If the terms `sqrt(a-x),sqrtx,sqrt(a+x)` are in A.P and all are integers where a,x`gt`0, then find the least composite value of a.

If the terms of the A.P. sqrt(a-x),sqrt(x),sqrt(a+x) are all in integers, w h e r ea ,x >0, then find the least composite value of adot

If f(x) is continuous function AAx in R and the range of f(x)i s(2,sqrt(26))a n dg(x)=[(f(x))/c] is continuous AAx in R , then find the least positive integral value of c , where [dot] denotes the greatest integer function.

If x=7+4sqrt3 then find the value of x+(1)/(x)

If the largest positive value of the function defined as f(x)=sqrt(8 x-x^2)-sqrt(14 x-x^2-48) , is m sqrtn where m, n in N , the find least value of (m+n)

If y = sqrt(x+sqrt(x+sqrt(x+sqrt(x)))) to infty, find dy/dx :

If f(x)=sqrt(x^2+a x+4) is defined for all x , then find the values of adot

If tan^(2) {pi(x+y)}+cot^(2) {pi (x+y)}=1+sqrt((2x)/(1+x^(2))) where x, y in R , then find the least possible value of y.

If a,x,b are in A.P.,a,y,b are in G.P. and a,z,b are in H.P. such that x=9z and gt0,bgt0 , then

Evaluate: int_(2)^(3)(sqrtx)/(sqrt5-x+sqrtx) dx.