and putty, wax are perfectly plastic bodies.

Rigid bodies: Bodies which do not get deformed or have very small deformation on applying external force are called rigid bodies.

(a) Consider a person who leaves home for work in the morning and returns home in the evening.

The magnitude of the displacement of the person during the interval is zero but the total length of path covered = 2 × distance between the home and the workplace.

Magnitude of displacement is the magnitude of the shortest length between the two points. The second quantity is clearly always greater than or equal to the first quantity. The equality holds if the body has not moved at all (path length = magnitude of displacement = 0)

(b) Average velocity = Δx/Δt, is zero (like in the example explained in) (a) then average velocity = 0.

Average speed = Total path length/Time taken

2 × (Distance between the home and the work place/Time taken to traverse this distance)

= Clearly average speed ≥ magnitude of average velocity. Equality exists when body does not undergo any motion.

The potential energy will increase in both the situations.

High relative humidity and dew point temperature of the air are the j prerequisites for condensation.

Negative charge is found at the low end of the cumulonimbus clouds.

Positive charge is found at the upper end of the cumulonimbus clouds.

1. The condensed water or fine particles of snow accumulate around dust particles at high altitudes leading to formation of clouds.

2. The condensed water or fine particles in the clouds are almost weightless. Therefore, clouds float in the sky.

(a) van der Waals equation for n moles of a gas:

PV = nRT

Where, P = Pressure

V = Volume

n = No. of moles

R = Gas constant

T = Absolute temperature

(b) Carbon dioxide (CO₂) can be easily liquefied because it has higher critical temperature that means it can be liquefied at higher temperature more easily. So, CO₂ has higher inter-molecular forces than methane.

Kinetic energy of a molecule is directly proportional to temperature and independent of its mass. So both the molecules, A and B at any temperature will have equal kinetic energy.

Highest energy - Gas

Lowest energy - Solid

Kinetic energy of a molecule is directly proportional to temperature and independent of mass so both the molecules will have the same kinetic energy.

The ratio pv/RT is equal to the number of moles of an ideal gas in the sample. This number should be constant for all pressure, volume and temperature conditions. If the value of this ratio changes with increasing pressure, the gas sample is not behaving ideally.

At S. T. P, R = 8.20578 x 10^-2 L at m k^-1 mol^-1.

Pressure exerted by saturated water vapors is called aqueous tension.

P_{Dry gas} = P_Total – aqueous tension

1. Monobasic acid

2. Weak acid

3. Hydracids

4. Less volatile acid

5.  Dibasic acid

• The degenerate orbitals like 4f and 5f acquire extra stability when they are half filled (4f⁷) or completely filled (5f¹⁴).
• The expected and observed electronic configuration of gadolinium is,₆₄Gd [Xe] 4f⁷ 5d¹ 6s².
• The expected and observed electronic configuration of lawrencium is ₁₀₃Lr [Rn] 5f¹⁴ 6d¹ 7s². 

(C) d-block elements

Brownian Movement:- In 1828, an English Botanist Brown observed that pollen grains suspended in water execute a continuous ig-zag motion. He named this phenomenon as Brownian movement. Later on it was found that the particles of the dispersed phase of all colloidal solutions also execute a continuous zig-zag motion (in the figure).

A proof of Brownian movement in furnished if we watch the smoke particles in the beam of light in a cinema hall. The smoke particles continue to move ceaselessly in a zig-zag fashion.

Cause of Brownian movement:- The dispersed phase particles of the colloidal solution are being constantly colloided by the molecules of the dispersion medium. It was stated by Wiener is 1863 that the dispersed phase particles increases, then the chances of unequal bombartment decrease. This can be confirmed by the fact that the suspensions do not show any such movement due to large molecule size.

Significance:- This movement opposes the force of gravity. On the colloidal particles. As a result, these particles always remain in the state of motion and do not settle.

This is responsible for the stability of the colloidal solution.

BCl₃ be have as Lewis as acid due to be electron deficient in BCl₃.

