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Answer is (B)

Let 2π – 5 = θ, 

⇒ 5 = 2π – θ tan 5 = tan (2π – θ) 

tan^-1 (tan 5) = tan^-1 tan (2π – θ) 

= tan-1 [-tan θ] 

= tan^-1 [tan (-θ)] = – θ 

= – (2π – 5) = 5 – 2π

1. Consult family members. Decide the time, place, date, menu, etc. 

2. List down the invitees. 

3. Inform the invitees well in advance, orally or in the written form. Give all the information needed. 

4. You have to impress your guests. Choose decorations which look the best. Choose the menu which the guests will love. 

5. List down the different means of entertainments and including games, you would want for your guests. 

6. List down the programme of your party, Recheck the list to see that everything is taken care of.

7. Distribute the task so that it wouldn’t be a burden on any one person.

1. Be ready and presentable before your guests trickle in 

2. Check whether decorations and food are ready before the guests arrive. 

3. Greet and introduce guests to everyone. 

4. Keep your guests comfortable and happy. 

5. Serve everyone food politely, keeping in mind their likes and dislikes. 

6. Make sure that everyone participates and enjoys the entertainment part. 

7. Bid (say) goodbye to every guest personally. 

8. It matters a lot.

9. All family members should help to clean up.

L.H.S = vector((a - b) x (a x b)) 

= vector(a x a + a x b - b x a - b x b)(distributive law)

= vector(a x b - b x b) [∵ vector(a x a) = 0]

= vector((a x b) + (a x b)) = 2vector(a x b)

Let the plane cuts intercept of 'a' unit on axes.

So, equation of the plane be 

x/a + y/b + z/a = 1

x + y + z = a

If this plane passes through the point P(2,3,5) then

2 + 3 + 5 = a 

a = 10   

Hence, require equation of plane is x + y + z = 10

Let vector a = 2i - j + k

and vector b = i - 3j - 5k

Now, |vector a| = √(2² + (-1)² + 1²) = √6

and |vector b| = √(1² + (-3)² + (-5)²) = √35

vector(a.b) = 2 x 1 + (-1) x (-3) + 1(-5) = 0

Hence, given vectors are at right angles.

Let equation of any plane parallel to the given plane is given by 

vector r(2i - 3j + 5k) = d ...(i)

If this plane passes through the point (3,4,-1) whose position vector is 3i + 4j - k

Then, (3i + 4j - k).(2i - 3j + 5k) = d

3.2 + 4.(-3) + (-1).5 = d

d = -11

By (i) we get vector r.(2i - 3j + 5k) + 11 = 0 

which is the required equation of the plane.

finding slope of the tangent by differentiating the curve

\(y+x\frac{dy}{dx}=0\)

\(\frac{dy}{dx}=-\frac{x}{y}\)

m(tangent) at \((ct,\frac{c}{t})\) = \(\frac{1}{t^2}\)

normal is perpendicular to tangent so, m₁m₂ = – 1

m(normal) at \((ct,\frac{c}{t})\) = t²

equation of tangent is given by y – y₁ = m(tangent)(x – x₁)

\(y-\frac{c}{t}=-\frac{1}{t_2}(x-ct)\)

equation of normal is given by y – y₁ = m(normal)(x – x₁)

\(y-\frac{c}{t}={t^2}(x-ct)\) 

finding slope of the tangent by differentiating the curve

\(\frac{x}{a^2}-\frac{y}{b^2}\frac{dy}{dx}=0\)

\(\frac{dy}{dx}=\frac{xb^2}{ya^2}\)

m(tangent) at \((\sqrt{2}a,b)=\frac{\sqrt{2}ab^2}{2a^2}\)

normal is perpendicular to tangent so, m₁m₂ = – 1

m(normal) at \((\sqrt{2}a,b)=-\frac{ba^2}{\sqrt{2}ab^2}\)

equation of tangent is given by y – y₁ = m(tangent)(x – x₁)

\(y-b=\frac{\sqrt{2}ab^2}{ba^2}(x-\sqrt{2}a)\)

equation of normal is given by y – y₁ = m(normal)(x – x₁)

