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Let the required zeroes be \(α\) , \(β\)

\(α + β = \frac{21}{8} = \frac{42}{16} = \frac{-b}{a}\) \(... (1)\)

\(​​​​αβ = \frac{5}{16} = \frac{c}{a}\) \(... (2)\)

From (1) and (2), 

\(b = -42\) , \(a = 16\) , \(c = 5\)

Required polynomial is

\(16x^2 - 42x + 5 \)

Let α & ß are zeros of quadratic polynomial.

α + ß = 21/8

⇒ -b/a = 21/8---(1)

αß = 5/16

⇒ c/a = 5/16--(2)

From (1), -b/a = 21/8 = 42/16

∴ a = 16, b = -42, c = 5

Required quadratic polynomial is

p(x) = ax² + bx + c

= 16x² - 42x + 5

2x² - √2x + 1 = 0

⇒ x = \(\frac{-(-\sqrt2)\pm\sqrt{2-8}}4\)

 = \(\frac{\sqrt2\pm\sqrt 6i}4\)(∵ i = √-1)

Roots are \(\frac{\sqrt2-\sqrt6i}4\) or \(\frac{\sqrt2+\sqrt6i}4\) 

No real root exist

α + ß = -3/4

αß = 7/4

(a) \(\frac{α+ß}{αß}=\frac{-3}7\)

⇒ \(\frac1\alpha+\frac1{\beta}\) = \(\frac{-3}7\) 

(b) α² + ß² - 3αß = (α + ß)² - 5αß

 = \((\frac{-3}4)^2 - 5\times\frac74\) 

 = \(\frac9{16}-\frac{35}4\) 

 = \(\frac{9-140}4\) = \(\frac{-131}4\)

(c) \(\frac4{\alpha}+\frac4{\beta}=\frac{-12}4\) (From (a))

(d) \((\frac{\alpha}{\beta}+\frac{\beta}{\alpha})+6\alpha\beta\) 

\(=\frac{\alpha^2+\beta^2 +2\alpha\beta-2\alpha \beta}{\alpha\beta}+6\alpha\beta\)

\(=\frac{(\alpha^2+\beta^2)^2-2\alpha\beta}{\alpha\beta}+6\alpha\beta\) 

\(=\cfrac{(-\frac34)^2-2\times\frac74}{\frac74}+6\times\frac74\)

\(=\cfrac{\frac{9-56}{16}}{\frac74}+\frac{21}2\) 

\(=\frac{-47}{7\times4}+\frac{21}2\)

\(=\frac{-47+294}{28}\)\(=\frac{247}{28}\)

We have,

f(x) = x² −p(x+1)−c = 0

f(x) = x²−px−(p+c) = 0

Since,

α,β are the zeroes of the above polynomial.

So,

α + β = p

αβ = −(p + c) 

Since,

(α + 1)(β + 1) = 0

αβ + α + β + 1 = 0

−p − c + p + 1 = 0

−c + 1 = 0

c = 1

(a) |x| = |x|

|x|² = Positive number

(b) |x| = |–x|

|x|² = Positive number

These are many importance of good manners in life. 

(i) Good manners are most desirable when a young man are with older people. They requires his sympathy. Young people should treat older persons kindly and sympathetically. They should try to make life easy for order people.

(ii) Good manners are also important when younger. people are in the company of their friends. They should be clear in they speech so that bearers.may have no difficulty in understanding them. young people should be polite in their day to day dealings.

(iii) Sometimes even complementary words from elderly person irritate young men. It is.only foolish people who take such remarks literlley. They should try to understand the intended meaning of the speaker. A man can by frank with those who welcomes frankness. otherwise he should be guarded in his speech.

(iv) When one is engaged in talk, one should also allow the listener to express himself. One who goes on speaking without allowing others to speak is called a bone. so a speaker should turn a listener after speaking for some time. Sometimes it is guise pleasant to be guite when the other min in company does not like the talk to continue.

(v) It is never decent to speak ill of someone behind his back. 

(vi) We should think that only we are right others are quite wrong. This over conficence is not wanted in polite society. So in our argument with other persons we should remember that there is all possibility of our being wrong, however confidence we may feel about it. 

Metaphor is a figure of speech in which likeness between two different objects is implied, not directly expressed. For example : The camel is the ship of the desert. The comparison is so complete that the two objects became one and the same.

Always - Never

Heavy -  Light

Cheerful - Cheerless

Freedom - Slavery

Confess - Deny 

(a) Simile

(b) Simile

(c) Metaphor. 

(a) energetic

(b) healthy

(c) broke into

(d) transmitted

(e) invade

(f) praise

(g) life time

Our mind is crowded with a lot of memories. In this situation there is left no space for lofty or big thoughts. Some of the commonest forms of forgetting are posting letters and taking medicine in time. We forget our pens, books, umbrellas, walking sticks and the like.

(a) He has had to buy the car.

(b) They have had to break the rule.

(c) She has had to refuse the proposal.