(i) ₆₄Gd [Xe] 4f⁷ 5d¹ 6s² (Observed) 

(ii) ₇₀Yb [Xe] 4f¹⁴ 5d°6s² (Observed)

Half life period:- Time taken to complete half portion of the first order reaction (t_1/2) is called half life period.

It is denoted t_1/2 We know that t = 2.303/t log{a}/{a - x}

Here a is the amount of the substance initially present and x is the amount that has reacted in time 'k'. In half life time (t_1/2), a will be reduced to a/2(x = a/2)

∴ Half life period

(t_1/2) = 2.303/k log{a}/{a - (a/2)} = 2.303/k log2 = 2.303/k x 0.3010

∴ t_1/2 = 0.693/k

The size of central atom H₂S is larger than that in H₂O. S-H bond is larger and weaker than O-H bond H₂O, hence H₂S is more acidic than H₂O.

Due to inert molecular H bond is find in H₂O atom H₂S is a gas while H₂O is a liquid at a room temperature.

• Gd³⁺ has electronic configuration, [Xe] 4f⁷
• Due to extra stability of half filled orbital, it does not allow f → f transition, and hence does not absorb radiations in the visible region.

 Hence Gd³⁺ is colourless.

H-O bond is more polar than H-S bond because of greater electronegativity difference in the bonding atoms. As a result, H₂O molecules are involved in the intermolecular hydrogen bonding and get associated to be liquid at room temperature. Since intermoecular hydrogen bonding is negligible in the molecules of H₂S, they do not get associated and remain in the gaseous state at room temperature.

(i) H₂SO₅ and H₂S₂O₈

Doping A semiconductor obtained after adding desirable impurity atoms in the intrinsic semiconductor is called extrinsic or depend semiconductor. The process of adding desirable impurities in the intrinsic semiconductor is called doping.

The difference between Electro Magnet and Permanent Magnet are as follows : 

Electro Magnet : 

(i) Its shows the properties of Magnet at that time were the current flows on that time is Magnetic properties is end even current is closed. 

(ii) When the direction of the current of electro Magnet is charged their the nature of its axis is also changed.

Permanent Magnet: 

(i) Its exists the Magnetic properties at maximum days

(ii) The nature of the axis of permanent magnet is fixed and permanent. We can not change this easily.

The cyclotron is used :

(1) To bombard nuclei with energetic particles, so accelerated by it, and study the resulting nuclear reactions. 

(2) It is also used to implant ions into solids and modify their properties or even synthesise new materials. 

(3) It is used in hospitals to produce radioactive substances which can be used in diagnosis and treatment. 

The oscillator frequency should be same as proton’s cyclotron frequency. 

we have B = 2πmv /q = 6.3 ×1.67 × 10^–27 × 10⁷ / (1.6 × 10^–19) = 0.66 T 

Final velocity of protons is 

v = r × 2πv = 0.6 m × 6.3 ×10⁷ = 3.78 × 10⁷ m/s. 

E = ½ mv² = 1.67 ×10^–27 × 14.3 × 10¹⁴ / (2 × 1.6 × 10^–13) = 7 MeV. 

Similarities:

Both electrostatic field and magnetic field:

Follows the principle of superposition.

Depends inversely on the square of distance from source to the point of interest.

Differences:

(i) Electrostatic field is produced by a scalar source (q) and the magnetic field is produced by a vector (I \(\overrightarrow{dI}.\)).

(ii) Electrostatic field is along the displacement vector between source and point of interest; while magnetic field is perpendicular to the plane, containing the displacement vector and vector source.

(iii) Electrostatic field is angle independent, while magnetic field is angle dependent between source vector and displacement vector.

Mass of the body = 2kg 

Initial velocity, u = 0 

Final velocity, v = 30 m/s 

Time, t = 1s

Acceleration, a = (v-u)/t = 30 m/s² 

Force = ma = 60N

(d) 15: 8

Because,

= A = 3B/2

= C = 4B/5

Then,

= A: C = (3B/2): (4B/5)

= (A/C) = (3B/2)/ (4B/5)

= (A/C) = (3B/2) × (5/4B)

= (A/C) = (15/8)

= A: C = 15: 8