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Above 1350°C, the standard Gibbs free energy of formation of Al₂O₂ from Al is less than that at MgO from Mg. Therefore, above 1350°C, Al can reduce MgO.

Depressants are the chemicals which are used for preventing certain type of particles from forming the froth. Zinc sulphide ore can be separated from lead sulphide ore by froth floatation process using sodium cyanide (NaCN) as depressant. Sodium cyanide act as depressants for ZnS but does not prevent PbS from the formation of froth. Thus, the two ores can be separated.

Hydrogen/Iron.

(i) It acts as flux to removiron oxide as silicate (slag).

FeO + SiO₂ → FeSiO₃ (Slag)

(ii) NaCN acts as the depressant. It selectively prevents ZnS from coming to the froth but allows pbs to came with the froth.

Roasting involves heating of an ore in the presence of excess of air while calcination involves heating of the ore in the presence of limited supply of air. Roasting of chalcocite is necessary because it not only removes the impurities of S, P, As, Sb, etc., present in it as their volatile oxides but also partially oxidises Cu₂S to Cu₂O.

Calcination, on the other hand will not be able to convert Cu₂S to CurO.

In spite of Evelyn’s deafness she joined the prestigious Royal Academy of Music and won the “Soloist of the Year” award. Evelyn used to practise for hours learning languages such as Japanese and French. She earned a lot but was kind at heart. She used to give free performances in prisons and hospitals and also proved a personal example of tireless hard work and firm determination.

Evelyn Glennie had a hearing loss and was discouraged by most of the teachers but she did not give up. Ron Forbes guided her to listen through her body not ears. Eventually, Evelyn learnt to open her body and mind to sound and vibrations. She scored the highest marks in the history of Royal Academy of Music. She also captured many top awards and brought percussion to the front of the orchestra. She has given pleasure to millions and in spite of her towering success, she does not accept any hint of heroic achievement and is a very modest person.

Evelyn’s message to the people is that-Strong determination and hard work with sincerity/honesty leads to success. Aim for your goal and try to reach your goal with full determination and concentration.

Evelyn’s secret of success was strong determination and hard work. The message that she gives to achievers is that work hard and get what you want.

Pandit Nehru likes being with children because for a moment he forgets that he is terribly old among them.

At the age of 8 when her name was announced to play on the piano, she did not respond. At the age of 11, her marks deteriorated. The headmistress urged her parents to take her to a specialist and her hearing impairment was discovered.

(i) True

(ii) False 

(iii) False 

(iv) True

(v) True

(i) (c) very like the children of India 

(ii) (b) mountains, forests and big rivers of India

When Evelyn wanted to pursue her career in music, everyone discouraged her. It was a Percussionist Ron Forbes who helped and encouraged her to listen to the music and feel the music through her body.

Evelyn heard music by sensing the notes in different parts of her body. When ? Ron Forbes tuned two drums and asked her l to sense the sound without using her ears, she realized that she could feel the higher drum ? from the waist up and the lower drum from S the waist down.

When she played the xylophone, she could, s sense the sound passing up the stick into her fingertips. By leaning against the drums, she could feel the resonances flowing into her body,s On a wooden platform, she removed her shoesso that the vibrations could pass through her bare feet. She herself said that music poured s in through every part of her body. It tingled in the skin, her cheekbones and even in her hair.

Context : The poet says that a calm and balanced man is always happy. He is free from worldly anxieties and worries. He does not fear from death and is very careful of flatterers. 

Explanation : In this stanza the poet says that a happy man does not believe in rumours. He is always guided by his conscience and follows its voice strictly. He does not like to keep company with flatterers. He is not influenced by his false praise. So he is never proud of himself. Even a cruel and unjust man cannot give him any harm., Such a man leads a happy and ideal life. 

Reference : This stanza refers to the famous poem ‘Character of a Happy Life’ composed by Sir Henry Wotton.

Context : In these lines the poet describes the character of a happy man. He points out some of the essential qualities for a happy life. He advises us to be independent and true if we want to be happy.. 

Explanation : In this stanza the poet points out the qualities of a happy man. He says that happy man is independent in his thinking and action. He is self-dependent. Either he has this quality by birth or he has been taught to have it. He is always honest and has no ill will for anybody. So he does not need any other weapon for his protection. The greatest quality of his character is only truth. For this quality he is honoured. Thus the man who has these quaļities will be happy beyond expectation.

Context : In these lines the poet describes the character of a happy man. He is free and self-dependent. He is honest and truthful. He has no ill will for anybody. 

