P and Q are centres of two circles, intersecting at B and C, and ACD is a striaght line. If angleAPB = 150^@ and angleBQD = x^@ , find the value of x.

p and q are two inegers such that p is the successor of q.Find the value of p-q.

Three points charges +q,+2q and Q are placed at the three vertices of an equilateral triangle. Find the value of charge Q (in terms of q), so that electric otential energy of the system is zero.

Find the values of p,q, so that the system of equations 2x + py + 6z = 8, x + 2y + qz = 5, x + y + 3 z = 4 may have infinitely many solutions.

Find the values of p,q, so that the system of equations 2x + py + 6z = 8, x + 2y + qz = 5, x + y + 3 z = 4 may have no solution.

Find the values of p,q, so that the system of equations 2x + py + 6z = 8, x + 2y + qz = 5, x + y + 3 z = 4 may have a unique solution.

Find the values of 'p' and 'q' for which: f(x) = {:{((1-sin^3x)/(3cos^2x), if x pi/2 is continuous at x = pi//2

Find the value of the following polynomials at the indicated value of variables: q(y) = 3y^3- 4y +sqrt11 at y = 2.

Find the values of y for which the distance between the points P (2,-3) and Q (10, y) is 10 units.

Find the value of x such that PQ = QR, where P, Q and R are (6,- 1), (1, 3) and (x, 8) respectively.