Mathematics Tes...

If distance between the foci of an ellipse is 6 and the distance between directrices is 12, then the length of its latus rectum is:

The differential equation of all non - horizontal lines in a plane is 

If three natural numbers between 1 and 100 are selected randomly, then the probability that all are divisible by both 2 and 3 is 

If the two pairs of lines x² – 2mxy – y² = 0 and x² – 2nxy – y² = 0 are such that one of them represents the bisector of the angles between the other, then

A man of 2 m height walks at a uniform speed of 6 km/h away from a lamp post of 6 m height. The rate at which the length of his shadow increases is

In how many ways can 8 students be arranged in a row?

If f(x) = | x |³, then f′(0) =

Let f(x)=${(x + 1)}^2$−1,(x≥−1). Then the set S={x:f(x)= $f^{-1}$(x)}is

Let f(x) = x^3/2, then f′(0) =

If f(x)=|x−2|and g(x)=f[f(x)], then g′(x)=

______ for x>20

Let f(x + y) = f(x)f(y), for all x, y ∈ R. If f'(0) = 2 and f(4) = 4, then f'(4) is equal to

What is \(\tan \left\{2 \tan ^{-1}\left(\frac{1}{3}\right)\right\}\) equal to?