Explanation : In this stanza the poet says that a man who is calm and balanced is always happy. He is not guided or controlled by the strong feelings of heart, e.g. anger, hate, love, etc. He leads a simple and honest life. He is always free from worldly anxieties and worries. So he is never afraid even of death. He neither likes flattery nor does he mind the public criticism. So he is always happy.

1. C. That Evelyn delights her audience

2. D. hitting, shaking or scraping the instrument.

3. B. she keeps herself engrossed in work all the time.

4. D. Both ‘A’ and ‘B’

1. 15(x – 1) + 4(x + 3) = 2(7 + x) 

⇒ 15x – 15 + 4x + 12= 14 + 2x 

⇒ 19x – 3 = 14 + 2x 

⇒ 19x – 2x = 14 + 3 

⇒ 17x = 17 

x = \(\frac{17}{17}\) = 1 

∴ x = 1

2. 3(5z – 7) + 2(9z – 11) = 4(8z – 7) – 111 

⇒ 15z – 21 + 18z – 22 = 32z – 28 – 111 

⇒ 33z – 43 = 32z – 139

⇒ 33z – 32z = – 139 + 43

 ∴ z = – 96

3. 8(x – 3) – (6 – 2x) = 2(x + 2) - 5(5 – x) 

⇒ 8x – 24 – 6 + 2x = 2x + 4 – 25 + 5x 

⇒ 8x – 30 = 5x – 21 

⇒ 8x – 5x= –21 + 30 

⇒ 3x = 9 

∴ x = 3

4. 3(n – 4) + 2(4n – 5) = 5(n + 2) + 16 

⇒ 3n – 12 + 8n – 10 = 5n + 10 + 16 

⇒ 11n – 22 = 5n + 26 

⇒ 11n – 5n = 26 + 22 

⇒ 6n =48 

⇒ n = \(\frac{48}6\) = 8 

∴ n = 8

0.18(5x - 4) = 0.50x + 0.8

0.90x - 0.72 = 0.50x + 0.8

On transposing 0.50x to LHS and 0.80 to RHS, we get

0.90x - 0.50x = 0.72 + 0.8

0.40x = 1.52

x = 3.8

Check:

Taking LHS

0.18(5x - 4)

On substituting x = 3.8, we get

0.18(5 x 3.8 - 4) = 2.7

Taking RHS

0.50x + 0.8

On substituting x = 3.8, we get

0.50 x 3.8 + 0.8 = 2.7

We got LHS=RHS

Correct option is  D) none

Correct option is (D) none

\(\frac{4}{3}\) x – x = 1\(\frac{1}{2}\)

\(\Rightarrow\) \(\frac{4x-3x}{3}\) = \(\frac{1\times2+1}{2}\)

\(\Rightarrow\) \(\frac x3\) = \(\frac 32\)

\(\Rightarrow\) x = \(\frac 32\) \(\times\) 3 = \(\frac92\).

Correct option is  A) -1/3

Correct option is (A) -1/3

3x = –1

\(\Rightarrow x=\frac{-1}3.\)

1. 9y + 5 = 15y – 1 

⇒ 9y – 15y = – 1 – 5 

⇒ -6y = -6

⇒ y = \(\frac{-6}{-6}\)

∴ y = 1

2. 3x + 4 = 5(x – 2) 

⇒ 3x + 4 =5x – 10 

⇒ 3x – 5x= – 10 – 4 

⇒ – 2x = – 14 

:. x = 71

3. 3(t – 3) = 5(2t – 1) 

⇒ 3t – 9 = 10t – 5 

⇒ 3t – 10t = – 5+ 9 

⇒ – 7t = 4 

∴ t = \(\frac{-4}{7}\)

4. 5 (p – 3) = 3 (p – 2) 

⇒ 5p – 15 = 3p – 6 

⇒ 5p – 3p = -6 + 15 

⇒ 2p = 9 

∴ p = \(\frac92\)

5. 5(z + 3) = 4(2z + 1) 

⇒ 5z + 15 = 8z + 4 

⇒ 5z – 8z = 4 – 15 

⇒ – 3z = – 11 

⇒ z = \(\frac{-11}3\)

∴ z = \(\frac{-11}3\)

(1-2x)/7 – (2-3x)/8 = 3/2 + x/4

Let us rearrange the equation

(1-2x)/7 – (2-3x)/8 – x/4 = 3/2

By taking LCM for 7, 8 and 4 which is 56

((1-2x)8 – (2-3x)7 – 14x)/56 = 3/2

(8 – 16x – 14 + 21x – 14x)/56 = 3/2

(-9x – 6)/56 = 3/2

By cross-multiplying

2(-9x-6) = 3(56)

