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Rotational symmetry of order more than 1 are (a ), (b ), (d ), (e) and (f ) because in these figures, a complete turn, more than 1 number of times, an object looks exactly the same.

Modulation index: It is the ratio of peak value of modulating signal to the peak value of carrier wave.

μ = A_m/A_c

Physical significance: It signifies the level of distortion or noise. A lower value of modulation index indicates a lower distortion in the transmitted signal.
Maximum amplitude, A_max = A_c + A_m
= 10 V
Minimum aptitude, A_min = A_c – A_m = 2V

Modulation index = (Amax - Amin))/(Amax + Amin) = (10 - 2)/(10 + 2) = 8/12 = 2/3.

(1) From Benzene

When benzene is chlorinate directly with Cl₂ in presence of FeCl₃ at room temperature chlorobenzene is obtained.

(2) From Aniline

To get chlorobenzene from aniline, aniline is first converted into benzene diazonium chloride.

The product thus obtained is then reacted with Cu₂Cl₂ in presence of HCl to get chlorobenzene.

-Was new to the place and had not much personal information about him/ had heard adverse remarks made by people about Mr. Lamb/ Lamb leading a lonely life, no contact with outside world/ earlier, children used to tease and chase him, so would not be a healthy company for her son.

Yes, the statement is correct. A convex lens of focal length 20 cm will produce a magnified virtual image if object is placed at a distance less than 20 cm from the lens.

A convex lens of focal length 20 cm will produce a magnified real image if object is placed at a distance greater than 20 cm and less than 40 cm from the lens.

(i) A diamagnetic substance is attracted towards a region of weaker magnetic field. 

(ii) (a) Permanent magnets are made of steel which is characterised by high retentivity and high coercivity. 

(b) Electromagnets are made of soft iron which is characterised by high retentivity and low coercivity

Mutual Inductance: The mutual inductance of two coils is defined as the magnetic flux linked with the secondary coil when the current in primary coil is 1 ampere.

Electromagnetic radiation produced by a Klystron or a Magnetron valve is microwave.

Wavefront: The locus of particles of a medium vibrating in the same phase is called a wavefront. From a point source, the wavefront is spherical; while for a line source the wavefront is cylindrical. The distant wavefront is plane.

Alexander Graham Bell, the inventor of the telephone was a good friend and companion of Helen. He remained a great support to her. 

Dr. Alexander Graham Bell first met Keller when she was six years old and her parents brought her to him for advice on how to teach her. This meeting was not only the beginning of a long friendship between Dr. Bell and Helen, but it also proved to be the foundation of Helen’s education and life. In fact, Helen has dedicated her autobiography ‘The Story of My Life’ to him. She has mentioned his sympathetic and tender nature that made her love him from her first visit itself. It was at his suggestion that Helen’s father wrote to Mr. Anagnos and subsequently found Miss Sullivan as a teacher for Helen. She visited him at his home and laboratory. He appears to be a wonderful and patient teacher who could instill enthusiasm and interest in his students. He was a humorous person and had love for children, particularly those who were deaf. Dr. Bell could understand Helen’s signs and acted like the door through which Helen could pass from darkness to light. He remained a good friend to Helen and Miss Anne Sullivan and accompained them on a trip to the world fare. He was a true friend who hleped Helen whenever she needed it.

Helen looked forward to her second year at Gilman’s school. However, she was confronted with unexpected difficulties that year which caused her a great deal of frustration. She had to study mathematics without the needed tools. The classes were larger and it was not possible for the Cambridge teachers to give her special instructions. Anne Sullivan had to read all the books to her. Helen had to wait in order to buy a Braille writer so that she could do her algebra, geometry and physics.When the embossed books and the other apparatus arrived, Helen’s difficulties began to disappear and she began to study with confidence. However, Mr. Gilman thought that Helen was overworked and was breaking down. He insisted that she overworked, and that she should remain at his school three years longer. He made changes in her studies. A difference of opinion between Mr. Gilman and Miss Sullivan resulted in Helen’s mother withdrawing Helen and Mildred from the Cambridge school. Helen went on to continue her studies under a tutor. Helen found it easier to study with a tutor than receive instructions in class.When Helen took her exam in June 1899, she faced many difficulties, as the administrative board of Radcliffe did not realize how difficult they were making her examinations. They did not understand the peculiar difficulties, Helen had to go through. However, Helen with her great determination, overcame them all.

