Answer: C Distance in 60 min = 66,000 m Distance in 1 min = 66000/60 = 1100 m. Hence, number of revolution per minute = 1100/(2πr) Where, r = 0.70m => 1100/(2*22/7 *0.70) = 250.
Q. No. 32:
A swimming bath is 24m long and 15m broad. When a number of men dive into the bath, the height of the water rises by 1cm. If the average amount of water displayed by one of the men be 0.1cm, how many men are there in the bath ?
Answer: D Let the number of men = x. Increase in volume = Total displacement => 24*15* 0.01 = 0.1*x => x = 36.
Q. No. 33:
A farmer owns a circular plot with diameter 56 m. He builds a 7 m wide garden (outside) the plot which costs Rs 260 square metre. What is the cost borne by the farmer for building the entire garden ?
Answer: D Diameter of inner circle = 56 m. Diameter of outer circle = 56+7+7 = 70 m Area of the garden = π(352 - 282 ) = 22/7 * 63 * 7 = 1386. Cost = 1386 * 260 = 360360.
Q. No. 34:
In a triangle ABC, the lengths of the sides AC and AB equal 20.5 cm and 36 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 9cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC ? (Area of triangle is equal to the product of all the sides of the triangle divided by four times the radius of the circle circumscribing the triangle).
Answer: D let the length of the rectangular plot be x and breadth be y m. Given that, perimeter = 34. 2(x+y) = 34 => x+y = 17..........(i) Given that area = 60 xy = 60................(ii) (x-y)2 = (x+y)2 - 4xy = (17)2 - 4(60) = 49 => x- y = 7.............(iii) From equation (ii) and (iii), we get y = 5 m and x = 12 i.e shorter side be of 5 m.
Q. No. 36:
A lawn is in the form of an isosceles triangle. The cost of turfing it came to Rs 1200 at Rs 4 per m2 . If the base of the lawn is 40 m long, then the length of each side is
Answer: A Area of triangle = 1200/4 = 300 m2 Also, area of isosceles triangle = b/4 * (4a2 - b2 )1/2 Here, b = 40 m i.e 40/4 * (4a2 -1600)1/2 = 300 => 4a2 -1600 = 900 => a2= 625 => a = 25. Length of each side be 25 m.