-18x – 12 = 168

-18x = 168+12

-18x = 180

x = 180/-18

x = -10

Let us verify the given equation now,

(1-2x)/7 – (2-3x)/8 = 3/2 + x/4

By substituting the value of ‘x’ we get,

(1-2(-10))/7 – (2-3(-10))/8 = 3/2 + (-10)/4

(1+20)/7 – (2+30)/8 = 3/2 – 5/2

21/7 – 32/8 = 3/2 – 5/2

3 – 4 = -2/2

-1 = -1

Hence, the given equation is verified.

0.18(5x – 4) = 0.5x + 0.8

Let us rearrange the equation

0.18(5x – 4) – 0.5x = 0.8

0.90x – 0.72 – 0.5x = 0.8

0.90x – 0.5x = 0.8 + 0.72

0.40x = 1.52

x = 1.52/0.40

= 3.8

Let us verify the given equation now,

0.18(5x – 4) = 0.5x + 0.8

By substituting the value of ‘x’ we get,

0.18(5(3.8)-4) = 0.5(3.8) + 0.8

0.18(19-4) = 1.9 + 0.8

2.7 = 2.7

Hence, the given equation is verified.

(9x+7)/2 – (x – (x-2)/7) = 36

Let us simplify the given equation into simple form

(9x+7)/2 – (7x-x+2)/7 = 36

(9x+7)/2 – (6x+2)/7 = 36

By taking LCM for 2 and 7 is 14

(7(9x+7) – 2(6x+2))/14 = 36

(63x+49 – 12x – 4)/14 = 36

(51x + 45)/14 = 36

By cross-multiplying

51x + 45 = 36(14)

51x + 45 = 504

51x = 504-45

51x = 459

x = 459/51

= 9

Let us verify the given equation now,

(9x+7)/2 – (x – (x-2)/7) = 36

(9x+7)/2 – (6x+2)/7 = 36

By substituting the value of ‘x’ we get,

(9(9)+7)/2 – (6(9)+2)/7 = 36

(81+7)/2 – (54+2)/7 = 36

88/2 – 56/7 = 36

44 – 8 = 36

36 = 36

Hence, the given equation is verified.

15 – 3 = 5x – x 

12 = 4x 

3 = x 

x = 3

Let Megha’s age = x years 

Three times Megha’s age = 3x years 

According to the statement :

 x + 3x = 60 

=> 4x = 60 

=> x = 15 

Megha’s age = 15 years

20 = 6 + 2x 

20 – 6 = 2x 

14 = 2x 

7 = x 

x = 7

3(x + 1) = 12 + 4(x – 1) 

3x + 3 = 12 + 4x – 4 

3x – 4x = 12 – 4 – 3 

-x = 5 

x = -5

Let Neetu’s age = x years 

3 times Neetu’s age = 3x years 

Fifteen more than 3 times Neetu’s age = (3x + 15) years 

4 times Neetu’s age = 4x 

According to the statement : 

4x = 3x + 15 

=> 4x – 3x = 15 

=> x = 15 

Neetu’s age = 15 years

Let present age = x years 

According to question, 

(x + 12) = 3(x – 4) 

x + 12 = 3x – 12 

2x = 24 

=> x = 12 years 

Present age = 12 years

Let the odd number be ‘x’.

The next two consecutive numbers are x + 2 and x + 4 

x + (x + 2) + (x + 4) = 219 

3x + 6 = 219 

3x = 219 – 6 

3x = 213 

x = \(\frac{213}{3}\)

x = 71 

x + 2 = 71 + 2 = 73 

x + 4 = 71 + 4 = 75 

Three consecutive odd numbers are 71, 73, 75

Let present age of the son = x years 

present age of the man = 3x years In 12 years : 

Son’s age will be = (x + 12) years 

The man’s age will be = (3x + 12) years 

According to the statement : 

3x + 12 = 2(x + 12) 

=> 3x + 12 = 2x + 24 

=> 3x – 2x = 24 – 12 

=> x = 12 

3x = 3 x 12 = 36 

Hence, present age of the man = 36 years 

Present age of the son = 12 years.

