The next term of the G.P. `x ,x^2+2,a n dx^3+10` is `(729)/(16)` b. `6` c. `0` d. `54`

If the 4th term in the expansion of (a x+1//x)^n is 5/2, then (a) a=1/2 b. n=8 c. a=2/3 d. n=6

The maximum slope of the curve y=-x^3+3x^2+9x-27 is 0 (b) 12 (c) 16 (d) 32

The number of real solutions of |x|+2sqrt(5-4x-x^2)=16 is/are a. 6 b. 1 c. 0 d. 4

Consider a G.P. with first term (1+x)^(n) , |x| lt 1 , common ratio (1+x)/(2) and number of terms (n+1) . Let 'S' be sum of all the terms of the G.P. , then sum_(r=0)^(n)"^(n+r)C_(r )((1)/(2))^(r ) equals

If the roots x^5-40 x^4+P x^3+Q x^2+R x+S=0 are n G.P. and the sum of their reciprocals is 10, then |S| is 4 b. 6 c. 8 d. none of these

The number of solution of x^(log)x(x+3)^2=16 is a)0 (b) 1 (c) 2 (d) oo

If a , b ,c real in G.P., then the roots of the equation a x^2+b x+c=0 are in the ratio a. 1/2(-1+sqrt(3)) b. 1/2(1-isqrt(3)) cdot1/2(-1-isqrt(3)) d. 1/2(1+isqrt(3))

If the first and the n^("th") term of a G.P. are a and b, respectively, and if P is the product of n terms, prove that P^2 = (ab)^n .

Consider a G.P. with first term (1+x)^(n) , |x| lt 1 , common ratio (1+x)/(2) and number of terms (n+1) . Let 'S' be sum of all the terms of the G.P. , then The coefficient of x^(n) is 'S' is