\(y-b=-\frac{ba^2}{\sqrt{2}ab^2}(x-\sqrt{2}a)\)

finding the slope of the tangent by differentiating the curve

\(\frac{x}{a^2}-\frac{y}{b^2}\frac{dy}{dx}=0\)

\(\frac{dy}{dx}=\frac{b^2x}{ya^2}\)

m(tangent) at (x₁, y₁) = \(\frac{b^2x_1}{y_1a^2}\)

normal is perpendicular to tangent so, m₁m₂ = – 1

m(normal) at (x1, y1) = \(-\frac{a^2y_1}{x_1b^2}\)

equation of tangent is given by y – y₁ = m(tangent)(x – x₁)

\(y-y_1=\frac{b^2x_1}{y_1a^2}(x-x_1)\)

equation of normal is given by y – y₁ = m(normal)(x – x₁)

\(y-y_1=-\frac{a^2y_1}{x_1b^2}(x-x_1)\)

finding slope of the tangent by differentiating the curve

\(2y\frac{dy}{dx}=4a\)

\(\frac{dy}{dx}=\frac{2a}{y}\)

m(tangent) at (x₁, y₁) = \(\frac{2a}{y_1}\)

normal is perpendicular to tangent so, m₁m₂ = – 1

m(normal) at (x₁, y₁) = \(-\frac{y_1}{2a}\)

equation of tangent is given by y – y₁ = m(tangent)(x – x₁)

\(y-y_1=\frac{2a}{y_1}(x-x_1)\)

equation of normal is given by y – y₁ = m(normal)(x – x₁)

\(y-y_1=-\frac{y_1}{2a}(x-x_1)\)

1. a. Magnetic Field

2. c. Circular

3. b. Its shape

4. c. It defects to south

5. d. Magnet

1. a. TRUE

2. a. TRUE

3. a. They are intersecting each other so direction can not be found

4. b. FALSE

5. d. Repel, attract

In this figure the magnetic field due to all wires passing through origin and directed towards origin is zero. 

And due to the circular path in first quadrant is that we integrate Biot savart law from o to πr/2

we get  µ.I/8r
And due to the circular path in 2nd quadrant is same but the r is double.
 µ.I/16r
And due to wire in the 3rd quadrant is we can't say as the angle is unknown.
apply the formula of straight wire and calculate that.

Total magnetic induction is the sum of the 3 equations obtained.

Avogadro Law : Equal volumes of all gases under the similar condition of temperature and pressure contain equal number of molecules 

 Intermolecular Forces: The forces of attractions and repulsion between interacting particles.

The volume of a fixed mass of a gas is directly proportional to its absolute temperature at constant Pressure. V α T , constant P. 

At -273 ⁰ C, volume of the gas approaches to zero i.e the gas ceases to exist.

Value Points :

• Both lived in close proximity

• Preferred being confined in their own comfort zones

• Would work together to bring potatoes from the attic

• They discussed their course of study and their plans

• Peter was polite and courteous

• Anne understood his need for affection

Detailed Answer :

Peter van Daan was the only son of the van Daans. When he joined the secret annexe, no one had thought that Anne and Peter would grow a liking for each other. But later on, both of them lived in close proximity. They shared their feelings with each other. They preferred being confined in their own comfort zones and often would work together to bring potatoes from the attic. Mr. Frank didn’t like the idea of Anne meeting Peter but she never listened to him. She was attracted towards him. Both of them became good friends. They discussed their course of study and their future plans. Peter was polite and courteous towards her and Anne liked his nature. She understood his need for affection because like Anne, Peter also didn’t like the interference of his parents in his life. That’s’ why both of them got on well with each other. In the initial stages, there was some hesitation but later on both of them became good friends.

Kunti said, “ It is the Pandavas you should lead, not Duryodhana’s armies. Leave them, come now! Join your brothers, defend them, against the Kauravas. My heart has been heavy within me all these years. Bring me peace now”.

Sage Durvasa had taught Kunti a mantra, It was a secret verse to invoke the Gods. When invoked, they would appear before her and bless her with son equal to themselves in glory.

Karma said, “Duryodhana gave me wealth of kingdom, power, armies-more than that he gave me friendship, a lifelong friendship. Would I not be a traitor and a cheat, if I deserted him now”?

No, Karma did not become a traitor.

