A man running around a race course notes that the sum of the distances of two flagposts from him a always 10m and the distance between the flag posts is 8m. Then the area of the path he encloses in square meters is 15`pi` (b) `20pi` (c) `27pi` (d) `30pi`

A man running a racecourse notes that the sum of the distances from the two flag posts from him is always 10 m and the distance between the flag posts is 8 m. Find the equation of the posts traced by the man.

Two circles touch each other externally. The sum of their areas is 58pi cm^(2) and the distance between their centres is 10 cm. Find the radii of the two circles.

Two circles touch internally. The sum of their areas is 116pi\ c m^2 and distance between their centres is 6 cm. Find the radii of the circles.

A circle is inscribed in a square of side 14 m. The ratio of the area of the circle and that of the square is (a) pi:3\ (b) pi:4 (c) pi:2 (d) pi:1

Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m, the distance between their tops is (a) 13 m (b) 14 m (c) 15 m (d) 12.8 m

A right circular cylindrical tunnel of diameter 2m and length 40m is to be constructed from a sheet of iron. The area of the iron sheet required in m^2, is (a) 40pi (b) 80pi (c) 160pi (d) 200pi

Concentric circles of radii 1,2,3,. . . . ,100 c m are drawn. The interior of the smallest circle is colored red and the angular regions are colored alternately green and red, so that no two adjacent regions are of the same color. Then, the total area of the green regions in sq. cm is equal to 1000pi b. 5050pi c. 4950pi d. 5151pi

Square of the distance between the integral points of intersection of L_1 : 2x+y=50 a n dL_2 :y=mx+1 for the greatest and the least integral values of m is a. 5 b. 20 c. 25 d. 30""

A stationary wave is given by y = 5 sin (pi x)/( 3) cos 40 pi t where x and y are in cm and t is in second. a. What are the amplitude and velocity of the component wave whose superposition can give rise to this vibration ? b. What is the distance between the nodes ? c. What is the velocity of a particle of the string at the position x = 1.5 cm when t = 9//8 s ?

0.27 g of a long chain fatty acid was dissolved in 100 cm^ 3 of hexane. 10 mL of this solution was added dropwise to the surface of water in a round watch glass. Hexane evaporates and a monolayer is formed. The distance from edge to centre of the watch glass is 10 cm. The height of the monolayer is 10 ^( -x ) m. what is numerical value of x ? [Density of fatty acid = 0.9 g cm ^ ( -3) , pi = 3 ]