The line `(x-2)/3=(y+1)/2=(z-1)/-1` intersects the curve `x y=c^(2),z=0` if `c` is equal to a. `+-1` b. `+-1//3` c. `+-sqrt(5)` d. none of these

Shortest distance between the lines (x-1)/1=(y-1)/1=(z-1)/1a n d(x-2)/1=(y-3)/1=(z-4)/1 is equal to a. sqrt(14) b. sqrt(7) c. sqrt(2) d. none of these

if the lines (x-1)/2=(y-1)/3=(z-1)/4 and (x-3)/2=(y-k)/1=z/1 intersect then the value of k is (a) 1/3 (b) 2/3 (c) -1/3 (d) 1

If the line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the plane 2x+3y-z+13=0 at a point P and the plane 3x+y+4z=16 at a point Q, then PQ is equal to

If the angle theta between the line (x+1)/1=(y-1)/2=(z-2)/2 and the plane 2x-y+sqrt(pz)+4=0 is such that sintheta=1/3 , then the values of p is (A) 0 (B) 1/3 (C) 2/3 (D) none of these

Find the points where line (x-1)/2=(y+2)/(-1)=z/1 intersects x y ,y z and z x planes.

The equation of the plane passing through lines (x-4)/1=(y-3)/1=(z-2)/2a n d(x-3)/2=(y-2)/(-4)=z/5 is a. 11 x-y-3z=35 b. 11 x+y-3z=35 c. 11 x-y+3z=35 d. none of these

The curve y=(lambda+1)x^2+2 intersects the curve y=lambdax+3 in exactly one point, if lambda equals a. {-2,2} b. {1} c. {-2} d. {2}

If angle theta bertween the line (x+1)/1=(y-1)/2=(z-2)/2 and the plane 2x-y+sqrt(lambda)z+4=0 is such that s intheta=1//3, the value of lambda is a. -3/5 b. 5/3 c. -4/3 d. 3/4

The slopes of the common tanents of the ellipse (x^2)/4+(y^2)/1=1 and the circle x^2+y^2=3 are (a) +-1 (b) +-sqrt(2) (c) +-sqrt(3) (d) none of these

The lines which intersect the skew lines y=m x ,z=c ; y=-m x ,z=-c and the x-axis lie on the surface a. c z=m x y b. x y=c m z c. c y=m x z d. none of these