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

If y=m x+c touches the parabola y^2=4a(x+a), then (a) c=a/m (b) c=a m+a/m (c) c=a+a/m (d) none of these

The equation of y-axis are (A) x=0,y=0 (B) x=0,z=0 (C) y=0,z=0 (D) none of these

A point (x,y,z) moves parallel to x axis. Which of the three variables x,y,z remains fixed? (A) x and y (B) y and z (C) z and x (D) none of these

If y=m x+c touches the parabola y^2=4a(x+a), then (a) c=a/m (b) c=a m+a/m c=a+a/m (d) none of these

If x ,y ,z are positive numbers is AdotPdot,t h e n (a) y^2geqx z (b) x y+y zgeq2x z (c) (x+y)/(2y-x)+(y+z)/(2y-z)geq4 (d) none of these

The equation of the plane through the intersection of the plane a x+b y+c z+d=0\ a n d\ l x+m y+n+p=0 and parallel to the line y=0,\ z=0. (A) (b l-a m)y+(c l-a n)z+d l-a p=0 (B) (a m-b l)x+(m c-b n)z+m d-b p=0 (c) (n a-c l)d+(b n-c m)y+n d-c p=0 (D) None of these

Value of |[x+y, z,z ],[x, y+z, x],[y, y, z+x]|, where x ,y ,z are nonzero real number, is equal to a. x y z b. 2x y z c. 3x y z d. 4x y z

Let the equation of the plane containing the line x-y - z -4=0=x+y+ 2z-4 and is parallel to the line of intersection of the planes 2x + 3y +z=1 and x + 3y + 2z = 2 be x + Ay + Bz + C=0 Compute the value of |A+B+C| .

The two lines x=ay+b,z=cy+d and x=a'y+b', z=c'y +d' are pendicular to each other if

The x-y plane is rotated about its line of intersection with the y-z plane by 45^0 , then the equation of the new plane is/are a. z+x=0 b. z-y=0 c. x+y+z=0 d. z-x=0