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LHS = tan 48° tan 23°tan 42°tan 67°

= Cot (90°-48°) cot (90°-23°) tan 42° tan 67° 

= Cot 42° cot 67° tan 42° tan 67° 

=1

∫cos 4x dx = sin 4x/4 + c

A₅ = a₁ + 4d = 0

1² + 4d = 0

d = - 3

P (Two Head) = 1/4.

Of all those outcomes, the ones for which a + b = 8 are: 

2+ 6, 3 +5, 4 +4, 5 +3, 6 +2 or 5 outcomes

P = 5/36 

Good bulbs = 25 – 5 = 20

P (good bulb) = 20/25 = 4/5.

(i) It can be observed that,

To get the sum as 2, possible outcomes = (1, 1)

To get the sum as 3, possible outcomes = (2, 1) and (1, 2)

To get the sum as 4, possible outcomes = (3, 1), (1, 3), (2, 2)

To get the sum as 5, possible outcomes = (4, 1), (1, 4), (2, 3), (3, 2) To get the sum as 6, possible outcomes = (5, 1), (1, 5), (2, 4), (4, 2), (3, 3)

To get the sum as 7, possible outcomes = (6, 1), (1, 6), (2, 5), (5, 2), (3, 4), (4, 3)

To get the sum as 8, possible outcomes = (6, 2), (2, 6), (3, 5), (5, 3), (4, 4)

To get the sum as 9, possible outcomes = (3, 6), (6, 3), (4, 5), (5, 4)

To get the sum as 10, possible outcomes = (4, 6), (6, 4), (5, 5)

To get the sum as 11, possible outcomes = (5, 6), (6, 5)

To get the sum as 12, possible outcomes = (6, 6)

(ii)Probability of each of these sums will not be 1/11

as these sums are not equally likely

The possible outcomes are

{HHH, TTT, HHT, HTH, THH, TTH, THT, HTT}

Number of total possible outcomes = 8

Number of favourable outcomes = 2 {i.e., TTT and HHH} 

P(Hanif will win the game) = 2/8 = 1/4

P (Hanif will lose the game) = 1-1/4 = 3/4

Total number of outcomes = 6 × 6

= 36

(i)Total number of outcomes when 5 comes up on either time are (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (1, 5), (2, 5), (3, 5), (4, 5), (6, 5) Hence, total number of favourable cases = 11

P (5 will come up either time) = 11/36

P (5 will not come up either time) = 1-11/36 = 25/36

(ii)Total number of cases, when 5 can come at least once = 11 

P (5 will come at least once) = 11/36

Total number of possible outcomes on the dice = 6

(i) Total number of faces having A on it = 2

P (getting A) = 2/6 = 1/3

(ii) Total number of faces having D on it = 1

P (getting D) = 1/6

Mass of nitrogen = 5.6 g
Atomic mass of N = 14 u
Molar atomic mass of N = 14 g/mol ,
Molar mass of N₂ = 2 x 14 g/ mol = 28 g mol^-1

(a) No. of moles of N₂ in 5.6 g of nitrogen
= 5.6 g/28 g mol^-1
= 0.2 mol

(b) No. of molecules of N₂ is 5.6 g of nitrogen
= 6.023 x 10²³ x No. of moles of N₂
= 6.023 x 10²³ x 0.2
= 1.2 x 10²³

(c) As one molecule of N₂ contains two N atoms.
No. of atoms of nitrogen
= 2 x No. of N₂ molecules
= 2 x 1.2 x 10²³ = 2.4 x 10²³

Rutherford conducted alpha scattering experiment and put forward a model of atom known as Rutherford’s nuclear model.

The salient features of this model are as follows:

• The atom of an element consists of a small, positively charged nucleus in the centre, which carries almost the entire mass of the atom.

• The electrons are revolving around the nucleus at high speed.

• The number of electrons in an atom is equal to the number of protons. Hence it is electrically neutral.

• The volume of the nucleus is negligibly small compared to the volume of the atom.

• Most of the space in the atom is empty.

The microorganisms that enter the body travel to a specific organ and multiply there. Different microbes are at home in different parts of the body. For instance, Mycobacterium tuberculosis is the bacteria that causes tuberculosis. It usually enters the body through the nose and migrates to the lungs. Other disease-causing bacteria such as the Salmonella enter through the mouth (through consumption of infected food or water) and travels to the gut lining.

