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Solution:
By Euclid’s division algorithm,
240 = 228 x 1 + 12
228 = 12 x 19 + 0
So, HCF (240, 228) = 12

Given:

Quotient = 76

Remainder = 536

Formula Used:

Dividend = Divisor × Quotient + Remainder

Calculation:

Let the Divisor be x
⇒ 76x+536 = 43628
⇒76x = 43628-536
⇒76x = 43092
⇒x = 43092÷76
x = 567

Concept used:

The remainder can be multiplied in the same way as the actual number when divided by any other number

Ex- 5²/4 = (5 × 5)/4 = (1 × 1)/4 = 1/4, Remainder = 1

Calculation:

45 is divided by 15

⇒ 45/15

⇒ (4² × 4² × 4)/15

⇒ (16 × 16 × 4)/15

⇒ (1 × 1× 4)/15      ----(When 16 and 4 is divided by 15 then it gives 1 and 4 as remainder respectively)

⇒ 4/15 

∴ The remainder is 4

 Given: 

The HCF and LCM of two numbers are 19 and 342 respectively and if dividing one number by 2 gives the quotient 19

Concept Used:

For two numbers, 

LCM × HCF = product of those two numbers

Calculation:

Given that, if dividing one number by 2 gives the quotient 19.

Here nothing is mention about the remainder, so, we have to assume that the remainder is 0

The number is 2 × 19 = 38

Accordingly,

19 × 342 = 38 × the other number

⇒ The other number = 171

∴ The second number is 171.

Given:

HCF of two number is 4 and the sum of those two numbers is 36.

Concept Used:

Concept of HCF

HCF is the least common factor among two or more numbers.

Calculation:

HCF of two number is 4

Let, those numbers be 4x and 4y where x and y are prime to each other

Accordingly,

4x + 4y = 36

⇒ 4(x + y) = 36

⇒ (x + y) = 9

Now,

9 = 8 + 1

9 = 7 + 2

9 = 6 + 3

9 = 5 + 4

In all these cases only (8,1); (7,2); and (5,4) are prime to each other. So, such three pair is possible

∴ Such three pair of number is possible.

Given :

Ratio of two numbers 7 : 9 

Their LCM is 945 

Formula used :

Multiplication of two numbers = LCM × HCF 

Calculations :

Let the HCF be x 

The number will be 7x and 9x 

⇒ 7x × 9x = x × 945 

⇒ x = 15 

∴ The HCF will be 15 

Given:

Sum of numbers = 36

HCF = 4

Concept used:

The H.C.F. of two or more than two numbers is the greatest number that divides each of them exactly.

Calculation:

Let, the numbers are 4x and 4y

⇒ 4x + 4y = 36

⇒ 4(x + y) = 36

⇒ x + y = 9

⇒ (1, 8)

⇒ (2, 7)

⇒ (4, 5)

We can see the 3 possible pairs.

∴ The possible number of pairs is 3.

To find the pairs we only can take those pair which are prime to each other. We can't take those pair which are not prime to each other.

For example: In this problem, 9 can be represent as 6 + 3 = 9

But, 6 & 3 are not prime to each other. So, it can't be a possible pair.

Given:

The product of two number is 1014 and their HCF is 13

Concept:

The HCF of two or more numbers is the greatest factor that divides each of them exactly.

Calculation:

Let the number be 13a and 13b

The product of the two number = 1014

⇒ 13a × 13b = 1014

⇒ a × b = 1014/169

⇒ a × b = 6

Possible pairs are (1, 6), (6, 1), (2, 3), (3, 2)

∴ The number of such possible pairs is 4.

Given:

The product of two numbers is 1083 and their HCF is 19

Concept:

The HCF of two or more numbers is the greatest factor that divides each of them exactly.

Calculation:

Let the number be 19a and 19b

The product of the two numbers = 1083

⇒ 19a × 19b = 1083

⇒ a × b = 1083/361

⇒ a × b = 3

Possible pairs is  (1, 3)

Assuming p = 1, q = -1,

We get,

\(\begin{array}{l} 1 + 1 + 4{r^2} + 3 = 2 - \left( { - 2} \right) + 4r\\ \therefore 4{r^2} - 4r + 1 = 0 \end{array}\)

∴ r = ½

Concept:

The HCF of two or more numbers is the greatest factor that divides each of them exactly.

