The number of solutions for the equation `sum_(i=1)^(100) |x-i| ` =2450 will be

The number of solutions of the equation sin^(2)x=1//4i

The number of solutions of the equation x/100=sinx is

The number of real solution of the equation sin^(-1) (sum_(i=1)^(oo) x^(i +1) -x sum_(i=1)^(oo) ((x)/(2))^(i)) = (pi)/(2) - cos^(-1) (sum_(i=1)^(oo) (-(x)/(2))^(i) - sum_(i=1)^(oo) (-x)^(i)) lying in the interval (-(1)/(2), (1)/(2)) is ______. (Here, the inverse trigonometric function sin^(-1) x and cos^(-1) x assume values in [-(pi)/(2), (pi)/(2)] and [0, pi] respectively)

The number of real solution of the equation sin^(-1) (sum_(i=1)^(oo) x^(i +1) -x sum_(i=1)^(oo) ((x)/(2))^(i)) = (pi)/(2) - cos^(-1) (sum_(i=1)^(oo) (-(x)/(2))^(i) - sum_(i=1)^(oo) (-x)^(i)) lying in the interval (-(1)/(2), (1)/(2)) is ______. (Here, the inverse trigonometric function sin^(-1) x and cos^(-1) x assume values in [-(pi)/(2), (pi)/(2)] and [0, pi] respectively)

The number of real solutions of the equation sin^(-1)(sum_(i=1)^oox^(i+1)-xsum_(i=1)^oo(x/2)^i)=pi/2-cos^(-1)(sum_(i=1)^oo(-x/2)^i-sum_(i=1)^oo(-x)^i) lying in the interval (-1/2,1/2) is ____. (Here, the inverse trigonometric function =sin^(-1)x and cos^(-1)x assume values in [pi/2,pi/2] and [0, pi] , respectively.)

The general solution of the equation sin^(100)x-cos^(100)x=1 is (where n in I)

Find the number of non zero integral solutions of the equation abs(1-i)^x = 2^x

Find the number of non-zero integral solutions of the equation abs(1-i)^x = 2^x