Following precautionary measures can be taken to take care of our eyes: 

(i) We should atleast always wash our eyes with plane cold water atleast three times a day.

(ii) We should not touch our eyes with dirty hands.

(iii) We should never rub our eyes.

(iv) We should not look at sun directly.

(v) Self-treatment could be dangerous to the eyes. You must consult a doctor in case of any injury to the eyes.

(vi) Good nutrition is very important for both your general and eye health. Good nutrition keeps the eye in good condition.

The inability of human brain to perceive more than two images formed on the retina within an interval of 1/16th of a second is called Persistance of vision.

After the modern Homo sapiens came into existence, the given human activities developed in the following manner: 

(i) Pre-historic cave art developed about 18,000 )years ago 

(ii) Agriculture started around 10,000 years ago. 

(iii) Then human settlement started.

Quantity of water flowing through pipe in 1 hour 

= (π  x 7/100 x 7/100 x 15000 m³)

Required time = (50 x 44 x 21/100) ÷ (π x 7/100 x 7/100 x 15000)

= 2 hours

The Correct option is (b) 42

Let, the unit’s digit = x

The ten’s digit = 12 – x

∴ The number = 10(12 – x) + x = 120 – 9x

After reversing,

Unit’s digit = 12 – x

Ten’s digit = x

∴The number after reversing = 10x + 12 – x = 9x + 12

According to problem,

⇒ 9x + 12 = 120 – 9x + 18

⇒ 18x = 126

⇒ x = 7

∴ The original number,

⇒ 120 – 9 × 7

⇒ 57

Let the digits be x and y

Then the two-digit number is 10x + y

Given that: 10x + y = 4 (x + y) 

10x + y = 4x + 4y

10x - 4x = 4y - y

6x = 3y

y = 6x/3

y = 2x  --------------- 1

And 10x + y + 8 = 10y + x

10x - x + y - 10y = -8

9x - 9y = -8

9y – 9x = 8 ---------------- 2

Substitute the value of y in eqn 2

18x – 9x = 8

9x = 8

x = 8/9

Therefore  y = 2x = 2 x 8/9 = 16/9

And the number is 10x + y = 10 x 8/9 + 16/9

= 80/9 + 16/9

= (80 + 16)/9

= 96/9

= 32/3

Answer: The two-digit number is 32/3.

1. Dead beat galvanometer: when a galvanometer is used for measuring current the coil is wound on a light aluminium frame to bring coil quickly to rest .This is because the motion of metal frame in magnetic field give rise  eddy current  in frame.
2.  Electric break : when current is to stop  the power supplies to rotates the axis is switched of .At same time a stationary magnetic field is applied to rotating durm give rise to strong eddy current in drum . This eddy current produce torque which oppose rotation and stop a train smoothly and quickly

(i) Due to low resistively of copper the heating loss can be minimize.

(ii) To Reduce the magnetic flux leakage the mutual coupling between the coils should be perfect.

(i) When a low frequency signal is superimposed on high frequency carrier signal called modulation

(ii) (a) Amplitude modulation

(b) Frequency modulation

Threshold. Freq: Minimum required frequency of incident light which allow the emission of electron from metal surface

Cut of potential : A min negative potential at which the max. kinetic energy photo electron can stoped.

When their is a relative motion between source and observer then their is change in wavelength as well frequency which is called the Doppler's effect

Red shift : When their is a receding case (moving away from each other) between two then wavelength will increases that called red shift. 

Blue shift : when their is approaching case (moving towards each other) between two then wavelength will decrease called blue shift.

C_AB = (10 x 10)/(10 + 10) + C = 15

5 + C = 15 ⇒ C = 5μF

Cuscuta has lost its chlorophyll and leaves during evolution and thus it derives its nutrition from host plant thus it is a parasitic plant.

Cattle avoid browsing on Calotropis plants because it produces poisonous cardiac glycosides.

Correct option: (3) 

Explanation: 

The oscillations, of a pendulum bob, in a medium (like air) are damped oscillations. For such damped oscillations, the amplitude decreases exponentially with time, i.e., its decrease is a non–linear one. 

The time period, for such damped oscillations, is (slightly) more than its the time period in free space. 

