If `z = x - iy` and `z'^(1/3) = p +iq,` then `1/(p^2+q^2)(x/p+y/q)` is equal to

If x, y, z are in A.P.; ax, by, cz are in GP. and 1/a, 1/b, 1/c are in A.P., then x/z+z/x is equal to

If p(x)=ax^(2)+bx and q(x)=lx^(2)+mx+n with p(1)=q(1), p(2)-q(2)=1 , and p(3)-q(3)=4 , then p(4)-q(4) is equal to

Let P(1, 2, 3) be a point in space and Q be a point on the line (x-1)/(2)=(y-3)/(5)=(z-1)/(3) such that PQ is parallel to 5x-4y+3z=1 . If the length of PQ is equal to k units, then the value of k^(2) is equal to

If z=x+iy is a complex number with x, y in Q and |z| = 1 , then show that |z^(2n)-1| is a rational numberfor every n in N .

A straight line intersects the same branch of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 in P_(1) and P_(2) and meets its asymptotes in Q_(1) and Q_(2) . Then, P_(1)Q_(2)-P_(2)Q_(1) is equal to

Let P and Q be 3xx3 matrices with P!=Q . If P^3=""Q^3a n d""P^2Q""=""Q^2P , then determinant of (P^2+""Q^2) is equal to (1) 2 (2) 1 (3) 0 (4) 1

Let P and Q be 3xx3 matrices with P!=Q . If P^3=""Q^3a nd""P^2Q""=""Q^2P , then determinant of (P^2+""Q^2) is equal to (1) 2(2) 1 (3)0 (4) 1

If P = {a,e,I,o,u} and Q = {x,y,z} , then P cap Q is

If (p+iq)/(r+is) = x + iy , prove that (p-iq)/(r-is) = x -iy and (p^(2)+q^(2))/(r^(2)+s^(2))=x^(2)+y^(2) ,where p,q,r,s,x,y,inR

If the angle between the lines, x/2=y/2=z/1 and (5-x)/(-2) = (7y-14)/(p ) = (z-3)/(4) is cos ^(-1) ((2)/(3)), then P is equal to