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(c) 36

Explanation:

Given n/2-3n/4+5n/6=21

On rearranging and taking L.C.M,

(6n_9n+10n)/12=21

7n=21(12)

n=36

(i), (ii), (v), (vi), (vii) are the linear equations.

Let the side of the cube be “a” unit 

Original Surface area = 6a² sq units 

Now, when each side of a cube is doubled than its surface area: 

New surface area = 6 (2a²) sq units 

= 24a² sq units 

Therefore, the surface area of the cube is 4 times than its original area 

Hence, option B is correct

Given, 

the radius of the cylindrical tube, r = 12 cm 

Level of water raised in tube, h = 6.75 cm 

Volume of cylinder = πr² h 

= π (12)² × 6.75 cm³ 

= π x 12² x 6.75 cm³----------(i) 

let r be the radius of a spherical shell balls 

volume of the sphere = \(\frac{4}{3}πr^3\)-------(ii) 

∵ volume of cylinder = volume of spherical ball 

∴ π x 12² x 6.75

= \(\frac{4}{3}πr^3\)

⇒ r³ = \(\frac{{12}^2\times{6.75}}{\frac{4}{3}\times{π}}\)

⇒ r = 9 cm 

∴ radius of spherical ball, r = 9 cm

Since A = {1, 2, 3, 4} and B = {5, 7, 9}. Therefore,

(i) A × B = {(1, 5), (1, 7), (1, 9), (2, 5), (2, 7), (2, 9), (3, 5), (3, 7), (3, 9), (4, 5), (4, 7), (4, 9)} 

(ii) B × A = {(5, 1), (5, 2), (5, 3), (5, 4), (7, 1), (7, 2), (7, 3), (7, 4), (9, 1), (9, 2), (9, 3), (9, 4)} 

(iii) No, A × B ≠ B × A. Since A × B and B × A do not have exactly the same ordered pairs. 

(iv) n (A × B) = n (A) × n (B) = 4 × 3 = 12

n (B × A) = n (B) × n (A) = 4 × 3 = 12 

Hence n (A × B) = n (B × A)

Given radius of cylinder (r’) = \(\frac{12}2\) = 6 cm 

Given radius of hemisphere (r’’) = \(\frac{6}2\) = 3 cm 

Given height of cylinder (h) = 15 cm 

Height of cone (l) = 12 cm 

Volume of cylinder = πr²h 

= πr(6)²(15) cm ………. (1) 

Volume of each cone = Volume of cone + Volume of hemisphere 

V = π(r)²(l) + \(\frac{2}3\) π(r)³ 

V = π(3)²(12) + \(\frac{2}3\) π(3)³ ………… (2) 

Let number of cone be n 

n (volume of each cone) = volume of cylinder 

n = [( \(\frac{1}3\) π(3)² (12) + \(\frac{2}3\) π(3)³] = π(16)² 15 

⇒ n = 10

Let us assume shape of well is like a solid circular cylinder 

Radius of cylinder, r = 2/2 = 1m 

Depth(height) of well, h = 14m 

Volume of right circular cylinder, V’ = πr² h 

= \(π\times{1}^2\times14\)---------(I) 

Given that, 

length of embankment, l = 40 cm 

Let width of the embankment be x m 

Volume of the embankment, V’’ = π^r2 h 

= π ((1+x)² – 1)² x 0.4 -----------(II) 

Since well is spread evenly to form the embankment, so their volumes, V’ = V’’ 

⇒ π × 14 = π ((1+x)² – 1)² x 0.4 

⇒ x = 5 m 

∴ Height of the embankment, x = 5cm

We have,

Diameter of well = 14 m

Radius of well = d/2 = 14/2 = 7m

Depth of well = 8 m

Volume of earth dug out from well = πr²h

= 22/7 × 7 × 7 × 8

= 1232 m³

This earth is spread out on width of 21 m.

Area × h = 1232

π(R² – r²) h = 1232

π(28² – 7²) h = 1232

22/7 (735) h = 1232

h = 1232×7 / 22×735

= 8624/16170

= 0.533 m

= 53.3 cm

∴ Height of embankment is 53.3 cm

Given,

Inner radius of the well = 4 m

Depth of the well = 14 m

We know that,

Volume of the cylinder = π r²h

= π × 4² × 14 …. (i)

From the question, it’s told that

The earth taken out from the well is evenly spread all around it to form an embankment

And, the width of the embankment = 3 m

So, the outer radius of the well = 3 + 4 m = 7 m

We know that,

Volume of the hollow embankment = π (R² – r²) × h

= π × (7² – 4²) × h …… (ii)

On equating both the equations (i) and (ii), we get

π × 4² × 14 = π × (7² – 4²) × h

h = 4² × 14 / (33)

h = 6.78 m

Therefore, the height of the embankment so formed is 6.78 m.