The formula for displacement in simple harmonic motion is: 

x = A sin (ωt) 

The derivative would therefore give speed: 
x' = Aωcos (ωt) 

The maximum speed is when cos(ωt) is at the maximum or 1. So max speed is: 
v(max) = Aω
36cm/s = A ((40 oscillations/minute) * (1 minute/second) * (2π/1 oscillation)) 
A = 36cm s^-1 / 4.188s^-1 
Amplitude A = 8.59 cm.

The stranger’s curious identity became the topic of speculation in the town. Mrs. Hall defended him, repeating his own words that he was an ‘experimental investigator.’ Several other people of the town were of the view that he was a criminal trying to escape justice. Mr. Gould, the probationary assistant, imagined that the man must be an ‘anarchist’ who was preparing explosives. Another group of people believed that he was a pie-bald and could make a lot of money if he chose to show himself at the fairs. There was another view that explained the entire matter by regarding the stranger as a harmless lunatic. Between these main groups were compromisers. Some believed that he had superstitious powers. But whatever they thought of him, people in Iping on the whole, agreed in disliking him. The young men called him ‘Bogey Man’.

I. (a) (4) both (1) and (3). 

(b) (4) both (1) and (3). 

(c) (1) economy is tough.

(d) (3) may be the reason children continue to play in school, 

II. (a) Some children do not consider themselves athletics and may prefer not to play organized school sports. They may be cut from the school team for lack of ability. 

(b) There are many important benefits of playing sports, so even the uninterested ones should be encouraged to participate in intramural games.

(c) As a parent it may be necessary to become involved on the school board to have a say about keeping athletic programs and not cutting the budget on them. 

(d) Sports motivate students enabling them to earn better grades. 

(e) According to Jean Zimmerman author of ‘Raising Our Athletic Daughters’, promoting athletics as a parent is a crucial factor in determining whether your child will be interested in participating in sports.

III. (a) imperative 

(b) intramural 

(c) prerequisite

When Silas enters the Rainbow Inn for the first time in fifteen years, the first reaction is shocking. Silas never ventured into the Rainbow despite it being the town’s public house. The townspeople feel that they are staring at a ghost. After Silas discovers the theft of his gold, in complete desperation Silas steps out of his cottage and ends up in the Rainbow, looking for Squire Cass and other people, to look into the theft. They feel that he is some ethereal version of Silas that was at the door, and not the enigmatic weaver himself. The landlord comes over and welcomes Silas, clearly noticing that Silas is not well. When Silas requests that “the Justice—and Squire Cass—and Mr. Crackenthorp” be summoned, the landlord can tell that Silas is out of his mind. In the end, the Rainbow guests simply make Silas sit down to tell them what had happened. They listen to Silas sympathetically due to the genuine state of alarm that he showed.

• relationship an administrator has with two bad, lazy, ineffective, and difficult employees who also happen to be related by blood to him/
• Squire Cass did not trust either of them enough to administer the Red House.
• The sons also knew that they would never be at par with their father because none of them had the work ethics, the strength of morale, nor the attitude to take over a job as well as the Squire.  
• Hence, it is the relationship of master and servant, soldier and commander, boss and employee/ 
• Godfrey seems to appear to the public as the gentler, kinder, and nicer of the two brothers/ 
• he is weak of character, prone to being misled, and easily fooled/
•  Dunstan is arrogant, senseless and selfish/
• is intellectually dull/reckless and morally depraved

Derry believes that his mother kisses him on the other side of his face and that even she cannot stand her scarred face. She advises him to keep away from Lamb whom she doesn’t trust. She is protective of Derry and always keeps an eye on him. She encourages him to mingle only with a select few like him. In fact Lamb asks Derry what kind of world would it be if all disabled people lived together. For Derry it is a tough task to disobey his mother and return to Mr. Lamb. This suggests that she is like all those stereotypical parents who are protective of their challenged children and thus through their attitude contribute to making them lonely and isolated. They would do well to teach their children to make friends and accept their disability cheerfully and be optimistic about life. Clearly Derry’s mother has failed in this regard.

