Find the interval of `alpha` for which `(alpha, alpha^2, alpha) and (3, 2, 1)` lies on same side of `x+y-4z+2=0`.

Number of integral values of 'alpha' for which the point (7-(5)/(4)alpha, -alpha) lies inside the ellipse (x^(2))/(25)+(y^(2))/(16) =1 is

If A= [(alpha,2),(2,alpha)] and |A^(3)|= 27 , then alpha = _______

If A= [(alpha,2),(2,alpha)] and |A^(3)|= 125 " then " alpha =

If alpha is a complex number such that alpha^(2)+alpha+1=0 then alpha^(31) is

Prove that sin^(4) alpha + cos^(4) alpha + 2 sin^(2) alpha cos^(2) alpha = 1 .

If alpha and beta are the roots of the equation x^(2) - p(x + 1) - q = 0 , then the value of : (alpha^(2) + 2 alpha + 1)/(alpha^(2)+ 2 alpha + q) + (beta^(2) + 2 beta + 1)/(beta^(2) + 2 beta + q) is :

If a variable takes the discrete values : alpha + 4, alpha - (7)/(2), alpha - (5)/(2), alpha - 3, alpha - 2, alpha + (1)/(2), alpha - (1)/(2), alpha + 5, (alpha gt 0) , then the median is :

The value of the integral int_0^(3alpha) cosec(x-alpha) cosec(x-2alpha)dx is

If A = [(alpha,2),(2,alpha)]and A^(3)=27 then alpha = _________