If the system of equations
$$x+2y+3z=3$$
$$4x+3y-4z=4$$
$$8x+4y-\lambda z=9+\mu$$
has infinitely many solutions, then the ordered pair ($$\lambda,\mu$$) is equal to :
Let the plane containing the line of intersection of the planes
P1 : $$x+(\lambda+4)y+z=1$$ and
P2 : $$2x+y+z=2$$
pass through the points (0, 1, 0) and (1, 0, 1). Then the distance of
the point (2$$\lambda,\lambda,-\lambda$$) from the plane P2 is :
The set of all values of $$a$$ for which $$\mathop {\lim }\limits_{x \to a} ([x - 5] - [2x + 2]) = 0$$, where [$$\alpha$$] denotes the greatest integer less than or equal to $$\alpha$$ is equal to
The locus of the mid points of the chords of the circle $${C_1}:{(x - 4)^2} + {(y - 5)^2} = 4$$ which subtend an angle $${\theta _i}$$ at the centre of the circle $$C_1$$, is a circle of radius $$r_i$$. If $${\theta _1} = {\pi \over 3},{\theta _3} = {{2\pi } \over 3}$$ and $$r_1^2 = r_2^2 + r_3^2$$, then $${\theta _2}$$ is equal to :