Sujeet Kumar

Question 1.Draw a rectangle ABCD such that l(AB) = 6.0 cm and l(BC) = 4.5 cm.Solution: Question 2.Draw a square WXYZ with side 5.2 cm.Solution: Question 3.Draw a rhombus KLMN such that its side is 4 cm and m∠K = 75°.Solution: Question 4.If diagonal of a rectangle is 26 cm and one side is 24 … Read more

Construct the following quadrilaterals of given measures. Question 1.In ∆MORE, l(MO) = 5.8 cm, l(OR) = 4.4 cm, m∠M = 58°, m∠O = 105°, m∠R = 90°.Solution: Question 2.Construct ∆DEFG such that l(DE) = 4.5 cm, l(EF) = 6.5 cm, l(DG) = 5.5 cm, l(DF) = 7.2 cm, l(EG) = 7.8 cm.Solution: Question 3.In ∆ABCD, … Read more

Question 1.Which of the following statements are of inverse variation?i. Number of workers on a job and time taken by them to complete the job.ii. Number of pipes of same size to fill a tank and the time taken by them to fill the tank.iii. Petrol filled in the tank of a vehicle and its … Read more

Question 1.The information about number of workers and number of days to complete a work is given in the following table. Complete the table. Number of workers 30 20 __ 10 __ Days 6 9 12 36 Solution:Let, n represent the number of workers and d represent the number of days required to complete a … Read more

Question 1.Write the following statements using the symbol of variation. Solution: Question 2.Complete the following table considering that the cost of apples and their number are in direct variation. Number of apples (x) 1 4 __ 12 __ Cost of apples (y) 8 32 56 __ 160 Solution:The cost of apples (y) and their number … Read more

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Question 1.Factorize Solution:i. y³ – 27= y³ – (3)³Here, a = y and b = 3∴ y³ – 27 = (y – 3)[y² + y(3) + (3)2]…[∵ a³ – b³ = (a – b) (a² + ab + b²)]= (y – 3)(y² + 3y + 9) ii. x³ – 64y³= x³ – (4y)³Here, a = … Read more

Question 1.Factorise:i. x³ + 64y³ii. 125p³ + q³iii. 125k³ + 27m³iv. 2l³ + 432m³v. 24a³ + 81b³ Solution:i. x³ + 64y³= x³ + (4y)³Here, a = x and b = 4y∴ x³ + 64y³ = (x + 4y) [x² – x(4y) + (4y)²]….[∵ a³ + b³ = (a + b)(a² – ab + b²)]= (x … Read more

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