• Marvel was a short, fat tramp who sported a shabby hat and thrived on charity.
• He was lazy and did not show any intention to work hard for improving his life.
• Griffin did not have a very high opinion about Marvel‟s abilities, still he made him his accomplice because Marvel was an obvious weakling who could be easily intimidated.
• His cowardice did not let him defy Griffins commands. Surprisingly, this apparently good -for-nothing fellow managed to cheat a wicked and dangerously evil man like Griffin.
• He was a simple person, ill-equipped in every sense, as compared to the all powerful Invisible Man. He had no choice but to obey each order coming from his self proclaimed master. 
• Marvel was more of a slave than an accomplice in crime. When he succeeded in sneaking away, it was actually to save his life.
• Of course towards the end he does show smartness by hiding the entire money and the three books of Griffin.
• He also exhibits his keen business acumen by wisely investing this money to open an inn.
• His decision to name this venture after the Invisible Man again shows that Marvel knew how to turn circumstances in his favour.
• He never revealed to anyone that the three books of Griffin were in his possession. He pondered over them in private trying to figure out the coded message. This was done for survival rather than treachery 

H.G. Wells introduces poetic justice to the story and gets Griffin killed as his powers were used against mankind. However innovative and ambitious plan may be, if it proves fatal to the mankind it needs to be curtailed. As such the ending is thoroughly justified. 

Though Griffin deserves punishment, his violent killing on the part of the public was too severe. It wast unwholesome and surprising that undeserving and a turn coat Marvel got hold of Griffin’s money in the end. 

On the other hand it was right that Marvel, who could not do anything of the formulae of invisibility, was found to have the books otherwise they could be misused by Kemp or if not by him, by any other scientist. In thus punishing Griffin so severely Wells expresses his own intolerance for depraved people like Griffin whose genius cannot absolve him from the grave injury to society.

• The narrator uses the Invisible Man to experiment with the depth to which a person can sink when there are no social restrictions to suppress his behavior.

• Griffin begins his road to decline in college when he becomes so obsessed with his experiments that he hides his work lest anyone else should receive credit.

• When he runs out of money, he kills his own father.

• He excuses it away by saying that the man was a “sentimental fool.”

• When he takes the potion himself, he endures such pain that he “understands” why the cat howled so much in the process of becoming invisible.

• Nevertheless he has no compassion for the cat, for his father or for any of the people he takes advantage of in the course of trying to survive invisibility.

• On the contrary, he descends from committing atrocities because they are necessary to his survival to committing them simply because he enjoys doing so.

• Griffin at no time expresses any remorse for his behavior or for the crimes, which he merely describes as “necessary.” 

Iping, a small town in the countryside of England, close-knit community, everyone on first name basis, no secrets

Prone to spreading rumours speculate issues, expand on each other‟s stories Rustic characters: 

Teddy Henfrey- clock repairman, convinces himself and Mr. Hall that the stranger has a suspicious nature, begins rumour that the man was a wanted by police Fearenside – cartman, notices darkness in the man‟s torn pant, starts stories of Griffin being either a black man or a piebald

Cuss- general practitioner, after seeing the emptiness of the stranger and getting hit by stranger, tells outrageous story to his companions Bunting- vicar, listens to cuss but doesn‟t believe him, suspects after getting robbed

All rustic characters help carry the story ahead, create more complications, make Griffin aggressive, frustrated due to their interfering nature. Results to his unveiling which complicates the plot further

• Godfrey attempts to broach the subject of adopting Eppie in a number of ways, first saying that his family owes Marner a great debt
• then that Marner seems too old to work at the loom.
• When these approaches fail, Godfrey states plainly and coarsely that they are offering to take Eppie into their care as their own child . 
• Godfrey insists that he has a claim on Eppie and confesses that he is her father.
• Godfrey tells Silas that he is standing in the way of Eppie‟s welfare/
• Eppie firmly refuses the Casses‟ offer saying that Marner was the only father she knew and would not leave him.
• Marner asks Godfrey why he waited 16 years to take Eppie back/
• Godfrey says that he is repenting now/ Marner argues that his repentance does not make Eppie rightfully his/

• Ambition and lust for unchallengeable power led Griffin to dissociate himself from his brethren and eventually caused his downfall.
• Unregulated human aspirations and follies leads to wasted lives.  
• Griffin was a young science student at the University College. He was a six feet albino, lacking pigment in skin, hair and eyes. He won a medal for excellence in Chemistry but his fascination for light made him drop medicine and he then took up physics.
• He pursued an unrealistic ambition to find a formula that could make a living being invisible.
• He followed his target with insane persistence because of which he withdrew himself from everything that could associate him with a normal life.
• His selfish nature hindered him from sharing the credit of his work with anybody else. He worked single handedly and was therefore always alone in his great moments‟. He worked in isolation for three long years with absolutely cramped means. Eventually he found it impossible to complete this research because of paucity of money.
• His obsession with invisibility stripped him of all human emotions and he stooped so low as to rob his own father driving him to commit suicide.  His overambition hurled him from the summit of success to the abyss of total disaster and his lust for power and money stripped him of all ethics.
• His untamed ambition and desire and unlimited power made him absolutely inhuman and heartless. An intelligent scientist, who could have made the world a better place, instead became a menace.
• The downfall caused by his inappropriate desires eventually drove him to his death at the hands of the people.
• Thus the story of the Invisible Man poignantly elucidates the theme of selfishness, isolation and overambition leading to the irrevocable destruction of a capable life.

