The sum of `0. 2+0.004+0. 00006+0. 0000008+...` to `oo` is `(200)/(891)` b. `(2000)/(9801)` c. `(1000)/(9801)` d. none of these

The sum of the series 0.4 + 0.004 + 0.00004 + infty is

If r/(r_1)=(r_2)/(r_3), then A=90^0 (b) B=90^0 C=90^0 (d) none of these

The function x^x decreases in the interval (0,e) (b) (0,1) (0,1/e) (d) none of these

In A B C ,a=5,b=12 ,c=90^0a n dD is a point on A B so that /_B C D=45^0dot Then which of the following is not true? C D=(60sqrt(2))/(17) (b) B D=(65)/(17) A D=(60sqrt(2))/(17) (d) none of these

lim_(x -> oo)(x(log(x)^3)/(1+x+x^2) equals 0 (b) -1 (c) 1 (d) none of these

If the equation a x^2+b x+c=0,a ,b ,c , in R have none-real roots, then a. c(a-b+c)>0 b. c(a+b+c)>0 c. c(4a-2b+c)>0 d. none of these

int_0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) pi (D) none of these"

In A B C , if the orthocentre is (0,0) and the circumcenter is (1,2), then centroid of A B C) is (a) (1/2,2/3) (b) (1/3,2/3) (c) (2/3,1) (d) none of these

("lim")_(xvec0)1/xcos^(-1)((1-x^2)/(1+x^2)) is equal to (a)1 (b) 0 (c) 2 (d) none of these