Given zeroes, 5+√2 and 5-√2 

Sum of the zeroes = 5+√2 + 5-√2 

Sum of the zeroes = 10

Product of zeroes = (5+√2)(5-√2) 

Product of zeroes = 25 - 2 = 23 

We know that quadratic polynomial is in the form of, =k{x²-(sum of zeroes)x+product of zeroes} 

By putting required values we get, = k{x² - 10x + 23}

= x² - 10x + 23 

Hence x² - 10x + 23 is the required polynomial.

Physics are the rules by which technology plays a game. Physics gives us electronics. Electronics gives us manipulation of information. Technology as defined today is the culture that has grown up around the manipulation of that information.

It has only been about 10 years that smart phones have come to dominate the world. Technology is the term that is used to describe the new behavior, but technology is only the enabling gadget that has yielded one of the most incredible changes in culture to hit humans ever.

There are millions of teenage girls who are addicted to “technology” but have no idea what electronics or physics is. And so technology is a new word. It describes the girl in seat 25c on the airplane frantically texting her ex-boyfriend that he just changed his status on Facebook. “Do you still love me?” Plane takes off and girl suffers for 2 hours until plane lands and the phone comes out again Well, this young gal is living technology, but that technology is all about her feelings, not Mawell’s Equations.

Northern Plains were formed by the sediments brought in by three major Himalayan rivers (Ganga, Indus and Brahamaputra) and their tributaries. When these rivers flowed through the Himalayas, they eroded rocks, transported and deposited the smaller fragments of rocks in the foothills of the Himalayas.  After million of years, the accumulation of sediments led to the formation of the Indian Northern Plains.

The kinetic energy of gases increases with the increase in the temperature. When the balloon is kept in the sun, due to Sun's heat, the kinetic energy of gaseous particles inside the balloons also gets increased and the balloon expands. This will increase the pressure on the walls of the balloon. It continues to expand and comes to a stage when the baloon bursts.

x can be any one of 1, 2, 3 or 4.
y can be any one of 1, 4, 9 or 16
Total number of cases of product of x and y = 16

Product less than 16 = (1×1, 1×4, 1×9, 2×1, 2×4, 3×1, 3×4, 4×1)
Number of cases, where product is less than 16 = 8

Required probability = 8/16 or 1/2

This is the story of a professional boxer who has a very intelligent son. The boy is ten years old and works hard at his studies. He is every inch a very civilized boy. Both the boxer and his wife are proud of him. But they think that the boy would feel humiliated if he came to know that his father was a mere boxer. To them, boxing was not a respectable profession. So they take all care that the boy doesn't come to know of his father's profession. They tell him that he is a commercial traveller. But in the end of the story, the boy comes to know that his father is a well-known boxer. He feels no humility at all in it. Rather, he expresses a sense of great pride in it. He had always longed to have a picture of Young Porky, the famous boxer, who now he knows is his own pa.

This is an interesting story which shows that it pays to show off one‘s knowledge. It is good to have wide knowledge but it becomes irritating when we try to show it off in season and out of season. A trainee soldier named Quelch has amazing knowledge of everything. That is really very nice fine. But he never loses any opportunity to make a show of it. He tries to outwit even his instructors and makes them feel small. Being fed up with his this habit, and instructor named Corporal Turnbull allots him permanent cookhouse duties. Thus in spite of all his knowledge, ProfessorQuelch fails to earn any rank as a soldier, what to say of earning a commission.

A lady wants to sell her house because she is in need of money. She decides to sell it for two hundred thousand francs, and puts up a ‗Villa for Sale‘ notice at the front of her house. But even after more than a month no costumer comes or calls up. The landlady feels desperate and decides to get rid off of it at any price. One day a lady and her husband call in with a mind to buy the house. While the lady seems very anxious to buy it, her husband does not show any interest. The landlady insists on their going round the house to have a look at it. The disinterested husband refuses to go but the wife goes upstairs with her. In the meantime a lady steps in. She takes the husband to be the owner of the house and stats talking to him. She seems to be in a tearing hurry to buy the house without having a look at it. She at once agrees to pay three hundred thousand francs and gives the man a cheque for that amount. She exits abruptly. When his wife comes down, she does not seem to have liked the house very much. But the husband starts praising it. He immediately takes out his cheque book and pays two hundred thousand francs to the land lady. He cleverly obtains a receipt for the amount from the lady. Thus sitting in the drawing room of the lady, he earns hundred thousand francs for himself and gets the maximum for the lady for her house.

