If `a(x-a^(2))-b(x-b^(2))=0` then `x` is equal to

In a /_\ABC if a^(2)-b^(2)-c^(2)+(x-2)bc=0 then x be equal to

If x, a, b, c are real and (x-a+b)^(2)+(x-b+c)^(2)=0 , then a, b, c are in

If A = int_(0)^((pi)/(2))(sin^(3)x)/(1+cos^(2)s)dx and B=int_(0)^((pi)/(2))(cos^(2)x)/(1+sin^(2)x)dx , then (2A)/(B) is equal to

Show that A.M. of the roots of x^(2) - 2ax + b^(2) = 0 is equal to the G.M. of the roots of the equation x^(2) - 2b x + a^(2) = 0 and vice- versa.

If f(x)=((x^2)/(x^b))^(a+b)*((x^b)/(x^c))^(b+c)*((x^c)/(x^a))^(c+a) , then f^(prime)(x) is equal to: (a) 1 (b) 0 (c) x^(a+b+c) (d) None of these

If |{:(x,2),(18,x):}|=|{:(6,2),(18,6):}| , then x is equal to : (a) 6 (b) +-6 ( c) -6 0

If b gt 1, x gt 0 and (2x)^(log_(b) 2)-(3x)^(log_(b) 3)=0 , then x is

If (1+x+x^(2)+x^(3))^(7)=b_(0)+b_(1)x+b^(2)x^(2)+….b_(21)x^(21) , then find the value of b_(0)+b_(2)+b_(4)+……+b_(20)

If lim_(xrarr0)(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, then (a) a=-3 and b=9/2 (b) a=3 and b=9/2 (c) a=-3 and b=-9/2 (d) a=3 and b=-9/2

If a f(x+1)+b f(1/(x+1))=x,x !=-1,a != b, then f(2) is equal to