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📐 Chapter 2: Introduction to Linear Polynomials • Exercise Set 2.2

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Exercise Set 2.1 5Exercise Set 2.2 7Exercise Set 2.3 5Exercise Set 2.4 4Exercise Set 2.5 3Exercise Set 2.6 1End-of-Chapter Exercises 14All Exercises 39
Q1

Exercise Set 2.2

1. Find the value of the linear polynomial 5x - 3 if:

(i) x = 0      (ii) x = -1      (iii) x = 2

  • (i) If x = 0: 5(0) - 3 = 0 - 3 = -3
  • (ii) If x = -1: 5(-1) - 3 = -5 - 3 = -8
  • (iii) If x = 2: 5(2) - 3 = 10 - 3 = 7
Q2

Exercise Set 2.2

2. Find the value of the quadratic polynomial 7s² - 4s + 6 if:

(i) s = 0      (ii) s = -3      (iii) s = 4

  • (i) If s = 0: 7(0)² - 4(0) + 6 = 0 - 0 + 6 = 6
  • (ii) If s = -3: 7(-3)² - 4(-3) + 6 = 7(9) + 12 + 6 = 63 + 12 + 6 = 81
  • (iii) If s = 4: 7(4)² - 4(4) + 6 = 7(16) - 16 + 6 = 112 - 16 + 6 = 102
Q3

Exercise Set 2.2

3. The present age of Salil's mother is three times Salil's present age. After 5 years, their ages will add up to 70 years. Find their present ages.

  1. Let Salil's present age be x years.
  2. His mother's present age is 3x years.
  3. After 5 years, Salil's age will be x + 5, and his mother's age will be 3x + 5.
  4. Their sum after 5 years is 70:
    (x + 5) + (3x + 5) = 70
    4x + 10 = 70
    4x = 60
    x = 15
  5. Therefore, Salil's present age is 15 years, and his mother's present age is 45 years (3 × 15).
Q4

Exercise Set 2.2

4. The difference between two positive integers is 63. The ratio of the two integers is 2:5. Find the two integers.

  1. Let the two positive integers be 2x and 5x based on their ratio.
  2. The difference between them is 63:
    5x - 2x = 63
    3x = 63
    x = 21
  3. The two integers are:
    Smaller integer: 2 × 21 = 42
    Larger integer: 5 × 21 = 105
Q5

Exercise Set 2.2

5. Ruby has 3 times as many two-rupee coins as she has five-rupee coins. If she has a total ₹88, how many coins does she have of each type?

  1. Let the number of five-rupee coins be x.
  2. Then the number of two-rupee coins is 3x.
  3. The total value of the coins is ₹88:
    (Value of five-rupee coins) + (Value of two-rupee coins) = 88
    5(x) + 2(3x) = 88
    5x + 6x = 88
    11x = 88
    x = 8
  4. So, she has 8 five-rupee coins and 24 two-rupee coins (3 × 8).
Q6

Exercise Set 2.2

6. A farmer cuts a 300 feet fence into two pieces of different sizes. The longer piece is four times as long as the shorter piece. How long are the two pieces?

  1. Let the length of the shorter piece be x feet.
  2. The length of the longer piece is 4x feet.
  3. The total length is 300 feet:
    x + 4x = 300
    5x = 300
    x = 60
  4. The lengths are:
    Shorter piece: 60 feet
    Longer piece: 4 × 60 = 240 feet
Q7

Exercise Set 2.2

7. If the length of a rectangle is three more than twice its width and its perimeter is 24 cm, what are the dimensions of the rectangle?

  1. Let the width of the rectangle be w cm.
  2. The length is 2w + 3 cm.
  3. The perimeter of a rectangle is 2 × (Length + Width). Given the perimeter is 24 cm:
    2 × ((2w + 3) + w) = 24
    2 × (3w + 3) = 24
    6w + 6 = 24
    6w = 18
    w = 3
  4. The dimensions are:
    Width: 3 cm
    Length: 2(3) + 3 = 9 cm