A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD which are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD (see figure). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to :

The Boolean Expression (p   q)  q  ( p  q) is equivalent to :

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he…

Let two fair sixfaced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E 2 is the e…

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

Let a, b and c be three unit vectors such that    3a b c b c . 2    If b is not parallel to c , then the angle…

If the line, x 3 y 2 z 4 2 1 3  lies in the plane, x + my  z = 9, then 2 + m2 is equal to :

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

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis i…

The centres of those circles which touch the circle, x 2 + y2  8x  8y  4 = 0, externally and also touch the x-axis,…

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), t…