Sujeet Kumar

Question 1.Factorize:i. x² + 9x + 18ii. x² – 10x + 9iii. y² + 24y + 144iv. 5y² + 5y – 10v. p² – 2p – 35vi. p² – 7p – 44vii. m² – 23m + 120viii. m² – 25m + 100ix. 3x² + 14x + 15x. 2x² + x – 45xi. 20x² – 26x … Read more

Question 1.Expand:i. (2p + q + 5)²ii. (m + 2n + 3r)²iii. (3x + 4y – 5p)²iv. (7m – 3n – 4k)²Solution:i. (2p + q + 5)² = (2p)² + (q)² + (5)² + 2(2p) (q) + 2(q) (5) + 2(2p) (5)… [(a + b + c)² = a² + b² + c² + 2ab … Read more

Question 1.Expand:i. (2m – 5)³ii. (4 – p)³iii. (7x – 9y)³iv. (58)³v. (198)³ Solution:i. Here, a = 2m and b = 5(2m – 5)³= (2m)³ – 3(2m)² (5) + 3(2m) (5)² – (5)³… [(a – b)³ = a³ – 3a²b + 3ab² – b³]= 8m³ – 3(4m²)(5) + 3(2m)(25) – 125= 8m³ – 60m² + … Read more

Question 1.Expand:i. (k + 4)³ii. (7x + 8y)³iii. (7x + m)³iv. (52)³v. (101)³ Solution:i. Here, a = k and b = 4(k + 4)³ = (k)³ + 3(k)² (4) + 3(k)(4)² + (4)³…[∵ (a + b)³ = a³ + 3a²b + 3ab² + b³]= k³ + 12k² + 3(k)(16) + 64= k³ + 12k² + … Read more

Question 1.Expand :i. (a + 2)(a – 1)ii. (m – 4)(m + 6)iii. (p + 8) (p – 3)iv. (13 + x)(13 – x)v. (3x + 4y) (3x + 5y)vi. (9x – 5t) (9x + 3t) Solution:i. (a + 2)(a – 1)= a² + (2 – 1) a + 2 × (-1)..[∵ (x + A) … Read more

Chapter 4 Altitudes and Medians of a Triangle Question 1.In ∆LMN, ___ is an altitude and __ is a median, (write the names of appropriate segments.) Solution:In ∆LMN, seg LX is an altitude and seg LY is a median. Question 2.Draw an acute angled ∆PQR. Draw all of its altitudes. Name the point of concurrence … Read more

Question 1.Find the cube root of the following numbers.i. 8000ii. 729iii. 343iv. -512v. -2744vi. 32768Solution:i. 8000= 2 × 2 × 2 × 10 × 10 × 10= (2 × 10) × (2 × 10) × (2 × 10)= (2 × 10)³= 20³ ii. 729= (3 × 3) × (3 × 3) × (3 × 3)= … Read more

Chapter 3 Indices and Cube Root Set 3.2 Question 1.Complete the following table. Solution:  Question 2.Write the following numbers in the form of rational indices.i. Square root of 5th power of 121.ii. Cube of 4th root of 324.iii. 5th root of square of 264.iv. Cube of cube root of 3.Solution:

Question 1.Express the following numbers in index form.i. Fifth root of 13ii. Sixth root of 9iii. Square root of 256iv. Cube root of 17v. Eighth root of 100vi. Seventh root of 30Solution: Solution:i. Fourth root of 81.ii. Square root of 49.iii. Fifth root of 15.iv. Ninth root of 512.v. Nineteenth root of 100.vi. Seventh root … Read more

Question 1.Draw a line l. Take a point A outside the line. Through point A draw a line parallel to line l.Solution:Steps of construction: Line m is the required line parallel to line l and passing through point A. Question 2.Draw a line l. Take a point T outside the line. Through point T draw … Read more