Lord Ullin's Daughter' is a romantic ballad of Thomas Campbell. It tells the tragic love-story of Lord Ullin's daughter and her lover, the Chieftain of Ulva's island. Lord Ullin was dead against their love. But his daughter defied him and eloped with her lover. In great fury Lord Ullin, accompanied by his armed men, gave them a hot chase. But when he was about to overtake them, he saw the two lovers rowing away from him in the stormy sea. The girl would rather face the deadly storm than her angry father. Soon the two lovers were caught in the violent storm. Lord Ullin's wrath changed into wailing when he saw his daughter struggling with the deadly waves. He cried to his daughter to come back. He was ready to forgive her and the Chieftain. But now it was too late. The ghostly water had swallowed the lives of the two lovers.

The poem begins with the speaker asking readers to behold a young girl 'reaping and singing by herself' in a field. The song the girl sings is a sad song, and anyone passing by, the speaker says, should either stop and listen or 'gently pass' so as not to disturb her. He is so struck by the sad beauty of her song that the whole valley seems to overflow with its sound.

In the second stanza, the speaker compares the girl's singing to that of a nightingale and a cuckoo bird. He says that the song she sings is more welcome than a nightingale might sing to weary travellers in the desert, and her voice is more thrilling to hear than the cuckoo-bird in spring. He is utterly enchanted, although, he cannot understand the language of the song and so cannot say what the song is about.

In the third stanza, the speaker tries to imagine what the song might be about. Given its sad tune, he speculates that her song might be about some past sorrow, pain or loss 'of old, unhappy things' or battles fought long ago. Or perhaps, he says, it is a humbler, simpler song about some present sorrow, pain, or loss, a 'matter of to-day.'

In this story, the writer tells us how she taught her grandmother to read. In her childhood, the grandmother was never sent to school. So she remained illiterate, but made it sure that her own children and grandchildren got good education. But when she was sixty-two, a strong desire filled her mind. She wanted to learn to read so that she could read stories and novels of her own. She did not want to depend on anyone to read out a story or novel to her. She talked of this desire to her granddaughter (the writer of this story). With the writer's help and through her true hard work and firm determination, she learnt to read in a very short time. She touched the feet of her little Guru and also gave her the gift of a frock material.

This poem is based on a very common experience. A traveller was going through a forest. He reached a point where the road diverged in two directions. Both the roads looked equally attractive to the traveller. But he decided to take the one that did not show many signs of having been used. It is true that if he had chosen the beaten path, he could be sure of reaching somewhere. He would not have faced many difficulties or problems in life. But he took the one 'less travelled by', and 'that has made all the difference'.

Frost suggests that the choices which one makes in one's life are for good. One cannot turn back and make a second choice regarding one's goal in life. Therefore, it is all the more essential that one should exercise great caution in making the choice. He also suggests that by choosing the ordinary course in life, one cannot hope to become extraordinary.

Once the poet was travelling through a forest. He came to a place from where the road diverged in two different directions. It was not possible for the poet to travel by both the roads at the same time. He had to choose one of the two. The poet stood there and thought for a long time. One of the roads was visible to some distance. It meant that the road had frequently been used, The other road was overgrown with grass. It meant that this road had not been used much. The poet decided to go by the second road. He kept the first one for another day.

The poet imagines a time many ages hence. He will then be in some other world. He will then recall how he had decided to travel by the less-frequented road. This choice had made all the difference for him. It affected not only the future course of his life on this earth but also his spiritual course after death.

Thus, with the help of symbols, the poet brings out the idea that man has to choose between the roads of materialism and spiritualism in his life. The choice once made is made for good. It cannot be altered later.

This poem describes the journey of a brook. The speaker in the poem is the brook itself. It describes its source and its passage through valleys, forests and plains.

The brook rises from a place visited by water birds. Then it flows down a valley. It passes by several villages, and a little town. A number of bridges have been built across it.

