The equation of the circle whose diameter is the common chord of the circles x2 + y2 + 2x + 2y + 1 = 0 and x2 + y2 + 4x + 6 y + 4 = 0 is
If a cylindrical vessel of given volume V with no lid on the top is to be made from a sheet of metal, then the radius (r) and height(h) of the vessel so that the metal sheet used is minimum is
8
12
10
6
C.
10
If a, b, c are non-zero real numbers and if the equations (a - 1) x = y + z, (b - 1)y = z + x, (c - 1)z = x + y have a non-trivial solution, then ab + be + ca = ?
a2b2c2
0
abc
a + b + c
If a system of three linear equations in three unknowns, which is in the matrix equation form of AX = D, is in consistent, then rank of A/rank of AD is
Less than one
Greater than or equal to one
One
Greater than one
ABC is formed by A(1, 8, 4), B (0, - 11, 4) and C(2, - 3,1). If D is the foot of the perpendicular from A to BC. Then the coordinates of D are
( - 4, 5, 2)
(4, 5, - 2)
(4, - 5, 2)
(4, - 5, - 2)