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The speed near the extreme position is near zero and the decision by the observer that the bob has reached the extreme position may have some error due to slow movement. But the bob crosses the mean position with maximum speed so there is no hesitation in deciding that the bob has crossed the mean position and hence better accuracy.

Yes. The projection of a point in a uniform circular motion on a diameter is a simple harmonic motion.

No. Since the particle at P and Q is not in uniform motion but in SHM and the same particle is in different phases at these points. Hence it is quite ok.

Mass (m), Length (l) and Time (t).

Meter, Kilogram and Second.

Some fundamental: Length, Mass, Time, Electricity, Light intensity, Quantity of quantities substance, Temperature, Plane angle.

• Fundamental quantities are those physical quantities that cannot be expressed in terms of other quantities.
• Fundamental quantities are also called base quantities

Length, mass, time electricity, light intensity, quantity of substance, temperature, plane angle.

Force = Mass x acceleration

 =\(mass\,\times\,\frac{velocity}{time}\)

= mass x \(\frac{displacement}{time\,\times\,time}\)

= kg x \(m\,\frac{m}{s\,\times\,s}\)

Hence fundamental units used to express force are kg, m, s.

B) after the magnitude

One litre is the volume of a cube with 10 cm sides. 

(10 cm × 10 cm × 10 cm) 

(or) 

1 L = 10^-3m³ 

Hence, litre is a derived unit.

Derived units of area = m² 

Derived units of volume = m³

Units should be placed right side of the magnitude of every physical quantity. 

For Example 2 kilograms, 100 grams.

Depending upon the quantity, different units to measure are required.

The quantities that are obtained by combining fundamental quantities either by multiplication or division or both operations are called derived quantities.

The expressed quantity depends on the independent and dependent variables taken for plotting the graph.

Some units are expressed in the names of the scientists like newton, joule, etc. When we use these units, scientists are remember once again.

• We can solve so many problems by using graphs. 
• We can know the relation between two physical quantities through graphs.

A. (v) 

B. (iii)

C. (vi) 

D. (ii) 

E. (iv)

(b) Mahbub-ul-Haq

The modern concept of GDP was first developed by Simon Kuznets in the year 1934.

(a) A is correct and R is the relevant explanation to A.

(a) A is correct and R is the relevant explanation to A.

(b) (i), (ii), (iii) are correct

(a) Developed

(a) quantitative

The GDP of India is 2.8 million United States dollars.

Human Resources, Natural Resources, Advancement in technology, Capital formation, Political and social economic factors are few parameters to measure economic growth.

Correct Answer is: (a) GNP

HDI helps to measure the real development of an economy.

Correct Answer is: (d) fourth

(i) Non – Marketed items are left out of GDP: GDP includes only the goods and services that are sold in the market, Non-Marketed items are not included. 

Eg: Services provided by parents to their children, clean air has no market value (or) price. Hence it is left out of GDP.

(ii) GDP measures only quantity not quality: At times, we can see some products which are available at large quantities in the product, at a very low price. Only the quantity sold and its price is measured in GDP. Quality of the product is not taken care of.

(iii) Income Distribution: The GDP of a country may be growing rapidly. But income may not be distributed equally. This brings a lot of unequal distribution of income and wealth. GDP actually do not suggest on income distribution.

(iv) Way of life of the people: A high level of Per-Capital real GDP, may lead to a very low health condition of the people, an undemocratic political system, High pollution, High suicidal rate.

In India GDP is measured both annualy and quarterly. The annual GDP is for a financial year which is from April 1 of one year, for example 2017 to March 31 of the next year, for example 2018.

This is written as 2017-18.

The quarterly GDP estimates are for each of the four quarters into which India’s financial year is divided.

First quarter, denoted Q1 : April, May and June .

Second Quarter – Q2 : July, August and September

Third Quarter – Q3 : October, November and December

Fourth Quarter – Q4 : January, February and March

(c) April, May, June

(i) 

रेलगाड़ी की चाल = (2x² + x +4) किमी/घण्टा

अत: 3x घण्टे में चली गई दूरी = (2x² + x + 4) x 3x

= 6x² + 3x² + 12x किमी

(ii)

यदि x = 5 तो रेलगाड़ी द्वारा चली गई दूरी।

= 6x² + 3x² + 12x = 6 (5)³ +3 (5)² + 12 x 5

= 6 × 125 + 3 × 25 + 60 = 750 + 75 + 60 = 885 किमी

एक विद्यालय में स्वच्छता के कारण बालिकाएँ बढ़ जाती हैं = (5x – 3)

