If the variance of the following frequency distribution :

Class         : 10–20 20–30 30–40

Frequency :    2          x          2

is 50, then x is equal to____

If the perpendicular bisector of the line segment joining the points P(1 ,4) and Q(k, 3) has y-intercept equal to –4, then a value of k is :

Let $$\mathop \cup \limits_{i = 1}^{50} {X_i} = \mathop \cup \limits_{i = 1}^n {Y_i} = T$$ where each X_i contains 10 elements and each Y_i contains 5 elements. If each element of the set T is an element of exactly 20 of sets X_i’s and exactly 6 of sets Y_i’s, then n is equal to :

Let $$\lambda \ne 0$$ be in R. If $$\alpha $$ and $$\beta $$ are the roots of the
equation, x² - x + 2$$\lambda $$ = 0 and $$\alpha $$ and $$\gamma $$ are the roots of
the equation, $$3{x^2} - 10x + 27\lambda = 0$$, then $${{\beta \gamma } \over \lambda }$$ is equal to: