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a. The pigtail is faithful.

b. He criticizes the sage’s ignorance and pities him in a serious tone, using the word ‘Alas’.

c. The back of the sage is referred to here.

Yes, this poem is an ironic poem because the word ‘sage’ is used in an ironic sense to refer to a person who is dull witted. It insists on how learned men lack practical common sense.

a. He turned round and round, out and in all day.

b. He was puzzled because he could not change the position of his pigtail, even though he turned round and round all day.

c. The rhyme scheme is ‘a a a b’.

The theme of the poem is ‘when men are too learned or too wise, they lose the sight of reality. Sages are considered more wise. The irony of the poem is that the sage shows total foolishness. The poet uses the words in old English such as ‘sage’ , ‘yore’ , ‘mused’ to emphasize that right from the olden days, the highly learned people are too foolish and irrational. He attacks them as people, who do not have practical common sense. He also conveys a message to the readers to be alert and thoughtful and always act in a meaningful manner.

The antics of the sage, usage of mock serious tone, absurdity of the sage’s ‘curious case’ and his solution, the way the poet organizes his materials and arranges the sentence structures makes the poem humorous. The repetition of the last line of each stanza add humour to the poem because it always brings to focus how the pigtail mocks at the sage’s efforts by stubbornly remaining behind him. The ending of the poem indicates the readers that the sage didn’t stop his rotation, although it is useless. This also gives a humorous touch to the poem.

Correct answer is (c) feet

Correct answer is (b) cattle

Correct answer is (c) twenty

Correct answer is (d) two

Mother Wolf talked about Shere Khan. She said that Shere Khan’s mother called him Lungri (the Lame One), as he had been lame in one foot from his birth. That is why he had only killed cattle. As the villagers of Waingunga were angry with him, he had come to Seeonee Hills to make their villagers angry.

Shere Khan’s mother called him Lungri (the Lame One).

She called him so because he had been lame in one foot from his birth.

The law of the jungle, forbids Shere Khan to change his quarters without due warning. ‘

Shere Khan had shifted his hunting grounds to Seeonee Hills for the next moon.

It praised them saying that they are beautiful, noble and young, with large eyes.

The law of the Jungle, which never orders anything without a reason, forbids every beast to eat Man, except when he is killing to show his children how to kill and then he must hunt outside the hunting grounds of his pack or tribe. The real reason for this is that Man-killing means, sooner or later, the arrival of men on elephants with guns and rockets and torches. Then everybody in the jungle suffers. The reasons the beasts give among themselves is that Man is the weakest and most defenceless of all living things.

The Jungle Book was written by Rudyard Kipling. The book has attracted audiences of all ages for its plot structure and characters. Children especially enjoy this story, as it deals with the early childhood of a boy in the midest of wild animals in the forest. It has many episodes such as the acceptance of Mowgli by the pack of wolves, the friendship between Bagheera, the black panther and Mowgli. Bagheera serves as a friend, protector and mentor to the man-cub. It has also episodes of Mowgli’s adventurous trips in the jungle with Baloo, the bear and the fight between Mowgli and the monkey’s gang. Mowgli was forced to leave the jungle. But after sometime, he decides to return to the jungle and lives there.

Mother Wolf shook herself clear of the cubs and sprang forward. Her eyes were , like the two green moons in the darkness. She faced the blazing eyes of Shere Khan bravely.

Mother Wolf named the man-cub as ‘Mowgli’. It means the little frog.

Volume of one hydrogen atom = 4/3πr³

= 4/3 x 3.14 x (0.5 x 10^-10)m³

= 5.23 x 10^-31 m³.

According to Avogadro's hypothesis, one mole of hydrogen contains 6.023 x 10²³ atoms.

Atomic volume of 1 mole of hydrogen atom

= 6.023 x 10²³ x 5.23 x 10^-31

= 3.15 x 10^-7 m³.

Since C₀ + C₁ + C₂ + C₃ + ….. + C_n = 2ⁿ

Putting n = 9, we get

C₀ + C₁ + C₂ + ….. + C₉ = 2⁹

∴ C₀ + C₁ + C₂ + …… + C₉ = 512

Since C₀ + C₁ + C₂ + C₃ + ….. + C_n = 2⁸

Putting n = 8, we get

C₀ + C₁ + C₂ + ….. + C₈ = 2⁸

∴ C₀ + C₁ + C₂ + ….. + C₈ = 256

(C) (n + 1)^th

(1 + x)²ⁿ has (2n + 1) terms.

\(\therefore\) (n + 1)^th term is the middle term.

(C) 3360

(x² – 2x)¹⁰ = x¹⁰ (x – 2)¹⁰

To get the coefficient of x¹⁶ in (x – 2x)¹⁰,

we need to check coefficient of x⁶ in (x – 2)¹⁰

∴ Required coefficient = ¹⁰C₆ (-2)⁴

= 210 × 16

= 3360

(B) 120

r = 7

t₈ = ¹⁰C₇ x⁷ = ¹⁰C₃ x⁷

∴ Coefficient of 8th term = ¹⁰C₃ = 120

Given s = 8t – 6t² 

v = \(\frac{ds}{dt}\)= 8 – 12t car stops when v = 0

∴ 8 – 12t = 0 ⇒ t = \(\frac{8}{12}\)= \(\frac{2}{3}\) sec.

Given S = 80t -16t² 

v = \(\frac{ds}{dt}\)= 80 – 32t 

At t = 2 sec, v = 80 – 32 (2) 

= 80 – 64 = 16 ft./sec. 

Acceleration =\(\frac{ds}{dt}\) = -22 ft/sec².

f(x) = x³ – 12x + 1 

f'(x) = 3x² – 12 

f'(x) = 0 ⇒ 3x² – 12 = 0 

3x² = 12 ⇒ x² = 4 ⇒ x = ±2 

The x values are -3, -2, 2, 5 

f(x) (at x = -3) = (-3)³ – 12 (-3) + 1 = -27 + 36 + 1 = 10

f(x) (at x = -2) = (-2)³ – (12)(-2) + 1 = -8 + 24 + 1 = 17 

f(x) (at x = 2) = 2³ – 12 (2) + 1 = 8 – 24 + 1 = -15 

f(x) (at x = 5) = 53 – 12 (5) + 1 = 125 – 60 + 1 = 66 

From the above four values 10,17,-15 and 66, we see that absolute maximum is 66 and the absolute minimum is -15.

f(x) = 1 – 2x – x² 

f'(x) = -2 – 2x 

f'(x) = 0 ⇒ 2x = -2 ⇒ x = -1; The points are -4, -1, 1 

At x = -4, f(x) = 1 – 2(-4) – (-4) = 1 + 8 – 16 = -7 

At x = -1, f(x) = 1 – 2 (-1) – (-1) = 1 + 2 – 1 = 2 

At x = 1, f(x) = 1 – 2 (1) – (1) = 1 – 2 – 1 = – 2 

Therefore, the absolute minimum is -7 and the absolute maximum is 2.

(b) 2πr(dr/dt)

Given A = πr²

Differentiating with respect to t on both sides,

dA/dt = 2πr(dr/dt)

(a) – cot θ

Given, the slope of normal = -1/m = tan θ

Slope of the tangent = m = - 1/tan θ = - cot θ

(i) Given s = 2t² + 3t 

(i.e.) f(t) = 2t² +3t 

Now f(3) = 18 + 9 = 27 = f(a) 

f(6) = 72 + 18 = 90 = f(b)

Now (f(b) - f(a))/(b - a) = (90 - 27)/(6 - 3) = 63/3

= 21m/s 

(ii) f(t) = 2t² + 3t 

f'(t) = 4t + 3 

f'(3) = 4(3) + 3 = 15 

f'(6) = 4(3) + 3 = 15

Sir C.V. Raman explained the phenomenon of scattering in gases and liquids.

Presbyopia: It is a vision defect when the ability of accommodation of the eye usually decreases with ageing.

Scattering: Atoms or molecules which are exposed to light absorb light energy and radiate some part of the light energy in different directions. This process is called scattering.

