Question

I need answers of all questions ​

Answer 1

Question 1

The HCF of 66 and 121 is

Solution :-

11

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Question 2

The sum of two natural numbers is 30. If their difference is 20, then the product of these two numbers is -

Solution :-

Let the numbers be x and y.

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According to the question,

x + y = 30 .......(1)

x - y = 20 ........(2)

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From (2)

x = 20 + y .......(3)

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Substituting x in (1)

20 + y + y = 30

20 + 2y = 30

2y = 10

y = 5

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Substituting y in (3)

x = 20 + 5

x = 25

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Product of x and y,

= 25 x 5

= 125

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Question 3

If x = 1 is a zero of the polynomial p(x) = x^4 - 5x^3 - 20x^2 + 130x - a then the value of a is -

Solution :-

Given,

• x = 1

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Substituting x in p(x),

${x}^{4} - {5x}^{3} - {20x}^{2} + 130x - a = 0\\ = {1}^{4} - {5(1)}^{3} - {20(1)}^{2} + 130(1) - a = 0 \\ = 1 - 5 - 20 + 130 = a \\ = - 4 - 20 + 130 = a \\ = - 24 + 130 = a \\ a = 106$

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Question 4

If α and α + 1 are the roots of the equation x^2 - 7x + a = 0 then a equals -

Solution :-

Given roots,

• α
• α + 1

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From equation,

Sum = α + α + 1 = 7/1

= 2α = 6

α = 3

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Also,

Product = α(α + 1)

= 3(3 + 1)

= 3 x 4

= 12

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Product of zeroes = c/a

12 = a/1

a = 12

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Question 5

The sum of 3 consecutive terms of an AP is 72. Then middle term is -

Solution :-

Let the 3 consecutive terms be,

• (a - d)
• a
• (a + )

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According to question,

a - d + a + a + d = 72

3a = 72

a = 24

= Middle term (a) is 24.

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