Let `S=4/(19)+(44)/(19^2)+(444)/(19^3)+ u ptooo` . Then `s` is equal to a. `40//9` b. `38//81` c. `36//171` d. none of these

One ticket is selected at random from 100 tickets numbered 00,01,02,...,98,99. If X, a n dY denotes the sum and product of the digits on the tickets, then 57 P(X=9//Y=0) is equal to 2//19 b. 19//100 c. 1//50 d. none of these

The projections of a line segment on X, Y and Z axes are 12,4 and 3 respectively. The length and direction cosines of the line segment are a. 13; (12)/(13),4/(13),3/(13) b. 19 ;(12)/(19),4/(19),9/(19) c. 11;(12)/(11),(14)/(11),3/(12) d. none of these

The coefficient of x^(19) in the polynomial (x-1)(x-2)(x-2^2)(x-2^(19)) is 2^(20)-2^(19) b. 1-2^(20) c. 2^(20) d. none of these

Let y=x^3-8x+7a n dx=f(t)dot If (dy)/(dt)=2 and x=3 at t=0, then (dx)/(dt) at t=0 is given by 1 (b) (19)/2 (c) 2/(19) (d) none of these

("lim")_(x->oo)sum_(x=1)^(20)cos^(2n)(x-10) is equal to (a) 0 (b) 1 (c) 19 (d) 20

( 1+3+5+7+9+11 )^ (3/2) = (a)36 (b) 216 (c)256 (d) none of these

if (6x^2-5x-3)/(x^2-2x+6)<=4 , then the least and the highest values of 4x^2 are : (a) 0 and 81 (b) 9 and 81 (c) 36 and 81 (d) None of these

The maximum sum of the series 20+19 1/3+18 2/3+...... is (A) 310 (B) 300 (C) 0320 (D) none of these

The value of cot sum_(n=1)^(19)(cot^(-1)(1+sum_(p=1)^(n)2p)) is equal to (a) (21)/(19) (b) (19)/(21) (c) -(19)/(21) (d) -(21)/(19)

There are only two women among 20 persons taking part in a pleasure trip. The 20 persons are divided into two groups, each group consisting of 10 person. Then the probability that the two women will be in the same group is a. 9//19 b. 9//38 c. 9//35 d. none