Consider the points `O(0,0), A(0,1)`, and `B(1,1)` in the x-y plane. Suppose that points `C(x,1) and D(1,y)` are chosen such that `0ltxlt1`. And such that `O,C, and D` are collinear. Let the sum of the area of triangles OAC and BCD be denoted by S. Then which of the following is/are correct?.

If the points (a,0),(0,b) and (1,1) are collinear , then show that (1)/(a)+(1)/(b)=1 .

(iv) Find the value of (1/x,1/y) if the point (x,0),(0,y) and (-1,-1) are collinear.

The equations of the sided of a triangle are x+y-5=0,x-y+1=0, and y-1=0 . Then the coordinates of the circumcentre are

Let O be the origin. If A(1,0)a n dB(0,1)a n dP(x , y) are points such that x y >0a n dx+y<1, then P

Let S be the area of the region enclosed by y=e^(-x^(2)),y=0, x=0 and x=1 . Then

A straight line joining the points (1, 1, 1) and (0, 0, 0) intersects the plane 2x+2y+z=10 at

let L be a straight line passing through the origin. Suppose that all the points on L are at a constant distance from the two planes P_1 : x + 2y-z +1 = 0 and P_2 : 2x-y + z-1 = 0 , Let M be the locus of the feet of the perpendiculars drawn from the points on L to the plane P_1 . Which of the following points lie(s) on M? (a) (0, - (5)/(6), - (2)/(3)) (b) (-(1)/(6), - (1)/(3), (1)/(6)) (c) (- (5)/(6), 0, (1)/(6)) (d) (-(1)/(3), 0, (2)/(3))

Let S be the area of the region enclosed by y= e^(-x^(2)) ,y=0 x =0 and x=1 ,Then -

Consider the hyperbola H:x^2-y^2=1 and a circile S with center N(x_2,0) . Suppose that H and S touch each other at a point P(x_1,y_1) with x_1gt1andy_1gt0 . The common langent to H and S intersects the x-axis at point M. If (l,m) is the centroid of the triangle trianglePMN , then the correct expression(s)is(are)

A straight line joining the point (1, 1, 1) and (0, 0, 0) intersects the plane 2x + 2y + z = 10 at-