The locus of the orthocentre of the triangle formed by the lines `(1+p) x-py + p(1 + p) = 0, (1 + q)x-qy + q(1 +q) = 0` and y = 0, where `p!=*q`, is (A) a hyperbola (B) a parabola (C) an ellipse (D) a straight line

The curve represented by the equation sqrt(p x)+sqrt(q y)=1 where p ,q in R ,p ,q >0, is a circle (b) a parabola an ellipse (d) a hyperbola

Three lines px + qy+r=0, qx + ry+ p = 0 and rx + py + q = 0 are concurrent of

Statement-l: If the diagonals of the quadrilateral formed by the lines px+ gy+ r= 0, p'x +gy +r'= 0, p'x +q'y +r'= 0 , are at right angles, then p^2 +q^2= p'^2+q'^2 . Statement-2: Diagonals of a rhombus are bisected and perpendicular to each other.

If the roots of the equation (1)/(x+p)+(1)/(x+q)=(1)/(r ),(x ne -p, x ne -q, r ne 0) are equal in magnitude but opposite in sign, then p+q is equal to

The coefficients of x^(p) and x^(q) in the expansion of (1 + x)^(p + q) are

If a and b are the roots of x^2 – 3x + p = 0 and c, d are roots of x^(2) – 12x + q = 0 , where a,b,c,d form a G.P Prove that (q+p):(q-p) = 17 : 15

If p+q+r=0=a+b+c =0, then the value of the determnalnt |p a q b r c q c r a p b r b p c q a|i s a 0 b. p a+q b+r c c. 1 d. none of these

Express 3.28 in the form of (p)/(q) (where p and q are intgers, q ne0 ).