If `27ak^2 < 4(h- 2a)^3` satisfied then three real and distinct normal are drawn from point (h, k) on parabola `y^2 = 4ax`.

If 11a^2 + 2b^2 + 2ak + 1 = 0 , where k is a fixed real number, then the value of k^4 for which ax+by+1=0 is tangent to a fixed circle is …

If a_k=1/(k(k+1)) for k=1 ,2……..,n then prove that (sum_(k=1)^n a_k)^2 =n^2/(n+1)^2

If (27+67+27?)-(FAT+?-)-0 then values of ?, ? are 2 27 2 27 1) 3, 27 2)353)?,34)3,

The following are the nth terms of certain sequences. Determine whether they are G.P. or not. If it is so find the first term and common ratio. ak^(2n-1) .

If a_k is the coefficient of x^k in the expansion of (1 +x+x^2)^n for k = 0,1,2,……….,2n then a_1 +2a_2 + 3a_3 + ………+2n.a_(2n) =

If a_k is the coefficient of x^k in the expansion of (1+x+x^2)^n for k = 0, 1, 2, ......., 2n then a_1+2a_2+3a_3+...+2na_(2n)=

If a_k is the coefficient of x^k in the expansion of (1 +x+x^2)^n for k = 0,1,2,……….,2n then a_1 +2a_2 + 3a_3 + ………+2n.a_(2n) =

If m(ax^2+2bx+c)+px^2+2qx+r can be expressed in the form n(x+k)^2 then show that (ak-b)(qk-r) =(pk-q)(bk-c).

The mean proportional of ak and ak^3 is………..

If the roots of the equation ax^(2)+bx+c=0 differ by K then b^(2)-4ac= O a^(2)k^(2) O ak O a^(2)k O ak^(2)