Let `A(0,1),B(1,1) ,C(1,-1) ,D(-1,0)` be four points. If P is any other point, then `PA+PB+PC+PDged`, where `[d]` represents greatest integer.

A (c,0) and B (-c,0) are two points . If P is a point such that PA + PB = 2a where 0 lt c lt a, then find the locus of P.

A(2,3) , B (1,5), C(-1,2) are the three points . If P is a point such that PA^(2)+PB^(2)=2PC^2 , then find locus of P.

Number of points of discontinuity of f(x) =[x^(3)+3x^(2)+7x+2], where [.] represents the greatest integer function in [0,1] is ___________.

Find lim_(xto0) [x]((e^(1//x)-1)/(e^(1//x)+1)), (where [.] represents the greatest integer funciton).

Let g(x)=1+x-[x] and f(x)={ -1,x 0. Then for all x, f(g(x)) is equal to (where [.] represents the greatest integer function). (a) x (b) 1 (c) f(x) (d) g(x)

Let g(x)=1+x-[x]a n df(x)={-1, x 0 . Then for all x ,f(g(x)) is equal to (where [.] represents the greatest integer function). (a) x (b) 1 (c) f(x) (d) g(x)

Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2) . Point D lies on a line L orthogonal to the plane determined by the points A, B and C. Q. The perpendicular distance of D from the plane ABC is

Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2) . Point D lies on a line L orthogonal to the plane determined by the points A, B and C. The equation of the plane ABC is

Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2) . Point D lies on a line L orthogonal to the plane determined by the points A, B and C. The equation of the line L is

Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2) . Point D lies on a line L orthogonal to the plane determined by the points A, B and C.