(5x+3) विद्यालय में स्वच्छता के कारण बालिकाएँ बढ़ जाती हैं = (5x – 3) (5x + 3)

= 25x² – 15x + 15x – 9

= 25x² – 9

(i) 

विद्यालय में कक्षाएँ = 2x

प्रत्येक कक्षा में विद्यार्थी = (x² + 2x + 2)

अत: विद्यालय में कुल विद्यार्थियों की संख्या = 2x × (x³ + 2x + 2)

= 2x⁴ + 4x² +4x विद्यार्थी

(ii)

विद्यार्थियों की संख्या = 2x⁴ + 4x² +4x

यदि x = 3, तो कुल विद्यार्थियों की संख्या = 2 (3)⁴ +4 (3)² +4 x 3

= 2 x 81 + 4 × 9+ 12

= 162 + 36 + 12 = 210

एक ग्राम सभा में नलकूपों की संख्या = x²+ 5x +6

(2x+3) ग्राम सभाओं में नलकूपों की संख्या = (x² + 5x +6) × (2x+3)

= 2x³ + 10x² + 12x + 3x² + 15x + 18

= 2x² + 13x² + 27x + 18

(i)

बाग में पंक्तियाँ = (x + 2y)

प्रत्येक पंक्ति में पेड़ = (x + 2y)

अतः पेड़ों की कुल संख्या = (x + 2y) (x + 2y) = (x + 2y)²

= x² + 2 × x × 2y + (2y)² = x² + 4xy + 4y²

(ii)

यदि x = 3. y = 2 है, तो

पेड़ों की कुल संख्या = (x + 2y)²

= (3 + 2 x 2) = (3 +4) = (7)² = 49

(i) 

कॉपियों की संख्या = (3x +7)

प्रत्येक कॉपी का मूल्य = ₹ (2x – 1)

अतः कॉपियों का कुल मूल्य = (3x + 7) (2x – 1)

= 3x (2x – 1) +7 (2x – 1)

= 6x² – 3x + 14x -7

= ₹ (6x² + 11x – 7)

(ii)

यदि x = 5 हो, तो मूल्य = 6x² + 11x – 7

= 6 (5)² + 11 (5) -7

= 150 + 55-7

= 205 – 7 = ₹ 198

1 कलम का मूल्य = (2x – y) रु०

(2x – y) कलमों का मूल्य = (2x -y) (2x -y) ,

= (2x -y)

= (2x)² – 2 × 2x × y + (y)²

= ₹ (4x² – 4xy + y²)

आयताकार मैदान की लम्बाई = (2x + 1) मी

आयताकार मैदान की चौड़ाई = (2x – 1) मी

आयताकार मैदार का क्षेत्रफल 

= (2x + 1) (2x – 1)

= (2x)² – (1)² = (4x² – 1) मी²

Area of parallelogram ABCD = 100 sq.cm 

From the given figure, 

ar (△APB) + ar (△CPD) = ar (△PD) + ar (△BPC)

ar (△APB) + ar (△CPD) = 1/2 a(▭ ABCD)

= 1/2 x 100

= 50 sq.cm

The sergeant was the loyal British servant. He wanted to catch the escaped prisoner for a reward. As the play unfolded the man who introduced himself as a ballad singer brought about changes in the mind of the sergeant. During their discussion the man arouse patriotism in his mind and reminded him of his youth when he had joined a group of patriots. The sergeant was torn between his duty and his nation. But finally patriotism won and the sergeant helped the man to escape. He misguided his assistants in order to let the prisoner escape easily.

Hermia and Lysander loved each other and they eloped in the forest to get married. Helena loved Demetrius but it was the effect of the love potion which was applied to Lysander’s eyes when he slept. Therefore, as he woke up he saw Helena and he started developing feelings for her. But Helena loved Demetrius. On her part Helena was very right. At the end both found their right companions Helena – Demetrius and Lysander – Hermia.

(i) The play is not restricted to only a part of the woods because the references, Quince’s cottage, in the another part of the wood etc., are there in the play.

(ii) The reference to the Indian boy is found in Act II scene I as Puck says “A lovely boy, stolen from an Indian king” and when Titania said that his mother was a votaress of my order and in the spiced Indian air. The reference of Titania’s Indian friend is also found.

(i) Bottom

(ii) Cobweb

The characters are the part of stage setting and the play starts with Theseus, Duke of Athens as he wins the queen of Amazons, Hippolyta. But later, in their marriage celebration there are the king and the queen of fairies, Oberon and Titania as well as other fairies and elves as imaginary characters. Characters are arranged from real to imaginary. I suggest that all characters should be real humans.