Intercept made by the circle ` z z +a+a z+r=0` on the real axis on complex plane is `sqrt((a+ a )-r)` b. `sqrt((a+ a )^2-r)` c. `sqrt((a+ a )^2-4r)` d. `sqrt((a+ a )^2-4r)`

Intercept made by the circle zbarz+bara+a barz+r=0 on the real axis on complex plane is

Intercept made by the circle zbar z +bar a+abar z+r=0 on the real axis on complex plane is sqrt((a+ bar a )-r) b. sqrt((a+ bar a )^2-r) c. sqrt((a+ bar a )^2-4r) d. sqrt((a+ bar a )^2-4r)

Three equal circles each of radius r touch one another. The radius of the circle touching all the three given circles internally is (2+sqrt(3))r (b) ((2+sqrt(3)))/(sqrt(3))r ((2-sqrt(3)))/(sqrt(3))r (d) (2-sqrt(3))r

Two equal circles of radius r intersect such that each passes through the centre of the other. The length of the common chord of the circles is sqrt(r) (b) sqrt(2)\ r\ A B (c) sqrt(3)\ r\ (d) (sqrt(3))/2\ r

The largest area of the trapezium inscribed in a semi-circle or radius R , if the lower base is on the diameter, is (a) (3sqrt(3))/4R^2 (b) (sqrt(3))/2R^2 (3sqrt(3))/8R^2 (d) R^2

If |z-4/2z|=2 then the least of |z| is (A) sqrt(5)-1 (B) sqrt(5)-2 (C) sqrt(5) (D) 2

If a point R ( 4, y, z ) lies on the line segment joining the points P ( 2, - 3, 4 ) and Q ( 8, 0, 10) then the distance of R from the origin is: A. 6 B. sqrt ( 53 ) C. 2 sqrt (14 ) D. 2 sqrt ( 21 )

Let oversetto a=3hati+2hatj+xhatk and oversettob=hati-hatj+hatK Some real x. Then |oversettoaxxoversettob|=r is possible if: A. 3 sqrt ((3 )/(2)) lt r lt 5sqrt ((3)/(2)) B. 0 lt r le sqrt ((3)/(2)) C. r ge 5 sqrt (( 3 )/(2)) D. sqrt (( 3 ) /(2) lt r le 3 sqrt ((3 ) /(2))

The radius of the circle r^(2)-2sqrt(2r) (cos theta + sin theta)-5=0 , is

If z is a complex number such that |z|=4 and a r g(z)=(5pi)/6 , then z is equal to -2sqrt(3)+2i b. 2sqrt(3)+i c. 2sqrt(3)-2i d. -sqrt(3)+i