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`

Two medians drawn from the acute angles of a right angled triangle intersect at an angle pi/6. If the length of the hypotenuse of the triangle is 3 units, then the area of the triangle (in sq. units) is (a) sqrt3 (b) 3 (c) sqrt2 (d) 9

The line x=c cuts the triangle with corners (0,0),(1,1) and (9,1) into two region. For the area of the two regions to be the same c must be equal to (A) 5/2 (B) 3 (C) 7/2 (D) 5 or 15

An urn contains 3 red balls and n white balls. Mr. A draws two balls together from the urn. The probability that they have the same color is 1/2 Mr. B. Draws one balls form the urn, notes its color and replaces it. He then draws a second ball from the urn and finds that both balls have the same color is 5/8. The possible value of n is (a) 9 b. 6 c. 5 d. 1

The total number of solution of |cotx|=cotx+1/(sinx),x in [0,3pi] , is equal to 1 (b) 2 (c) 3 (d) 0

The radius of a right circular cylinder increases at the rate of 0.1 cm/min, and the height decreases at the rate of 0.2 cm/min . The rate of change of the volume of the cylinder, in cm^2//min , when the radius is 2c m and the height is 3cm is (a) -2pi (b) -(8pi)/5 -(3pi)/5 (d) (2pi)/5

If vec aa n d vec b are two unit vectors incline at angle pi//3 , then { vec axx( vec b+ vec axx vec b)}dot vec b is equal to (-3)/4 b. 1/4 c. 3/4 d. 1/2

There are two sets of parallel lines, their equations being x cos alpha+y sin alpha=p and x sin alpha- y cos alpha=p , p=1,2,3,….n and alpha in (0,pi//2) . If the number of rectangles formed by these two sets of lines is 225 , then the value of n is equals to (a) 4 (b) 5 (c) 6 (d) 7

If inside a big circle exactly n(nlt=3) small circles, each of radius r , can be drawn in such a way that each small circle touches the big circle and also touches both its adjacent small circles, then the radius of big circle is r(1+cos e cpi/n) (b) ((1+tanpi/n)/(cospi/pi)) r[1+cos e c(2pi)/n] (d) (r[s inpi/(2n)+cos(2pi)/n]^2)/(sinpi/n)

Consider square A B C D of side length 1. Let P be the set of all segments of length 1 with endpoints on the adjacent sides of square A B C D . The midpoints of segments in P enclose a region with area Adot The value of A is (a) pi/4 (b) 1-pi/4 (c) 4-pi/4 (d) none of these

A bag initially contains 1 red and 2 blue balls. An experiment consisting of selecting a ball at random, noting its color and replacing it together with an additional ball of the same color. If three such trials are made, then (A) Probability that a t least one blue ball is drawn is 0.9 (B) Probability that exactly one blue ball is drawn is 0.2 (C) Probability that all the drawn balls are red given that all the drawn balls are of same color is 0.2 (D) Probability that at least one red bal is drawn is 0.6