It is a theorem that the sum of the exterior angles of any (convex) polygon is a constant, namely two straight angles. Hence, option (3) is correct.

Of all the triangles inscribed in a semi-circle, with the diameter as base, the one with the greatest area is the one with the largest altitude (the radius), i.e. the isosceles triangle. Thus, the area = 1/2 * 2r * r = r². Hence, option (1) is correct.

It is the correct option. (57 x 27) + (85 x 9) + 23 - 35 = 2292 So, option (2) is correct.

29 x 7 = 203 35 x 13 = 455 25 x 16 = 400 203 + 455 + 400 = 1058 So, option (3) is correct.

p² + 1 will always give a positive number.

Work done by X in 5 days = 5*1/10 = 1/2 Balance work to be done = 1 - 1/2 = 1/2 (X + Y) 's one day's work = 1/10 + 1/12 = 11/60 Number of days Y worked = 1/2 * 60/11 = 30/11 So, option (2) is correct.

It is the correct option. First term = 2 Second term = 1/4*(23) = 2 Third term = 1/4*(23) = 2 Fourth term = 1/4*(23) = 2 So, each term of the given sequence is 2 only. So, option (2) is correct.

Let the expenditure and savings be 3x and 2x respectively. Total income = 3x + 2x = 5x Increased income = 5.7x Increased expenditure = 3.3xI Increased savings = 5.7x - 3.3x = 2.4x, i.e. 20% increase So, option (1) is correct.

Unit's digit in 57¹ = 7 Unit's digit in 57² = 9 Unit's digit in 57³ = 3 Unit's digit in 57⁴ = 1 Unit's digit in 57⁵ = 7 => Digit is repeated in (4n+1) terms, where n = 1, 2. 3, 4......... => In 57²⁵ i.e. 57^(4*6+1), the unit's digit is 7 Thus, required digit = 7 + 1 = 8 So, option (2) is correct.

a/2b = 3/2 => a/b = 3 (2a - b)/(a + 2b) ={ 2(a/b) - 1}/{(a/b) + 2} = {(2*3) - 1}/(3 + 2) = 5/5 = 1 So, option (3) is correct.

Is the correct option. 23 = 2 + 21...............(21 is not prime) = 3 + 20..............(20 is not prime) = 5 + 18..............(18 is not prime) = 7 + 16..............(16 is not prime) = 11 + 12............(12 is not prime) = 13 + 10............(10 is not prime) = 17 + 6..............(6 is not prime) = 19 + 4..............(4 is not prime). So, option (3) is correct.

If the dimensions are designated by l, w and h, then the bottom, side and front areas are lw, wh and hl. The product of these areas = l²* w²* h² = (lwh)² = the square of the volume. So, option (4) is correct.

A = 1/2 * b * h = 1/2* h* (b₁ + b₂) Therefore, b₁ + b₂ = b = 18 cm So, median = 1/2 * (b₁ + b₂) = 9 cm Therefore, option (2) is correct.

It is the correct option. (78 x 88) + (10 x 95) = 7814 So, option (3) is correct.

Let 's' be the side of the square and 'h' be the altitude of the triangle. Then, area of triangle = area of square 1/2* 2s* h = s² h = s Therefore, h/s = 1 So, option (3) is correct.