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Question 1.Factorise the following expressions and write them in the product form.i. 201a³b²ii. 91xyt²iii. 24a²b²iv. tr²s³i. 201a³b²= 3 × 67 × a³ × b²= 3 × 67 × a × a × a × b × b ii. 91xyt²= 7 × 13 × x × y × t²= 7 × 13 × x × y … Read more

Question 1.Use the formula to multiply the following:i. (x + y)(x – y)ii. (3x – 5)(3x + 5)iii. (a + 6)(a – 6) Solution:i. Here, a = x, b = y(x + y)(x – y) = x² – y²…. [(a + b)(a – b) = a² – b²] ii. Here, a = 3x, b = … Read more

Question 1.Expand: Solution:i. (5a + 6b)²Here, A = 5a and B = 6b(5a + 6b)² = (5a)² + 2 × 5a × 6b + (6b)²…. [(A + B)² = A² + 2AB + B²]∴ (5a + 6b)² = 25a² + 60ab + 36b² iii. (2p – 3q)²Here, a = 2p and b = 3q(2p – … Read more

Question 1.Find the Pythagorean triplets from among the following sets of numbers:i. 3,4,5ii. 2,4,5iii. 4,5,6iv. 2,6,7v. 9,40,41vi. 4,7,8Solution:i. 3² = 9,4² = 16, 5² = 25Now, 9 + 16 = 25∴ 3² + 42 = 5²∴ 3, 4 and 5 is a Pythagorean triplet. ii. 2² = 4, 4² = 16, 5² = 25But, 4 … Read more

Question 1.In the figures below, find the value of ‘x’. Solution:i. In ∆LMN, ∠M = 90°.Hence, side LN is the hypotenuse.According to Pythagoras’ theorem,l(LN)² = l(LM)² + l(MN)²∴ x² = 72 + 24²∴ x² = 49 + 576∴ x² = 625∴ x² = 25²∴ x = 25 units ii. In ∆PQR, ∠Q = 90°.Hence, side … Read more

Question 1.Find the total surface area of cubes having the following sides:i. 3 cmii. 5 cmiii. 7.2 miv. 6.8 mv. 5.5 mSolution:i. Total surface area of cube = 6l²= 6 × (3)²= 6 × 9= 54 sq. cm. ii. Total surface area of cube = 6l²= 6 × 5²= 6 × 25= 150 sq. cm. … Read more

Question 1.A page of a calendar is 45 cm long and 26 cm wide. What is its area?Solution:Area of page of a calendar = length × breadth= 45 × 26= 1170 sq. cm.∴ The area of the page of the calendar is 1170 sq. cm. Question 2.What is the area of a triangle with base … Read more

Question 1.If the side of a square is 12 cm, find its area.Solution:Area of a square = (side)² = (12)²= 144 sq. cm.∴ The area of the square is 144 sq. cm. Question 2.If the length of a rectangle is 15 cm and breadth is 5 cm, find its area.Solution:Area of a rectangle = length … Read more

Question 1.If the length and breadth of a rectangle are doubled, how many times the perimeter of the old rectangle will that of the new rectangle be?Solution:Let the length of the old rectangle be l and breadth be b.∴ Perimeter of old rectangle = 2(l + b)Length of new rectangle = 2l and breadth = … Read more

Question 1.Choose the correct option.If arc AXB and arc AYB are corresponding arcs and m(arc AXB) = 120° then m(arc AYB) =(A) 140°(B) 60°(C) 240°(D) 160°Solution:(C) 240° Hint:Measure of major arc = 360° – measure of corresponding minor arc∴ m (arc AYB) = 360 – m (arc AXB)∴ m (arc AYB) = 360 – 120∴ … Read more