The brook makes a chattering sound as it flows over stones. It makes a deep gurgling sound. Sometimes, it produces a soft murmur. At some places its flow is very fast. But at other places it slides very gently. The brook winds in and out while flowing. It cuts many curves on its banks.

Flakes of foam are formed on the surface of the brook. Flowers float in it. Here and there, little fish are also seen. The rays of the sun are reflected through its clear water.

The brook goes on flowing day and night. It never stops. It flows on and on to join the river. The brook says, "Men may come and men may go, but I go on for ever."

In this story, the writer tells how a dog helps his master who has been paralysed in his left side after an accident. The dog is named Duke. It is a Doberman Pinscher. It is four years old and weighs about 23 kilos. His master Charles Hooper, nicknamed Chuck, works as a zone manager for a chemical company. His master's wife, Marcy, does not like Duke very much because she prefers to have a small dog, like a Pomeranian. One evening, coming back home, Chuck has an accident. He is taken to hospital where he remains for about two months. One side of his body being completely paralysed, he is sent home in a wheelchair. Duke, the dog, begins to feel that his master has difficulty in walking. Like a clever physiotherapist, he begins to exercise his master. The way he does it has been described in the story in great detail. The master is able to move a few steps on his own and resumes his duty in his office. Impressed by his great willpower and doggedness, the company promotes him to a higher rank. But unfortunately, the dog who enables his master to live a respectable life once again, gets badly wounded in an accident. Marcy immediately takes the dog to hospital but the poor dog dies the next day.

(5/7)(-2i - 3j + 6k)

Many different Methods of soil conservation:

1. Contour Plowing – Originating in ancient Phoenicia, Contour Plowing involves plowing grooves into the desired farmland, then planting the crop furrows in the grooves and following the contours. It a very effective way for farmland on slopes to prevent run off improve crop yields.

2. Terrace Farming – Terracing is a method of carving multiple, flat leveled areas into hills. Steps are formed by the terraces which are surrounded by a mud wall to prevent run off and hold the soil nutrients in the beds. More commonly found in lesser developed nations due to the difficulty of using mechanized farming equipment in the terraces. Very popular in Asia for planting rice.

3. Keyline Design – A more enhanced version of Contour Plowing, maximum water retention is achieved by taking into account all the watershed properties when making the contour lines. The Keyline refers to topographic feature linked to water flow. This allows the water run off to run directly into an existing water channel, and prevent soil erosion caused by the water.

5. Cover Crops/ Crop Rotation – Cover crops such as turnips and radishes are rotated with cash crops in order to blanket the soil all year- round and produces green manure the replenishes nitrogen and other critical nutrients. Using cover crops can also suppress weeds.

7. Soil Conservation Farming – A mixture of farming methods intending the mimic the biology of virgin land. These practices can be used to prevent erosion and even restore damaged soil and encourage plant growth. Eliminating the use of nitrogen fertilizer and fungicides can increase yields and protect crops from drought and flooding.

Lower members aldehydes are able to form intermolecular hydrogen bonds with water molecules. Hence, they are easily miscible with water.

Lyophilic sols: Lyophilic sols are those sols in which the particles of dispersed phase have great affinity for the dispersion medium, e.g., sols of gum, gelatine, starch, etc.

  Lyophobic sols: In this type of sols the particles of dispersed phase have little or no affinity for the dispersion medium, e.g., gold sol, Fe (OH)₃ sol, As₂O₃ sol., etc. Lyophobic sols easily coagulate on the addition of small amount of electrolyte because these are not stable. The stability of Lyophobic sols is only due to the presence of charge on the colloidal particles, on the other hand stability of lyophilic sol. is due to charge as well as solvation of colloidal particles.

(i) The principle of froth floatation process is that sulphide ore particle are preferentially wetted by pine oil, whereas the gangue particles are wetted by water.
(ii) Zone refining is based on the principle that the impurities are more soluble in (liquid state) than in the solid state of the metal.
(iii) The principle of refining by liquation is that the impurities whose melting points are higher than the metal are left behind on melting the impure metal. Hence pure metal separates out.

Here given, 

a₃ = 9 

⇒ a + 2d = 9 ....(i) 

a₈ – a₅ = 6 

⇒ (a + 7d) – (a + 4d) = 6 

⇒ 3d = 6 

⇒ d = 2 ....(ii)

Substituting (ii) in (i), we get 

⇒ a + 2(2) = 9 

⇒ a = 5

So, AP is 5, 7, 9, 11, ......

