Solution : 1st expression : x2 - 9 = (x+3)(x-3) 2nd expression : x3 - 27 = (x -3)(x2 + 3a + 9) 3rd expression : x2 + x -12 = x2 + 4x - 3x - 12 = x(x+4)-3(x+4) = (x+4)(x-3) HCF = .....

Solution : 1st expression : a2  - 4  = (a +2)(a-2) 2nd expression : a3  + 8 = (a + 2) (a2 -2a + 4) 3rd expression : a2 + 5a + 6 = a2 + 3a + 2a + 6 = a(a+3)+2(a+3) = (a+3)(a+2) HCF = .....

Solution: First expression = 16x4 - 4x2 - 4x - 1                           = 16x4 - (4x2 + 4x + 1)               .....

Solution : 1st expression : a3 - 1 = (a-1)(a2 + a + 1) 2nd expression: a4 + a2 + 1 = (a2)2 + (1)2 + a2 = (a2 + 1 )2 - 2a2 + a2 = (a2 + 1 )2 - a2 = (a2 + 1 + a ) (a2 + 1 - a ) = (a2 + a + 1 ) (a2 - a + 1 ) HCF = (a2 + 1 + a .....

Solution: First expression = 16x4 - 4x2 - 4x - 1                           = 16x4 - (4x2 + 4x + 1)               .....

A cataract is a  problem of eye due to clouding of the lens of the eye which leads to a decrease in vision. Cataracts often develop slowly and can affect one or both eyes. Symptoms may include faded .....

1st expression = p4 - 16 = (p2)2 - 42 = (p2 -  4) (p2 + 4)                                            .....

Solution : 1st expression : x3 - 8y3 = (x)3 - (2y)3 = (x-2y) (x2 +2xy + 4y2) 2nd expression : = x2 +2xy + 4y2 HCF = (x2 +2xy + .....

Solution : 1st expression : a2-b2-2a+1 = a2 - 2a + 1 - b2 = (a - 1)2 - b2 = (a-1+b)(a-1-b) = (a+b-1)(a-b-1) 2nd expression : a2 - ab - a =a (a - b -1) HCF = ( a - b - 1 .....

Solution : 1st expression : 4x3 + 8x2 = 4x2  (x +2) 2nd expression : 5x3 - 20x = 5x(x2 - 4)= 5x(x+2)(x-2) HCF = .....

Solution : 1st expression : x2 - y2 = (x - y ) ( x + y ) 2nd expression : x2 + 2xy + y2  = (x + y )2 = (x + y ) ( x + y ) HCF  = (x + .....

Solution : 1st expression : x2 - 9 = x2 - 32 = (x-3) (x+3) 2nd expression : 3x + 9 = 3 (x +3 ) HCF = (x + .....

Solution : 1st expression : a3 - 4a = a ( a2 - 4) = a (a+2)(a-2) 2nd expression : a4 - 8a = a (a3 - 23) = a (a-2)(a2 + 2a + 4) HCF = .....

Solution : 1st expression : a2-b2 = (a-b)(a+b) 2nd expression : a3 + b3 = (a+b) (a2 -ab + b2) HCF = .....

Solution : 1st expression : 6a2b2(a-b)(2a+3b) = 2.3.a.a.b.b.(a-b)(2a+3b) 2nd expression : 9a3b3 (2a+3b)(a+b) = 3.3.a.a.a.b.b.b.(2a+3b)(a+b) HCF = 3.a.a.b.b(2a+3b) = .....

Solution : 1st expression : 4xy2(x-1)(x+2) = 2.2.x.y.y.(x-1)(x+2) 2nd expression: 6x2y(x-1)(x-4) = 2.3.x.x.y.(x-1)(x-4) HCF = 2.x.y.(x-1) = .....

1st expression : 2x2(x+2)(x-2) = 2.x.x.(x+2)(x-2) 2nd expression: 4x(x+2)(x+3) =2.2.x.(x+2)(x+3) So, HCF = .....

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Solution : Internal diameter d = 2 m radius r = 1 m then area a = πr2 = 22/7 * 1 = 22/7 m2 height h = 3.5 m volume v = a * h = 22/7 * 3.5 = 10.05 m3  = 10.05 * 1000 = 10057.14 litres So, 10057.14 litres of water will make it .....

Solution : Area of circular base a = 6.16 m2 height h = 1.5 m volume v = a * h = 6.16 * 1.5 = 9.24 m3 = 9.24 * 1000 = 9240 litres So, the capacity of the tank in litre is 9240 .....

Solution : length l = 2m breadth b = 2 m height h = 1.5 m volume v = l * b * h = 2 * 2 * 1.5 = 6 m3  = 6 * 1000 l = 6000 litres so, 6000 litres of water can be hold in square base water .....

Here,  3x+1. 22x+1 = 6 or, 3x+1. 22x+1 = 31 ⨯ 21 Now, compare the corresponding exponents, x + 1 = 1 ⟹ x = 0 and, 2x + 1 = 1 ⟹ x = .....

Solution : Area a = 8 m * 5 m = 40 m2 Rate R = Rs. 75 / m2 Total Cost TC = R * a = 75 * 40 = Rs.3,000 So, the cost of carpeting its floor is .....

Solution : Area of floor a = 35 m2 Rate R = 90 per m2 Cost of carpeting C = ? We know, C = R * a = 90 * 35 = Rs. 3150 So, the cost of carpeting the floor is .....

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Solution : Volume of brick = v Number of bricks = N Volume of wall V = .....

Solution : Number of bricks N = Volume of a wall V / Volume of a brick .....

Area of floor A = total cost T / rate .....

Solution : Rate of cost R = Total cost T / Area .....

Solution : Total cost T = area A * rate .....

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Solution, circuference of circle = 44cm        or, 2π r = 44cm        or, r = 7cm height (h) = 30 cm Now, Volume of cone = 1/3 π r2 h                 .....

Solution, radius (r)= 2.1 cm height(h) = ? Now, Volume of cone = 23.1 cm3 or, 1/3 π r2 h = 23.1 or, h = 1.67 cm Therefore, vertical height of cone is 1.67 .....

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Solution, Given, diameter(d) = 14cm radius(r) = 7cm C.S.A of cone = 220 cm2 or, πrl = 220 or, l = 10cm Therefore, slant height is 10 .....

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solution, In a eauilateral triangle based pyramid, length of base(a) = 20cm height of pyramid(h)= 24cm Now, Volume of pyramid= 1/3 *area of base * height                           .....

solution, In a rectangular based pyramid, length(l) = 10cm breadth(b)= 6cm height of pyramid(h)= 15cm Now, area of base(A)= l*b                         =10 * 6         .....

solution, In a square based pyramid, length of base(a) = 12cm height of pyramid(h) = 8 cm Now, Volume of pyramid = 1/3 a2 * h                                 = 1/3 .....