If for some x $$ \in $$ R, the frequency distribution of the marks obtained by 20 students in a test is :

Marks	2	3	5	7
Frequency	(x + 1)2	2x - 5	x2 - 3x	x

then the mean of the marks is

ABC is a triangular park with AB = AC = 100 metres. A vertical tower is situated at the mid-point of BC. If the angles of elevation of the top of the tower at A and B are cot^–1 (3$$\sqrt 2 $$ ) and cosec^–1 (2$$\sqrt 2 $$ ) respectively, then the height of the tower (in metres) is :

If a₁, a₂, a₃, ............... a_n are in A.P. and a₁ + a₄ + a₇ + ........... + a₁₆ = 114, then a₁ + a₆ + a₁₁ + a₁₆ is equal to :

Let f(x) = e^x – x and g(x) = x² – x, $$\forall $$ x $$ \in $$ R. Then the set of all x $$ \in $$ R, where the function h(x) = (fog) (x) is increasing, is :