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📐 Chapter 2: Introduction to Linear Polynomials • Exercise Set 2.3

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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 2.3

1. A student has ₹500 in her savings bank account. She gets ₹150 every month as pocket money. How much money will she have at the end of every month from the second month onwards? Find a linear expression to represent the amount she will have in the nth month.

  • At the end of the 1st month: ₹500 + (1 × ₹150) = ₹650
  • At the end of the 2nd month: ₹500 + (2 × ₹150) = ₹800
  • At the end of the 3rd month: ₹500 + (3 × ₹150) = ₹950, and so on.
  • The linear expression for the amount in the nth month is: 500 + 150n.
Q2

Exercise Set 2.3

2. A rally starts with 120 members. Each hour, 9 members drop out of the group. How many members will remain after 1, 2, 3, ... hours? Find a linear expression to represent the number of members at the end of the nth hour.

  • After 1 hour: 120 - 9 = 111 members
  • After 2 hours: 120 - 2(9) = 120 - 18 = 102 members
  • After 3 hours: 120 - 3(9) = 120 - 27 = 93 members
  • The linear expression for the members remaining at the end of the nth hour is: 120 - 9n.
Q3

Exercise Set 2.3

3. Suppose the length of a rectangle is 13 cm. Find the area if the breadth is (i) 12 cm, (ii) 10 cm, (iii) 8 cm. Find the linear pattern representing the area of the rectangle.

Area of a rectangle = Length × Breadth. Given Length = 13 cm.

  • (i) If breadth is 12 cm: Area = 13 × 12 = 156 cm²
  • (ii) If breadth is 10 cm: Area = 13 × 10 = 130 cm²
  • (iii) If breadth is 8 cm: Area = 13 × 8 = 104 cm²
  • The linear pattern representing the area as a function of the breadth b is: 13b.
Q4

Exercise Set 2.3

4. Suppose the length of a rectangular box is 7 cm and breadth is 11 cm. Find the volume if the height is (i) 5 cm, (ii) 9 cm, (iii) 13 cm. Find the linear pattern representing the volume of the rectangular box.

Volume of a rectangular box = Length × Breadth × Height. Base Area = 7 × 11 = 77 cm².

  • (i) If height is 5 cm: Volume = 77 × 5 = 385 cm³
  • (ii) If height is 9 cm: Volume = 77 × 9 = 693 cm³
  • (iii) If height is 13 cm: Volume = 77 × 13 = 1001 cm³
  • The linear pattern representing the volume as a function of height h is: 77h.
Q5

Exercise Set 2.3

5. Sarita is reading a book of 500 pages. She reads 20 pages every day. How many pages will be left after 15 days? Express this as a linear pattern.

  • Pages read in 15 days: 15 × 20 = 300 pages
  • Pages left after 15 days: 500 - 300 = 200 pages
  • The linear pattern representing the number of pages left after d days is: 500 - 20d.