If the radii of the circle `(x-1)^2+(y-2)^2=1` and `(x-7)^2+(y-10)^2=4` are increasing uniformly w.r.t. times as 0.3 unit/s is and 0.4 unit/s, then they will touch each other at `t` equal to (a) `45s` (b) `90s` (c) `10s` (d) `135s`

If the radii of the circle (x-1)^2+(y-2)^2=1 and (x-7)^2+(y-10)^2=4 are increasing uniformly w.r.t. times as 0.3 unit/s is and 0.4 unit/s, then they will touch each other at t equal to 45s (b) 90s (c) 11s (d) 135s

If the radii of the circles (x-1)^2+(y-2)^2+(y-2)^2=1 and (-7)^2+(y-10)^2=4 are increasing uniformly w.r.t. time as 0.3 units/s and 0.4 unit/s, respectively, then at what value of t will they touch each other?

If the lines (x-1)/2=(y+1)/3=z/(5t-1) and (x+1)/(2s+1)=y/2=z/4 are parallel to each other, then value of s, t will be

A rhombus is inscribed in the region common to the two circles x^2+y^2-4x-12=0 and x^2+y^2+4x-12=0 with two of its vertices on the line joining the centers of the circles. The area of the rhombus is (a) 8sqrt(3)s qdotu n i t s (b) 4sqrt(3)s qdotu n i t s 6sqrt(3)s qdotu n i t s (d) none of these

The point at which the circles x^(2)+y^(2)-4x-4y+7=0 and x^(2)+y^(2)-12x-10y+45=0 touch each other is

The area of the smaller region bounded by circle x^2+y^2=1 and |y|=x+1 (a) pi/2-1/2s qdotu n i t s (b) pi/2-1s qdotu n i t s (c) pi/2s qdotu n i t s (d) pi/2 +1s qdotu n i t s

Area bounded by the curve x y^2=a^2(a-x) and the y-axis is (pia^2)/2s qdotu n i t s (b) pia^2s qdotu n i t s 3pia^2s qdotu n i t s (d) None of these

The area of the loop of the curve a y^2=x^2(a-x) is 4a^2s qdotu n i t s (b) (8a^2)/(15)s qdotu n i t s (16 a^2)/9s qdotu n i t s (d) None of these

Consider two circles S, =x^2+y^2 +8x=0 and S_2=x^2+y^2-2x=0 . Let DeltaPOR be formed by the common tangents to circles S_1 and S_2 , Then which of the following hold(s) good?

If a circle S(x,y)=0 touches the point (2,3) of the line x+y=5 and S(1,2)=0, then radius of such circle is (1)/(sqrtlamda) units then the value of lamda is.