1. This is because there is no atmosphere containing air in the outer space to scatter light. 

2. Since there is no scattered light which can reach our eyes in outer space, the sky looks dark and black there. 

3. This is why the astronauts who go to outer space find the sky to be dark and black instead of blue.

u = 108 km/h = 108 \(\times\frac{5}{18} = \) 30 m/s; m = 1000 kg ; v = 0 m/s

F = m\((\frac{v\,-\,u}{t}) = 1000(\frac{0\,-\,30}{4})\) = -7500 kg ms^-2  = -7500 N

The law of conservation of momentum is not violated by stopping vehicles on applying brakes. Some retarding force is being applied due to brakes and the vehicles comes to rest such that the total loss of its momentum is equal to the impulse of the applied force. Thus the law of conservation of momentum is not violated.

Here, m= 0.1 kg

h = 0.24 m

x = 0.01 m

When particle is dropped from a height h and spring is compressed by x, then loss in P.E. of particle = mg(h + x), while gain in elastic potential energy of spring will be, 1/2 kx²

Hence, mg(h + x) = 1/2 kx²

Similarly, mg(h' × x') = 1/2 kx¹²

Dividing, we get

{h + x}/{h' + x'} = (x/x')²

⇒ {0.24 + 0.01}/{h' + 0.04} = (0.01/0.04)²

On solving, we get, h' = 3.96 m

Thermal conductivity of copper is greater as compared to the conductivity of steel. With copper bottom, more heat is conducted inside which helps in the preparation of meals quickly.

The heat lost by water in going from 20 °C to 0°C,

Q₁ = Ms_w ∆T = \(\frac{M}{1000}\) × 4.2 × 10³ × (20) = 84M J

Now, heat required to convert m g of ice into water at 0 °C,

Q₂ = mL = \(\frac{M}{1000}\) × 3.36 × 10⁵ = 336m J

1. For temperature of mixture to be 0 °C,

Q₂ > Q₁

⇒ 336m > 84M

⇒ m > \(\frac{M}{4}\)

2. For temperature of mixture to exceed 0 °C,

Q₂ < Q₁ ⇒ m < \(\frac{M}{4}\)

(B) low specific heat and high conductivity.

1. 

• At high altitude density of air is low which causes reduction in atmospheric pressure. 
• As pressure is less, boiling point of water lowers. 
• Water, at high altitude, starts boiling below 100°C. 
• As food is cooked mostly through the water boiling, cooking of food becomes difficult. 

2. 

• Pressure cooker operates by expelling air within the cooker and trapping steam produced from the liquid. (mostly water) boiling inside. 
• Due to high internal pressure, boiling point of liquid increases and liquid boils at temperature higher than its boiling point. 
• The increased boiling point allows more absorption of heat by liquid and steam formed is superheated.
• As a result, food gets cooked quickly.

Correct option is: (A) 35 °C

Black pain absorbs more heat. The black painted bottoms absorbs more heat and help in cooking meals faster.

The energy radiated per unit time is directly proportional to the surface area of the body. By curling into a ball, the surface area of the body of the animals decreases and hence loss of heat is reduced.

Inertial mass: The mass of a body which determines its inertia in translatory motion is called its inertial mass. It is measured from Newton’s second law of gravitation.

M_i = F/a

Gravitational mass: The mass of a body which determines the gravitational pull upon it due to the earth is called its gravitational mass. It is measured by using Newton’s law of gravitation.

M_g = FR²/GM

Method for measurement of mass:

1. Mass, until recently, was measured with a standard mass of the international prototype of the kilogram (a platinum-iridium alloy cylinder) kept at international Bureau of Weights and Measures, at Serves, near Paris, France.

2. As platinum – iridium piece was seen to pick up microparticles and found to be affected by atmosphere, its mass could no longer be treated as constant.

3. Hence, a new definition of mass was introduced in terms of electric current on 20th May 2019.

4. Now, one kilogram mass is described in terms of amount of current which has to be passed through electromagnet to pull one side of extremely sensitive balance to balance the other side which holds one standard kg mass.

5. To measure mass of small entities such as atoms and nucleus, atomic mass unit (amu) is used.

It is defined as (\(\frac{1}{12}\))^th mass of an unexcited atom of carbon -12(C¹²).

1 amu ≈ 1.66 × 10^-27 kg.

The two walls enclose air between them which provide heat insulation.