Calculation:

Statement 1

The factor of (p + q) = (p + q)

The factor of (p² – q²) = (p + q) (p – q)

The HCF of (p + q) and (p² – q²)

⇒ (p + q)

Statement 2

The factor of (p – q) = (p – q)

The factor of (p² – q²) = (p + q) (p – q)

The HCF of (p – q) and (p² – q²)

⇒ (p – q)

Statement 3

The factor of (p + q) = (p + q)

The factor of (p³ + q³) = (p + q) (p² – p × q + q²)

The HCF of (p + q) and (p³ + q³)

⇒ (p + q)

Statement 4

The factor of (p – q) = (p – q)

The factor of (p³ – q³) = (p – q) (p² + p × q + q²)

The HCF of (p – q) and (p³ – q³)  

⇒ (p – q)

∴ Only statement 1 and 3 are correct.

Answer is (3) 3.07 cm

Least count of V.C = \(\Big(1-\frac{9}{10}\Big)\times1mm\)

= 0.1 mm

∴ Zero error = 7 × 0.1 = 0.7 mm

positive error

Measured value = (31 + 4 × 0.1) mm 

= 31.4 mm

∴ Length of cylinder = 31.4 – 0.7

= 30.7 mm

= 3.07 cm

Rhizobium, Azotobactor.

(d) Warm blooded nature

(b) Crocodiles, Birds, Mammals

Correct option: a. Wheat

a) When heat is applied on protein it coagulates from opaque to white in colour

(c) Frog and Pigeon

Major pests of oil seed crops: 

Aphids, white grub, cut worm, pod borer, jassids.

Major Kharif cereal crops of India: 

Paddy, maize.

Rice, wheat, maize.

Correct answer is c) Wheat 

Correct option: c) Salad

c. Medium size

Salamander is an example of Medium size equipment.

Major Rabi cereal crops of India:

Wheat, barley

Correct option: b) Dry heat

Correct option: a) Soggy

Coarse cereals of India are:

Sorghum, Bajra (Pearl millet), maize, Ragi (finger millet)

Guru Angad Dev-the second Sikh guru

Guru Arjun Dev-fifth Guru (1563-1606)

We get the information of the things like big pieces of stone, the tools left by the primitive man and the tools which were not well prepared, from the ‘workshops’ of primitive man.

Classification is done in age group like 0-14 years, 15-59 years and 60 and above years. Labour force participation rate is the ratio of the population in the age group 15- 59, who are either employed or actively looking for jobs. This age group has a capability to con-tribute to the progress of the nation. The age group 0-14 years and 60 years and above are included in the dependent group. 

a. Labor force participation rate proportion in total population is known as dependency rate. The age group 0-14 years and 60 years and above are included in this. 

b. Education, healthcare, training, social capital

Labor force participation rate is the ratio of the population in the age group 15-59, who are either employed or actively looking for jobs.

• It leads to the progress of the nation.
• Per capita income will increase.
• Standard of living of the people will increase.
• Increase in production of goods and services.
• Natural resources can be utilized properly.

Disadvantages due to increase in dependency rate

• Economic progress of the country will decrease.
• It decreases percapita income.
• Standard of living of the people will decrease.
• Production of goods and services also will decrease.

• Labour force participation rate – Ratio of the population in the age group of 15 – 59, who are either employed or actively looking for jobs
• Dependency ratio – The number of people in the age group 0-14 and 60 above and their proportion to the population.

The birth rate, The death rate and Migration.

Migration is the settlement of people of a region to another region.

• Human resource availability is more in areas of high density of population.
• Human resource availability is less in areas of less population density.

• July -11 
• Seminar on population growth – Awareness classes (any one such programme)

• Increase in birth rate – Results in the in-crease in population decrease in death rate
• Decrease in birth rate – Results in the decrease in population increase in death rate
• Birth rate and death rate equal – No change in population
• Migration – Population of a region increases Population decreases at another place

Birth rate is the number of live births per 1000. Death rate is the number of deaths per 1000.

• Education
• Improving the skills of the individuals 
• Imparting the technological knowhow
• Improve labor skills 
• Health care (any four)