- Under what condition are the two
lines y=^ and
orthogonal?
(a) αα’ + ββ’ + = 0 (b) (α + α’)(β + β’)=
0 (c)II’ + mm’ + nn’= (d) II’ + mm’ +
nn’=0
- The equation of a sphere is
. If one end
point of a diameter of the sphere is (-3,
- 4, 5), what is the other end point?
(a) (-3, -4, -5) (b) (3, 4, 5) (c) (3, 4, -5)
(d) (-3, 4, -5)
- Which one of the following is the
plane containing the line^
are parallel to z-^ axis?^
(a) 2x – 3y= 0 (b) 5x – 2z= 0 (c) 5y –
3z= 0 (d) 3x – 2y= 0
- What is the centre of the sphere
, if the radius
is 1 unit?
(a) (0, 0, 0) (b) (1, 0, 0) (c) (3, 0, 0) (d)
Cannot be determined as values of a, b,
c are unknown - Under what condition do 〈√^ 〉
represent direction cosines of a line?
(a) k=^ (b) k= - (c) k= ±^ (d) k can
take any value
- If the angle between the lines
whose direction ratios are (2, -1, 2) and
(x, 3, 5) is^ , then the smallest value of x
is:
(a) 52 (b) 4 (c) 2 (d) 1
- The equation of the sphere whose
centre is (1, 1, 1) and which passes
through (3, 3, 2), is:
(a)
(b)
(c)
(d) - The line passing through the points
(1, 2, -1) and (3, -1, 2) meets the yz-
plane at the point is:
(a). / (b). / (c)
. / (d). / - The co-ordinates of a point
equidistant from four distinct points (0,
0, 0), (a, 0, 0), (0, b, 0) and (0, 0, c) are:
(a).^ / (b) (a, b, c)
(c).^ / (d) (^ ) - The equation of the sphere through
, 2x + 3y + 4z= 7 and
(1, 2, 0) is given by:
(a) (b)
(c)
(d)- The point of intersection of the line
x + 1=^ with the plane 3x + 4y
- 5z= 10 is:
(a) (-2, 6, -4) (b) (2, -6, -4) (c) (2, 6, -4)
(d) (2, 6, 4)