(d) I have had to leave the town.

(e) She has had to dance on the stage. 

There is a difference between a good letter and a good essay. A good letter is written in a simple and formal style. It reflects the personality of the writer. On the other hand a good essay is written in formal style. It is formal in style elaborated in size and orderly in manner. 

David Copperfield is a very famous novel of Charles Dickens, the Victorian novelist. David Copperfield is the hero of the novel. The story of David Copperfield from his childhood to adulthood has been narrated in the novel. David was born after the death of his father. His mother, Clara loved David heart and soul. His nurse looked after him like her own son. David's mother married Murdstone. Murdstone and her sister were cruel to David. David was often beaten and ill treated by Mr. Murdstone. Once he bit Murdstone. David was beaten and confined to his room for five days. He was sent to Salem House, a boarding school where principal was also unkind to him. In the mean time, his mother died. He felt as if he were left alone in the world. His schooling stopped. He was forced to do the job of a bottle cleaner. He was unable to work under horrible conditions and finally ran away to his aunt Betsey in Dover. His aunt arranged for his education.

David was intelligent and books provided him a great fascination. He learnt typewriting and became a reporter. He fell in love with Agnes but married Dora who died very soon. Later he married Agnes as promised to his wife Dora. David always remained honest, hard working and sincere. I like him most for all these qualities.

c. Itinerary

Itinerary is a detailed tour program for any person or a party.

Given S = f(t) = 8t + t³

i) ds/dt = 8 + 3t²

(ds/dt)_{t = 2} = 8 + 3(2)²

= 8 + 12 = 20 

∴ The velocity at time t = 2 is 20 cm / sec

ii) (ds/dt)_{t = 0} = 8 + 0 = 8

∴ Initial velocity = 8cm / sec

iii) d²s/dt² = 0 + 6t

(d²s/dt²)_{t= 2} = 6(2) = 12 cm / sec²

Acceleration at t = 2 is 12 cm / sec²

\(\frac{\pi}{2}<\alpha<\pi\) sin \(\alpha=\frac{4}{5}\)

\(\alpha\) lies in second quadrant

so , cos \(\alpha\) is negative

∵ sin² \(\alpha\) + cos² \(\alpha\) = 1

⇒ cos \(\alpha\) = \(\pm\sqrt{1-sin^2\alpha}\)

But cos \(\alpha\) is negative

∴ Cos \(\alpha\) = \(-\sqrt{1-sin^2\alpha}\)

\(=-\sqrt{1-(\frac{4}{5})^2}\)

\(=-\sqrt{1-(\frac{4}{5})^2}\)

\(=-\sqrt{\frac{25-16}{25}}{}\)

\(=-\sqrt{\frac{9}{25}}=-\frac{3}{5}\)

sin²θ +cos²θ +2sinθ cosθ =1

1+2sinθ cosθ =1

2sinθ cosθ=0

1-2sinθ cosθ=1

sin²θ +cos²θ-2sinθ cosθ=1

(cosθ -sinθ)²=1

cosθ -sinθ=±1

(a) Statement is not true because Area is proportional to a².

(b) statement is true because Area of equilateral  Δ =  √3a²/4 

(c) Statement is not true because Area is proportional to a² and the proportionality constant is √3/4   

It is a cheque payable by the drawee bank over the counter to the bearer or presenter of the cheque.

Current Account is usually maintained by a businessman to facilitate any number of deposits and withdrawals in a single day.

If mutual friendship among different countries and communities is established, wars can be prevented. Mutual friendship creates good will and harmony. 

(a) The thief was caught by the local police.

(b) The house was sold by the original owner. 

(c) It was found by the old lady.

(d) Meal was cooked by her mother.

(e) The poem was taught by the English teacher. 

Firstly we should think whether the man, whom we are talking, is listening or understanding our words. We should speak carefully, clearly, softly and lucidly. We should make him feel friendly. No harsh word should be spoken.  

(a) penetrate

(b) violent

(c) direction

(d) promptly

(e) collapse

(f) disappear

(g) resume

(a) complains

(b) uniform

(c) sympathy

(d) defer

(e) artificial

(f) insult

(g) filtered 

(a) Metaphor

(b) Simile

(c) Simile. 

Defeat - Beat 

 Birth - Origin

Refuse -  Reject

Gather -  Collect

Vague -  Obscure 

(a) Metaphor

(b) Simile

(c) Metaphor. 

Departure - Arrival

Strange - Familiar

Narrow - Broad

Moral - Immoral

Brave - Coward. 

Profit - Benefit

Obstacle - Barrier

Random - Causal

Peril - Danger

Tasty - Delicious 

In modern society, technology is an inevitable part of our everyday life. It has a role in everything we do even though we sometimes do not realize it. Thanks to development in technology there have been many breakthroughs in different fields such as communication, transportation, education, medicine, entertainment and agriculture. Our life has become simpler and more enjoyable than before. We have mobile phones and so we can talk with anybody, anytime, anywhere in the world. The planes, trains, buses and trucks transport people and goods fast from one place to another.

