Two sides of a rhombus are along the lines, x−y+1=0 and 7x−y−5=0. If its diagonals intersect at (−1, −2), then which one of the following is a vertex of this rhombus?

• (−3, −9)

• (−3, −8)

• (1/3, -8/3)

• (1/3, -8/3)

The centres of those circles which touch the circle, x²+y²−8x−8y−4=0, externally and also touch the x-axis, lie on:

• a circle

• an ellipse which is not a circle

• a hyperbola.

• a hyperbola.

If one of the diameters of the circle, given by the equation, x²+y²−4x+6y−12=0, is a chord of a circle S, whose centre is at (−3, 2), then the radius of S is:

• 5√2

• 5√3

• 5

• 10

24.

Let P be the point on the parabola, y²=8x which is at a minimum distance from the centre C of the circle, x²+(y+6)²=1. Then the equation of the circle, passing through C and having its centre at P is:

• x²+y²−4x+8y+12=0

• x²+y²−x+4y−12=0

• x²+y²− 4 x +2y−24=0

• x²+y²− 4 x +2y−24=0

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is:

• 4/3

• 4/√3

• 2/√3

• √3

The distance of the point (1, −5, 9) from the plane x−y+z=5 measured along the line x=y=z is:

• 3√10

• 10√3

• 10/√3

• 20/3

If the line  lies in the plane lx +my -z = 9, then l² +m² is equal to 

• 26

• 18

• 5

• 2

Let  be three unit vectors such that  then the angle between  is

• 3π/4

• π/2

• 2π/3

• 5π/6

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

• 3a²−26a+55=0

• 3a²−32a+84=0

• 3a²−34a+91=0

• 3a²−34a+91=0

The Boolean Expression (p∧~q)∨q∨(~p∧q) is equivalent to:

• ~p ∧ q

• p ∧ q

• p ∨ q

• p ∨ q