In the given figure, what is the radius of the inscribed circle? `3/2` (b) `5/2` (c) `7/5` (d) none of these

The number of integral values of lambda for which the equation x^2+y^2+lambdax+(1-lambda)y+5=0 is the equation fo a circle whose radius cannot exceed 5, is 14 (b) 18 (c) 16 (d) none of these

If a , b in [0,2pi] and the equation x^2+4+3sin(a x+b)-2x=0 has at least one solution, then the value of (a+b) can be (a) (7pi)/2 (b) (5pi)/2 (c) (9pi)/2 (d) none of these

In a hurdle race, a runner has probability p of jumping over a specific hurdle. Given that in 5 trials, the runner succeeded 3 times, the conditional probability that the runner had succeeded in the first trial is (a) 3//5 (b) 2//5 (c) 1//5 (d) None of these

Two congruent circles with centered at (2, 3) and (5, 6) which intersect at right angles, have radius equal to (a) 2 sqrt(3) (b) 3 (c) 4 (d) none of these

A given right cone has volume p , and the largest right circular cylinder that can be inscribed in the cone has volume qdot Then p : q is (a) 9:4 (b) 8:3 (c) 7:2 (d) none of these

The locus of the center of the circle such that the point (2,3) is the midpoint of the chord 5x+2y=16 is (a) 2x-5y+11=0 (b) 2x+5y-11=0 (c) 2x+5y+11=0 (d) none of these

The number of real solutions of the (log)_(0. 5)|x|=2|x| is (a) 1 (b) 2 (c) 0 (d) none of these

C_1 is a circle of radius 1 touching the x- and the y-axis. C_2 is another circle of radius greater than 1 and touching the axes as well as the circle C_1 . Then the radius of C_2 is (a) 3-2sqrt(2) (b) 3+2sqrt(2) 3+2sqrt(3) (d) none of these

The number of real solutions of the (log)_(0. 5)(x)=|x| is (a) 1 (b) 2 (c) 0 (d) none of these

A four figure number is formed of the figures 1, 2, 3, 4, 5 with no repetitions. The probability that the number is divisible by 5 is 3//4 b. 1//4 c. 1//8 d. none of these