Mathematics Tes...

If  x – 2y + 4 = 0  is a common tangent to y² = 4x and  = 1, then the equation of other common tangent is :-

The vertex of  a parabola is at  (4, 3)  and directrix is  x – y + 1 = 0. Then the equation of  its latus rectum is :-

Water is dropped at the rate of  2 cm³/sec into a cone of semivertical angle 45°. The rate at which periphery of water surface changes when height of  the water in the cone is  2 cm,  is :-

The eccentricity of locus of z satisfying | z – 5 | – | z + 5 | = ± 6, is :- (where z is complex number)

The dual of statement (p ∨ ~ q) ∧ (~ p), is :-

The number of ways in which  A A B B C C can placed in squares of given figure so that no row remains empty are :-

(where c is constant of integration)

The average salary of male employees in a firm was Rs. 520 and that of females was Rs. 420. the mean salary of all the employees was Rs. 500. The percentage of male employees is

Let y = f(3x), where x takes all values only in [–1, 1] and y takes all values only in [–3, 5] then domain and range of g (x) = 2 + 3f (2x + 1) are [a, b] and [c, d] respectively, then the value of  (a + b + c + d)  is equal to