The dimensions of the well are

Radius = 5m

Depth = 8.4m

We know that

Volume of the earth dug out = Volume of well = πr²h

By substituting the values

Volume of the earth dug out = (22/7) × (5)² × 8.4

So we get

Volume of the earth dug out = 660 m²

It is given that

Width of embankment = 7.5m

We know that

External radius of embankment R = 5 + 7.5 = 12.5m

Internal radius of embankment r = 5m

We know that

Area of embankment = π (R² – r²)

By substituting the values

Area of embankment = (22/7) × (12.5² – 5²)

On further calculation

Area of embankment = (22/7) × (156.25 – 25)

So we get

Area of embankment = (22/7) × 131.25 = 412.5 m²

We know that

Volume of embankment = volume of earth dug out = 660m²

So the height of embankment = volume of embankment/ area of embankment

By substituting the values

Height of embankment = 660/ 412.5 = 1.6m

Therefore, the height of the embankment is 1.6m.

It was a struggle for the children to dry their clothes because there was always a wind – which blew away the clothes.

1. Walk straight and turn to the left at the end of the bend. 

2. Again reach the end and turn to the right, walking along the foot hills.

3. At the bend near the pond now turn to the right again and then to the left 

4. Walk straight passing the single coconut tree at the end of the path. 

5. Finally turn the curve to reach the rocky area where the key is kept behind the first rock.

Usha bought soap, matches, spices, sugar, a new pipe stem for grandfather’s hookah, an exercise book and marbles for Suresh and a necklace for herself.

1. rapid 

2. glancing 

3. join 

4. dull 

5. whisper 

6. foot hill 

7. mewed 

8. rooted 

9. slowly

Grandfather told Usha and Suresh about the English people who lived on the hill a hundred years ago. During a terrible storm one of the houses was hit by lightning and all the English people in it were killed, including the children – a brother and sister. Grandfather had seen the ghosts many times playing in the moonlight.

Usha thought it was the two ghostly creatures that she had seen in the night at the old fireplace. When the top of the plum tree swayed, it looked like a hand waving. Even the voices of the wind seemed like someone saying goodbye.

(b) pines and deodars

Correct answer is (c) Tibetan

Correct answer is (b) villains

(b) help with the cows

Usha goes for shopping

The wooing wind blew from the Himalayas over the hills and trees. It passed the haunted hill and reached the village, on the slope of the next hill. It tried to blow away the tin roofs, doors, windows, chimneys and clothes even on sunny days.

Usha, her brother Suresh and her friend Binya spread their clothes out to dry, firmly holding them by rocks. They rested awhile there. Usha planned to go for weekly shopping. Binya could not go with her. Suresh was willing but he had to help Grandpa. He was worried about how she would return alone in the dark passing the Haunted hill.

Grandfather told a story about an English family which lived on the Haunted hill a hundred years ago and the family members were killed by lightning. Grandfather had seen the two children of the family often playing in the moonlight near the ruins even now. This frightened them.Usha went for weekly shopping passing the fields, hill, ruins and valley. The ruined house had crumbling walls with wild flowers, a wild plum tree in the floor of the large hall, lizard on the stones and singing bird on the empty window.

She went to Aunt Lakshmis house for tea and when the clouds gathered for rain she hurried home after collecting her mother’s slippers from the cobbler.

Storm on the haunted hill 

The clouds and thunder were threatening to rain. So Usha hurried to reach home before dark. She did not have an umbrella but only a shawl and a scarf. Now the raindrops came faster. It was dark and lightning. Usha ran to the ruins to take shelter from the heavy winds and rain. She moved sideways to reach the corner of the old roof for shelter but touched a wild cat and was frightened. It was dry and more sheltered at the old fireplace opposite, but she did not know the way in the darkness. Her clothes and long black hair were soaked. The sound of the tin sheets and the storm blotted out all other sounds.

The lightning and thunder were often, Usha remembered grandpas story about lightning killing the English family and prayed it would not strike her. Suddenly when the lightning flashed again, Usha saw two small figures at the opposite wall near the disused fireplace – they could have been the children.

