If `P=2+sqrt3`,`Q=2-sqrt3`, then `P/Q=?`

If P=[[sqrt(3)/2,1/2],[-1/2,sqrt(3)/2]], A=[[1,1],[0,1]] and Q=PAP^T and X=P^TQ^(2005)P , then X equal to:

If P =3^sqrt(log_(3)2)-2^(sqrt(log_(2)3))and Q=log_(2)log_(3)log_(2)log _(sqrt(3))81, then

Let p, q in R . If 2- sqrt3 is a root of the quadratic equation, x^(2)+px+q=0, then

If {:P=[(sqrt3/2,1/2),(-1/2,sqrt3/2)],A=[(1,1),(0,1)]:}and Q=PAP^T," then" P^TQ^2015P , is

If P+Q=R and |P|=|Q|= sqrt(3) and |R| ==3 , then the angle between P and Q is

If P and Q are two points on the circle x^2 + y^2 - 4x + 6y-3=0 which are farthest and nearest respectively from the point (7, 2) then. (A) P-=(2-2sqrt(2), -3-2sqrt(2)) (B) Q-= (2+2sqrt(2), -3 + 2 sqrt(2)) (C) P-= (2+2sqrt(2), -3 + 2 sqrt(2)) (D) Q-= (2-2sqrt(2), -3 + 2 sqrt(2))

If 2+sqrt(3)i is a root of the equation x^2+p x+q=0 , then write the values of p\ a n d\ q .

Let x=sqrt(3-sqrt5) and y=sqrt(3+sqrt5) If the value of the expression x-y+2x^2y+2xy^2-x^4y+xy^4 can be expressed in the form sqrtp+sqrtq where p. q in N, then find the value of (p+q).

Let P-=sqrt(3)e^(ipi/3), Q-=sqrt(3)e^(-pi/3) and R -=sqrt(3)e^(-ipi) . If P,Q,R form a triangle PQR in the Argand plane, then /_\ PQR is (A) isosceles (B) equilateral (C) scalene (D) none of these