In medicine, X-ray, Scanning etc. help doctors to diagnose the disease. Laser treatment and surgery is common. We have video, audio and TV to keep us entertained all the time. Even in religion, technology is playing a role. Using powerful sound system, cassettes and CDs, religious leaders propagate their beliefs. Agriculture is revolutionized by the use of technology.

The Adlestrop

The poem Adlestrop has been composed by the poet Edward Thomas. Thomas Edward is very famous as an English poet. But to his misfortune he became famous as a poet after his death. He was a Soldier. He was killed during the first world war.

In this poem we see that a train reaches the station Adlestrop without any planning. The journey is pleasant but the platform has no passenger at all. The poet is surprised to know that platform is empty. There is no human activity at all. But the poet sees there natural activity is not inactive. It is full of natural activity. A bird is singing. Another bird comes and picks it up. The poets seems to be very sensitive towards natural activity. The willow is covered with herbs and grass. Music amidst stillness is very soothing and heart touching. Thus we see the poet sensitiveness towards the nature

Girls and Boys have a similar brain with equal abilities and skills of the same age. There are no differences seem in terms of understanding level, reasoning ability, problem-solving skills, cognitive skills on basis of the gender of the same age.

Option(1) and  (3) are not correct because girls and boys both have similar abilities at the same age. They are generally similar in cognitive functions of similar age. It is not necessary that girls can perform better or face problems competently than boys of their age. 

Similarly, Option(4) is eliminated because it is not necessary that girls possess more linguistic and musical abilities.

So, Option(2) is correct. Girl Students are good in Mathematics as boys of their age.

i. 17¹⁶ ÷ 17¹⁶

= 17⁰ 

= 1

ii. 10^-3

\(=\frac{1}{10^3}\)

\(=\frac{1}{1000}\)

iii. (2³)²

= 2^3×2

= 2⁶

iv. 4⁶ × 4^-4 

= 4^{6 + (-4)} 

= 4² 

= 4 × 4 

= 16

1. Are fond of purities because purity promotes health-bodily and mental.

2. The purity of body is physical health, of speech is unsullied truth and of heart is unselfish love.

3. The purity of thought is righteous reason of mind is wholesome peace, and of action is sincere and unselfish service.

4. It was so because the pure minded Yudhishthira found everyone to be pious and pure. The impure minded Duryodhana found everyone to be evil and impure.

5. Drona was the guru of both the Pandavas and the Kauravas.

6. In the presence of purity villains who come to harm stand in adoration, and murderers become votaries of peace.

7. The author highlights that environmental purity is overall health. Purity of -environment in soul-elevating serenity.

8. (i) yearn

(ii) votaries.

The probability that you will get admission in exactly one college is P(1) = k = \(\cfrac18\).

Here, ∠PRQ and ∠PRT are angles in a linear pair. 

m∠PRQ + m∠PRT = 180° 

∴ 70 + m∠PRT = 180 

∴ m∠PRT = 180 – 70 

∴ m∠PRT = 110° 

Now, ∠PRT is the exterior angle of ∆PQR. 

∴ m∠P + m∠Q = m∠PRT 

∴ m∠P + m∠P = m∠PRT 

….(The measures of ∠P and ∠Q is same) 

∴ 2m∠P = 110

∴ m∠P = 110/2

∴ m∠P = 55° 

∴ m∠Q =

1. India can emerge a major developed country by vowing to do our jobs keeping the nation’s interests in mind.

2. A politician can frame policies and laws that are conducive to development.

3. A clerk can work more efficiently for clearing a new project.

4. A worker in a factory can increase productivity and quality.

5. A contractor should spend on his own to improve some part of the town.

6. A banker can contribute by encouraging youth to take up some innovative project.

7. According to Dr. Kalam, a doctor can provide face and inexpensive medical aid to the poor at least to a limited extent.

8. (i) student
(ii) exservicemen
(iii) grocers.

1. India has rich heritage. Doing one’s duty has been preached and practised here since vedic times.

2. Lord Krishna, Lokmanya Bal Gangadhar Tilak, Kautilya and so on advocated for the performance of duty.

3. Arthshastra is a book having the philosophy of Karma Yoga written by Kautilya.

4. No one was to interfere in the affairs of one’s neighbour without due cause. However, everyone was to help one’s neighbour in distress.

5. The fundamental rights mentioned here are : right to equality, to freedom, to life and individual freedom, to religious freedom, to cultural and educational freedom.

6. After independence the citizens began neglecting their duties and started giving greater importance to their rights.

7. Action should be performed without seeking the fruit. The Geeta explains karma in this way.

8. (i) salvation
(ii) amend.

Machines have made man's life easy and comfortable. Now man is accustomed to lead easy life but man should not depend on machine only. A man should make a creative use of his time and energy. He should continue to create good will, love and harmony on the basis of art, culture and music. A man should try to depend on his own hand, and it should be made free from hunger injustice and diseases.