A night at the haunted hill

Usha wanted to leave the ruined building after seeing the two ghostly creatures. As she rushed out she bumped on something and screamed. There were reply screams and it was of Suresh and Binya. They had come looking for Usha in the stormy night. They were surprised, relieved and happy. They decided not to go home in the dark, thunder, lightning and rainy night when the paths also had fallen. Together they had warmth and confidence and stayed in the ruins all night, till the morning. They left the ruins on the top of the hill as the rain had stopped, birds began to sing, the sky was pink and bright and Suresh was hungry. As they were climbing down home, Usha saw a hand waving at them from the brow. Binya said it was the sway of the plum tree. But Usha also heard voices on the wind saying ‘Good Bye’. Usha wondered if it was just the wind.

1. b 

2. f 

3. a 

4. e 

5. c 

6. d

Mr. Phileas Fogg was a rich, English man. He was a member of the Reform Club of London. He orders his life precisely by the clock and makes a bet with fellow club members that he can travel around the world in 80 days. He travels with his French servant Passepartout. He is a precise and intelligent man. He is perfect in his manners and is very punctual as well as particular about what he wants. This is evident in this extract, when he is determined to travel to Allahabad as planned. He even goes to the extent of purchasing an elephant for 2000 pounds to continue his travel to Allahabad. These qualities of Mr: Fogg are highlighted in his extract.

The elephant driver was intelligent and a skilled young man. He covered the elephant’s back with saddle-cloth. He attached seats on each of its side. He sat on the neck of the elephant and set out from the village with the three passengers.

Snakes and tigers fled at the noise Of the train. The elephants stood gazing with sad eyes at the train, as it passed

1. journey – The act of travelling from one place to another. 

2. picnic – a trip or excursion to the country, seaside etc, on which people bring food to be eaten in the open air 

3. pilgrimaga – a religious journey.

4. tour – a journey for pleasure in which several places are visited 

5. vacation – holiday.

6. excursion – a short journey or trip.

To make travel convenient, we must book tickets well in advance. Then we have to Pack our things and schedule our trip. We have to reach the railway station in time and board the train in order to reach our destination.

Correct answer is (c) elephant

(a) Hongkong

(a) realistically

(b).collection

Correct answer is (b) furious

(a) work done regularly

(c) extremely

(b) assumes as truth.

The Sutpour mountains separated the Khandesh from Bundelcund.

It stopped at Burhampoor at half-past twelve.

(c) predicted

Correct option is: (b) displacement

C) displacement reaction

Zn + 2 Hcl → Zn cl₂+H₂ ↑

Gram atomic mass of zinc is = 65 g and Gram molecular mass of Hydrogen = 2 g From the above equation we can under stand that 65 g of zinc gives 2 g of hydrogen molecules. To prepare 1 g of hydrogen molecules we need 32.5 g of zinc.

Answer: (c) blue

B) Chemical decomposition

M is more reactive than lead since it is able to displace lead from lead acetate solution

To calculate the mass of 1 atom of sodium:

Atomic mass of sodium = 23

1 mole of atom = 6.022 × 10²³ (Avogadro’s no.)

Hence, mass of one sodium atom = \(\frac{Atomic\,mass\,of\,a\,mole\,of\,atom}{Avogadro's\,no.}\)

Hence, mass of 1 sodium atom = \(\frac{23}{6.022\times10^{23}}\)

Mass of 1 oxygen atom = 3.81 x 10²³g

A) Strontium chloride.

C) Redox reaction

1. B is most reactive metal.

2. If B is added to a solution of copper sulphate it displaces copper from copper sulphate.

3. If metals are written in the order of decreasing reactivity it is B > A > C > D.

(i) When sodium, magnesium and copper are left in air, sodium reacts vigorously with oxygen to form sodium oxide, magnesium reacts with oxygen to form magnesium oxide only on heating , whereas copper does not burn in air even on strong heating. It reacts only on prolonged heating. This shows that sodium is most reactive, then magnesium and copper is the least reactive among the three.

(ii) Sodium reacts vigorously with cold water to form sodium hydroxide and hydrogen, magnesium does not react with cold water but reacts with hot water to form magnesium hydroxide and hydrogen but copper does not react even with steam. This shows that sodium is highly reactive; magnesium is less reactive than sodium and copper is the least reactive among the three.

Iron nails when left dipped in blue copper sulphate solution become brownish in colour and the blue colour of copper sulphate fades away.

Fe + CuSO₄→ FeSO₄ + Cu

The above reaction is a type of displacement reaction in which one element displaces another element from its compound and takes its place therein. In the reaction, Fe replaces Cu and form a new compound.