Remaining total number of bulbs = 19

Remaining total number of non-defective bulbs = 16 − 1 = 15

P (getting a not defective bulb) =15/19

Total number of discs = 90

(i) Total number of two-digit numbers between 1 and 90 = 81

P (getting a two-digit number) = 81/90 =9/10

(ii) Perfect squares between 1 and 90 are 1, 4, 9, 16, 25, 36, 49, 64, and 81. Therefore, total number of perfect squares between 1 and 90 is 9.

P (getting a perfect square) = 9/90 = 1/10

(iii) Numbers that are between 1 and 90 and divisible by 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, and 90. Therefore, total numbers divisible by 5 = 18

Probability of getting a number divisible by 5 =18/90 = 1/5

Total number of marbles = 24

Let the total number of green marbles be x.

Then, total number of blue marbles = 24 − x

P (getting a given marble) =x/24

According to the condition given in the question,

x/24 = 2/3

\x = 16

Therefore, total number of green marbles in the jar = 16 Hence, total number of blue marbles = 24 − x = 24 − 16 = 8

Cosec A = 17/15

Area of quadran = 1/4 x 22/7 r² 

= 38.5 (use π = 22/7)

r = 7 cm

∴ diameter = 14 cm

AD/BD = AE/EC (By B.P.T.)

= 1.5/3 = 1/EC

 ∴ EC = 2Cm

x² -3x-10 = 0 

x² -5x + 2x-10 = 0 

x(x-5) + 2(x-5)=0 

(x-5) (x+2)=0 X = 5, -2

Sum of the roots = -b/a = 3/1

which is same as 5 - 2 = 3

product of the roots = c/a = -10

which is same as 5x(-2) = -10

Hence verified

(i) 3 Students

(ii) x² +2x +1/x+1

= (x+1)/x+1 = x +1

dy/dx = e^x + e^y

dy/e^y = e^x dx

integrating both sides

= - e^-y + c = e^x

= e^x + e^-y

= c

= 7/2

Area of Circle= πr²/4 = 77/2 cm²

(a) The observed characteristics of photoelectric effect could not be explained on the basis of wave theory of light due to the following reasons. 

(i) According to wave theory, the light propagates in the form of wavefronts and the energy is distributed uniformly over the wavefronts. With increase of intensity of light, the amplitude of waves and the energy stored by waves will increase. These waves will then, provide more energy to electrons of metal; consequently, the energy of electrons will increase. Thus, according to wave theory, the kinetic energy of photoelectrons must depend on the intensity of incident light; but according to experimental observations, the kinetic energy of photoelectrons does not depend on the intensity of incident light. 

(ii) According to wave theory, the light of any frequency can emit electrons from metallic surface provided the intensity of light be sufficient to provide necessary energy for emission of electrons, but according to experimental observations, the light of frequency less than threshold frequency cannot emit electrons; whatever the intensity of incident light may be. 

(iii) According to wave theory, the energy transferred by light waves will not go to a particular electron, but it will be distributed uniformly to all electrons present in the illuminated surface. Therefore, electrons will take some time to collect the necessary energy for their emission. The time for emission will be more for light of less intensity and vice versa. But experimental observations show that the emission of electrons take place instantaneously after the light is incident on the metal; whatever the intensity of light may be.

(b) Features of the photons: 

(i) Photons are particles of light having energy E = hn and momentum p = h/ λ, where h is planck constant. 

(ii) Photons travel with the speed of light in vacuum, independent of the frame of reference. 

(iii) Intensity of light depends on the number of photons crossing unit area in a unit time.

 m_e = 1 + 25/5 = 6

m_o = 30 / m_e = 5

m_o = v_o / -u_ov_o = - 5 u_o 

1/f_o = 1/v_o – 1/u_of_o = - (5/6) u_o

u_o = 1.5 cm , v_o = 7.5 cm

u_e = - 4.17 cm

Length of the tube = u_e + v_o = 11.67 cm

LAN (Local Area Network)

m = - f_o / f_e

f_o = 5 f_e

L = f_o + f_e

f_e = 36/6 = 6 cm

f_o = 30 cm

(D) CO₂/CO₃ ^–