Let the number be x 

Number subtracted by 30 = 30 – x 

14 subtracted by 3 times the number 3x – 14 

∴30 – x = 3x — 14 

30+ 14 = 3x + x 

44 = 4x 

x = \(\frac{44}{4}\)

x =11

∴ The number is 11

6(3x+2)-5(6x-1)=3(x-8)-5(7x-6)+9x

=> 18x +12- 30x+5 = 3x-24-35x+30+9x

=> 18x-30x-3x+35x-9x = -24-+30-12-5

=> 11x = -11

=> x= -11/11=-1

6(3x + 2) – 5(6x – 1) = 3(x – 8) – 5(7x – 6) + 9x 

18x + 12 - 30x + 5 = 3x - 24 - 35x + 30 + 9x 

- 12x + 17 = - 23x + 6 

- 12x + 23x = 6 - 17 

11x = - 11 

x = -11/11 

x = -1

Let the required number be x.

Then, given that 5 subtracted from 3 times x i.e. 3x – 5

⇒ 3x – 5 = 16

Adding 5 to both sides, we get

⇒ 3x – 5 + 5 = 16 + 5

⇒ 3x = 21

Dividing both sides by 3, we get

⇒ 3x/3 = 21/3

⇒ x = 7

Thus, the required number is x = 7.

Let the number be x, 5 is subtracted from 3 times the number the result is 16. 

3x – 5 = 16 

3x= 16 + 5 

3x = 21 

x = \(\frac{21}{3}\)

x = 7 

∴ The number is 7

The squirrel is a naughty playful animal. It loves to be chased, by other squirrels and kids as well. When poet and his friends ran around the tree on which the squirrel is sitting, it went the other way teasing them and playing with them.

Ravi had named the kitten Mahendravarma Pallava Poonai, M. P. Poonai !in short. They were calling him Mahendran. Mridu liked the name because it sounded; real to her and was different from the usuals cute names kept for cats in general.

Correct option is: (b) Bible

Once Tom nearly went to prison, George was terribly upset.

(i) \((\frac{5}{-11}) + (\frac{-12}{7})\)

\(= (\frac{-12}{7}) +(\frac{5}{-11})\)

(ii) \([(-10) +\frac{5}{6}] +(\frac{-7}{12})\)

\(= (-10) + [\frac{5}{6}+(\frac{-7}{12})]\)

(i) \((\frac{-36}{5})\times(\frac{20}{-3})\)

= \(\frac{12\times(-3)\times4\times5}{5\times(-3)}\)

= \(12\times4\)

=\(48\)

(ii) \(\frac{13}{15}\times(\frac{-25}{26})\)

= \(\frac{13\times(-25)}{15\times26}\)

= \(\frac{13\times(-5)\times5}{5\times3\times13\times2}\)

= \(\frac{-5}{6}\)

\(\frac{3}{7} + (\frac{-5}{14}) +(\frac{-11}{14})\)

\(= \frac{3}{7} + [-\frac{5}{14}-\frac{11}{14}]\)

\(= \frac{3}{7} +[\frac{-5-11}{14}]\)

\(= \frac{3}{7} -\frac{16}{14} = \frac{6-16}{14}\)

\(= \frac{-10}{14} = \frac{-5}{7}\)

(i) \(\frac{2}{3}\times x=1\)

⇒ \(x=\frac{3}{2}\)

(ii) \((\frac{-3}{4}) + x =0\)

⇒ \(x=0-(\frac{-3}{4})\)

⇒ \(x=\frac{3}{4}\)

(iii) \(x \times(\frac{-5}{4})=1\)

⇒ \(x=1\div(\frac{-5}{4})=1\times(\frac{4}{-5})\)

⇒ \(x=\frac{-4}{5}\)

(iv) \(x \times(\frac{-6}{-7})=1\)

⇒ \(x=1\div(\frac{-6}{-7})=1\times(\frac{-7}{-6})\)

⇒ \(x=\frac{7}{6}\)

(v) \((\frac{-5}{4})\times(\frac{4}{-5})=x\)

⇒ \(x=\frac{-20}{-20}=1\)

(vi) \((\frac{-7}{6})+\frac{7}{6}=x\)

⇒ \(x=0\)

(i) \((\frac{-3}{4})+{3}\)

\(= \frac{-3+12}{4}\)

\(= \frac{9}{4}\) 

\(= 2\frac{1}{4}\)

जो कि परिमेय संख्या है।

(ii) \((-1) + (\frac{-2}{3})\)

\(= \frac{-3-2}{3}\)

\(= \frac{-5}{3}\)

जो कि परिमेय संख्या है।

0 का निरपेक्ष मान शून्य है।