Find the value of `x ,` for which `1//(sqrt(5+4x))` can be expanded as infinite series.

Find the value of a and b for which the given system of linear equation has infinite number of solutions 3x-(a +1 ) y = 2 b -1 , 5x + ( 1-2a ) y = 3b

Find the values of x for which expression sqrt(1-sqrt(1-sqrt(1-x^(2)))) is meaningful.

Find the value of x for which the points (x, -1) (2,1) and (4, 5) are collinear.

Find the value of x^(2)+1/x^(2)" when "x=4 +sqrt15

Find the range of f(x) = sqrt(x-1)+sqrt(5-x)

Find the value of x for which following expressions are defined: 1/(sqrt(x-|x|)) (ii) 1/(sqrt(x+|x|))

Find the value of x for which f(x) = 2 sin^(-1) sqrt(1 - x) + sin^(-1) (2 sqrt(x - x^(2))) is constant

Find the domain of f(x)=1/(sqrt(|[|x|-1]|-5))