 1.  (D) Saving the Arctic 

2. (c)  Polar Bears

3. (B) Hobie Cat

4. (B) The ominous sail 

1. senses their presence and quickly sounds/author disappointed because they only had good intentions/sad to know the whale doesn’t trust humans 

2. Mike thinks how foolish it would be for this mighty beast to put any faith in them. After all, they are members of the species that had almost sent the bowhead into extinction with the greed for whale oil and bone.

3. on the edge of a huge shoal where the frigid ocean currents upswell and mix nutrients that provide a feast for the food chain 

4. In some regions the land is totally devoid of life, while in others the pulse of life takes our breath away/ It's wastelands flow into oasis' that are found nowhere else on the face of the earth

5. knowledge, skill, teamwork, and spirit 

6. adaptability

(a)  profusion 

(b) ominous

Lions Club organizes Summer Camp by Gyan 

Gurgaon, 24th May, 20xx: To ensure that the much awaited summer break becomes a time to relax and rejuvenate, Lions Club, Gurgaon organized a special ‘Summer Camp’ for the students of Gurgaon from 15th May, 20xx to 24th May, 20xx in the premises of Akash Public School. 

The camp saw overwhelming participation by 300 students, eager to avail the rich experience offered by the camp in Sports, Craft, Music, Dance, Theatre, French and Robotics. Special coaches/trainers and expert faculty members held sessions every day from 6.00 a.m. to 9.30 a.m. 

The school ground was abuzz with hectic sports activities in Basket Ball, Football, Badminton, Cricket, Table Tennis, Short Tennis, Taekwondo, Skating, Yoga and Swimming. The students also got an opportunity to fine tune their steps in western dance, and learnt the intricacies of Indian Classical Dance. 

The camp lasted till 24th May, 20xx. Several displays, namely, Art Display, Sculpture Display, French Conversations, Mime and Musical displays were showcased. The parents appreciated the efforts made by the students and teachers.

•  wearing green coat, frilled shirt, black silk cap
• announced last lesson in French, German to be taught
• Proud of being French
• upset by occupation of Alsace by Germans 
• attached to town, school, people

C-6, Sector 7 

Gurgaon 

7th October, 2019

Dear madam 

It was a great honour to receive your invitation to judge the flower show on ‘gardening day’. I thank you heartily for the invite. However I regret that I shall not be able to reach the school and judge the contest as I shall be out of station on that day. 

I wish you all the best for this event. 

Regards 

Karan

(a) (i) explain some differences in the upbringing of girls and boys

(b)  (iv) useful social skills

A. TITLE: Medicinal Plants – A Natural Way to Health

NOTES: 

1. Facts about medicinal plants: 

1. seen as a sol to disease 

2. part of cult of 3rd world 

2. Impact of synthetic med 

1. med’l plants lost poplrity 

2. rural people hard hit as have no access to primary health care 

3. History of plant therapy 

1. part of all civilzn 

2. before synthetic med man depended on plants for cure 

4. Research on plant revealed: 

1. toxic, curative nature of plants 

2. herbal med effaceable beyond doubt 

3. can cure stress, depression 

4. plants like allamandin can cure cancer by inhibiting tumors 

Key to Abbreviations

sol : solution 

cult : culture 

poplrity : popularity 

civilzn : civilization 

med : medicine 

med’l : medicinal 

B. SUMMARY 

Medicinal plants are being seen as a solution to diseases. They have always been a part of the culture of the third world countries. With the popularity of synthetic medicines the use of plant therapy declined due to which the rural poor were hard hit since they had no access to primary health care. Historically civilizations have always depended on plants for cure. Scientific research on plants has revealed that they indeed have curative powers and can cure stress and depression. Allamandin can even cure cancer by inhibiting tumor.