Karma came to dislike the Pandavas because Bhima flung hot words at Karma at the tournament, where Krupa challenged Karma to reveal his parentage.

Duryodhana gave Karma wealth, a kingdom, power, armies more than that, he gave Karma friendship, a lifelong friendship.

The lesson ‘Friend in Need’ is an extract from the holy epic ‘Mahabaratha’ written by the great sage Ved Vyasa.

The given extract is about Karma, who was bom to Kunthi before her marraige? Karma is the elder brother of the the Pandavas.

Once Kunti served sage Durvasa with utmost devotion when he was a guest at then palace. Sage Dhurvasa was greatly Pleased and the taught Kunti a mantra, to invoke the Gods. Accordingly, when the mantra was invoked, the Gods would bless her with sons equal to themselves in glory.

Kunti who was a very young maiden, she, out of curiosity invoked Lord Surya, the Sun God. He blessed her with a child a male child, who eventully became one of the greatest of all heroes.

A Swayamvara had been arranged for Kunti to choose a husband. Kunti wondered how she could explain the child bom to her after Lord Surya blessed her. So she placed the baby in a basket and set it afloat on the river Ganga.

The baby, later was found by a washer man name Adiratha, who brought him up as Karma. After many years, the enemity between Padavas and Kauvravas lead to a war. Sri Krishna, the benevolent guide to the Pandavas informed Kunthi that a warimminent between the Pandavas and their cousins, the Kauravas, leaving too much bloodshed.

Kunti was in a great dilemma, because Karma, her first bom was with the Kauravas and he would fight with his brothers the Pandavas. He might kill his own brothers and be killed by them.

Kunti made up her mind to tell Karma the truth regarding his birth and persuade him to leave Duryodhana and to join his brothers, the Pandavas, against the Kauravas.

With Karma on their side, the Pandavas could easily defeat the Kauravas. The next Morning she went to the banks of the Ganga where Karma had the habit of praying every morning After his prayers, he opened his eyes and saw Kunti. He greeted her respectfully.

Kunti, realated the story of his birth and begged him to join his brothers, the Pandavas and defend them against the Kauravas. Karma gently told Kunti, that he is indeed the son of Kunti but Adiratha and Radha cared for him and brought him up.

He told her that things would have been different if only she had revealed the truth when Krupa had challenged to reveal his parentage at the tournament. Duryodhana had befriended him, even though he was a charioteer ’s son and gave him wealth and feme.

Karma asked her if it would be honorable to desert Duiyodhana. Karma smiled sadly and made the difficult choice without any hesitation. He held honour, duty and friendship above everything else.

He questioned Kunti that would he not be a traitor and a cheat if he deserted Duryodhana. Kunti had no answer to Karma’s question. She bent her head shamefully and left him, with a heavy heart.

1. Who is the “I”? 

‘I’ is Karma. 

2. Who was this person speaking to? 

Karma was talking to Kunti. 

3. What was the answer? 

Kunti had no answer.

Kunti pleaded thus, “ It is the Pandavas you should lead, not Duryodhana’s armies leave them, come now! Join your brothers, defend them against the Kauravas.

When Krupa challenged Karma to reveal his parentage and when Bhima flung hot words at Karma, it was Duryodhana who befriended him and gave him wealth, a kingdom, power, armies more than that he gave him friendship, a lifelong friendship. So Karma refused to leave Duryodhana.

1. Your ambition :

 My ambition is to study well and become a teacher. I want to educate the future generation of India. I want to fulfil Dr.Kalam’s dream to some extent.

2. Thing you enjoy doing most :

 I like to mind the class when there is no teacher in the class. I like to tell them stories and entertain them with word game heam the lessons in a playway and get good marks.

3. Your hobby :

 My hobby is to collect pictures from magazines and newspapers on the theme natural calamities, paste those pictures and prepare a scrapbook and present that to the school library.

The author’s mother was afraid that he would not be able to achieve his goal.

The author’s mother was afraid that he would not be able to achieve his goal.

The author’s mother was very weak and sick. He had no hope of seeing her again. So, he was very sad on leaving her.

We usually exchange old clothes with steel utensils. This depends mostly on the seller.

The talking fan was demanding that someone must oil its whirling motor.

The poet imagined that the sound coming from the fan was its chatter. Actually, there was a sound due to friction between the parts of its motor. They needed oiling.

