21.

If P and Q are the points of intersection of the circles x²+ y²+ 3x + 7y + 2p – 5 = 0 and x²+ y²+ 2x + 2y – p² = 0, then there is a circle passing through P, Q and (1, 1) for

• all values of p

• all except one value of p

• all except two values of p

• all except two values of p

The shortest distance between the line y – x = 1and the curve x = y² is 

The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz−plane at the point . Then

• a = 2, b = 8

• a = 4, b = 6

• a = 6, b = 4

• a = 6, b = 4

If the straight lines  intersect at a point, then the integer k is equal to

• -5

• 2

• 5

• 5

Let L be the line of intersection of the planes 2x + 3y + z = 1 and x + 3y + 2z = 2. If L makes an angle α with the positive x-axis, then cos α equals-

• 

• 1/2

• 1

• 1

The resultant of two forces P N and 3 N is a force of 7 N. If the direction of the 3 N force were reversed, the resultant would be N. The value of P is

• 5N

• 6N

• 4N

• 4N

If a line makes an angle of π/4 with the positive directions of each of x-axis and y-axis, then the angle that the line makes with the positive direction of the z-axis is

• π/6

• π/3

• π/4

• π/4

If (2, 3, 5) is one end of a diameter of the sphere x²+ y²+ z² − 6x − 12y − 2z + 20 = 0, then the coordinates of the other end of the diameter are

• (4, 9, –3)

• (4, –3, 3)

• (4, 3, 5)

• (4, 3, 5)

Let A(h, k), B(1, 1) and C(2, 1) be the vertices of a right-angled triangle with AC as its hypotenuse. If the area of the triangle is 1, then the set of values which ‘k’ can take is given by  

• {1, 3}

• {0, 2}

• {–1, 3}

• {–1, 3}

Let P = (−1, 0), Q = (0, 0) and R = ( 3, 3 √3) be three points. The equation of the bisector of the angle PQR