`lim_(y->p) (sqrt(y-p)-sqrt(p-q))/(y^2-p^2)`

The lines 1) (p-q)x+(q-r)y+(r-p)=0,2)(q-r)x+(r-p)y+(p-q)=0,3)(r-p)x+(p-q)y+(q-r)=0

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

If the number x,y,z are in H.P. , then sqrt(yz)/(sqrt(y)+sqrt(z)),sqrt(xz)/(sqrt(x)+sqrt(z)),sqrt(xy)/(sqrt(x)+sqrt(y)) are in

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 tangents P Q and P R are drawn from a point on the circle x^2+y^2=25 to the ellipse (x^2)/16+(y^2)/(b^2)=1,(b (a) (sqrt(5))/4 (b) (sqrt(7))/4 (c) (sqrt(7))/2 (d) (sqrt(5))/3

If the locus of the moving point P(x,y) satisfying sqrt((x-1)^(2)+y^(2))+sqrt((x+1)^(2)+(y-sqrt(12))^(2))=a is an ellipse, then find the values of a.

The value of lim_(x to1)(p/(1-x^p)-q/(1-x^q)),p ,q , in N , equal (a) (p+q)/2 (b) (p q)/2 (c) (p-q)/2 (d) sqrt(p/q)

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 sqrt(1-x^2)+sqrt(1-y^2)=a(x-y),p rov et h a t(dy)/(dx)=sqrt((1-y^2)/(1-x^2))

Prove that the equation p cos x - q sin x =r admits solution for x only if -sqrt(p^(2)+q^(2)) lt r lt sqrt(p^(2)+q^(2))