(i) The chatter is electrical because it is the sound of the parts of motor that runs on electricity .

(ii) It is mysterious because the sound produced by the fan seems to say something but the poet is unable to understand it.

Studies have shown that optimists generally live longer than pessimists.

Yes, i have a metallic fan in my house.

Mechanic: How are you doing?

Fan: Not well, Suffering from the heat and friction. Can you do something?

Mechanic: I will try to help you. Let me check you first.

Fan: Yes, sure. Please do your best and help me.

Mechanic: I will. Please wait, let me finish my job.

Fan: Go ahead.

(After repairing)

Mechanic: Now, are you okay?

Fan: Yes, now i am feeling well. It feels so good.

Mechanic: That is great. Remember me when you are in trouble.

Fan: Yes, i will. Thanks for helping me. Greetings to you.

Mechanic: You are welcome. Bye. Take care.

Fan: Bye. You too take care.

When an electric fan is switched on, its motor starts whirling i.e. rotating which makes the metallic blades move, cutting the air and we can feel the moving air.

(a) To avoid loss of heat from solar cooker to the surroundings. 

(b) Black surface absorbs more heat radiations of incident energy. 

(c) Transparent glass sheet does not allow the reflected heat radiation to go outside the box. 

(d) To increase the amount of solar energy incident on the transparent glass sheet.

The waste obtained from nuclear power plants is highly radioactive in nature which emits harmful radiations, whereas waste produced in a thermal power plant is non-radioactive. Management of nuclear waste is given as follows: Some products of nuclear waste are buried in sealed steel/lead containers for a long term storage, buried under the ground or dumped in vacated coal mines. Other waste products transforms into less harmful products or to products with a shorter half life.

Were formed millions of years ago, when plants and animal remains got buried under the earth and were subjected to high temperature and pressure conditions. E.g.Coal, Petroleum, etc.

These fossil fuels are non-renewable sources of energy and cause environmental problems due to pollution.

An electrical fan comprises of three blades and a whirling motor. The moment it is switched on, the motor starts and begins to rotate forcing the blades to move in circular movement. This generates a lot- of pressure, which forces the air downwards in all directions.

(i) Use coal, petroleum and natural gas to produce thermal electricity.

(ii) Electricity transmission is very efficient.

(iii) The steam produced by burning the fossil fuels runs the turbine to produce electricity

(i) Energy released when some changes take place in the nucleus of the atom of a substance, is called Nuclear energy.

(ii) It is used for heat generation, fuel for marine vessels.

• Advantages or Nuclear Energy:

(i) Alternative source of energy due to depletion of fossil fuels.

(ii) From a small amount of fuel, a large amount of energy is released.

• Disadvantages of Nuclear Energy:

(i) Risk of nuclear waste leakage

(ii) High cost of setting up of nuclear plant

(iii) Pollution of environment.

(i) Energy harnessed from the heat of the sun is called Geo thermal energy.

(ii) Magma is formed when this heat melts the rocks. The molten rocks and hot gases are called magma

(iii) The magma gets collected at some depths below the earth’s surfaces. These places are called “Hot spots”

(iv) When underground water comes in contact these hot spots, it changes into steam, which can be used to generate electricity.

• Advantages of Geo thermal energy:

(i) Renewable

(ii) Inexpensive

• Disadvantages of Geo thermal energy:

(i) Only few sites available for harnessing energy.

(ii) Expensive

• Tidal Energy: Locations in India – Gulf of Kutch, Gujrat & W. Bengal

(i) Depends upon harnessing the rise and fall of sea level due to tidal action.

(ii) Dams are constructed across a narrow part of sea and turbine converts tidal energy into electrical energy.

Disadvantages: Uniform tidal action is not seen

• Wave Energy:

(i) Kinetic energy of the waves of sea are used to rotate turbines.

(ii) These turbines generate electrical energy

Apparently, the poet imagined the noise of the fan to be the chatter of the fan. When a fan moves a sound is sometimes created in the whirling motors. When we do not oil a fan’s motor properly, it does make such sounds. This very sound assumed as the chatter of the fan.

Tom blackmailed his brother George. Sometimes he assured him that he would improve himself. Thus, he got money from George.