where  and 

For such questions, we should know different formulas of limit.

Let PQ and RS be tangents at the extremities of the diameter ‘PR’ of a circle of radius ‘r’. If PS and RQ intersect at a point ‘X’ on the circumference of the circle, then 2r equals :

For such questions, we should be know different formulas of limit.

If and are two tangents to a circles then radius of the circle is

The locus of center of a circle which passes through the origin and cuts off a length of 4 units from the lineis:

AB is a chord of the circle If (1, -1) is the mid point of the chord AB then the area of the triangle formed by AB and the coordinate axes is

The equation of a plane that passes through (1,2,3) and is at maximum distance from (-1,1,1) is

If the four faces of a tetrahedron are represented by the equations and then volume of the tetrahedron (in cubic units) is

If are distinct non-zero complex numbers and such that then is always equal to

 Equivalent weights of  and 
respectively are

Let and . Then, the line of intersection of planes one determined by and other determined by is perpendicular to

A non - zero vector is parallel to the line of intersection of the plane determined by and and plane determined by vector and , then angle between and vector is

Let a,b,c be distinct non - negative numbers and the vectors lie in a plane, then the quadratic equation has