If `p and q` are the intercept on the axis cut by the tangent of `sqrt((x/a))+sqrt((y/b))=1,` prove that `p/a+q/b=1`

Locus of the middle points of the line segment joining P(0, sqrt(1-t^2) + t) and Q(2t, sqrt(1-t^2) - t) cuts an intercept of length a on the line x+y=1 , then a = (A) 1/sqrt(2) (B) sqrt(2) (C) 2 (D) none of these

If the ratio of the roots of the equation lx^2+nx+n=0 is p:q prove that sqrt(p/q) +sqrt(q/p)+sqrt(n/l)=0

Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x . They intersect at P and Q in first and fourth quadrant respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents at the parabola at P and Q intersect the x-axis at S.

The abscissa of the point on the curve sqrt(x y)=a+x the tangent at which cuts off equal intercepts from the coordinate axes is -a/(sqrt(2)) (b) a//sqrt(2) (c) -asqrt(2) (d) asqrt(2)

If (p+q)t h term of a G.P. is a and its (p-q)t h term is b where a ,b in R^+ , then its pth term is (a). sqrt((a^3)/b) (b). sqrt((b^3)/a) (c). sqrt(a b) (d). none of these

If p ,\ q are prime positive integers, prove that sqrt(p)+sqrt(q) is an irrational number.

A circle with center in the first quadrant is tangent to y=x+10,y=x-6 and the Y-axis. Let (p,q) be the centre of the circle. If the value oif (p+q)=a+bsqrta when a, binQ , then the value of |a-b| is

If 2p=x+1/x and 2q=y+1/y , then the value of ((pq+sqrt((p^2-1)(q^2-1)))/(xy+1/(xy))) is

If p and q are positive, then prove that the coefficients of x^p and x^q in the expansion of (1+x)^(p+q) will be equal.

P is a point on the line y+2x=1, and Q and R are two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is (a) 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these