Three numbers are such that if the average of any two of them is added to the third number, the sums obtained are 168, 174 and 180 respectively. What is the average of the original three numbers?

A corner of a cube of side length 8 m. When cut by a plane which bisects the sides of the cube, we get a pyramid whose volume is : 

Directions:  In the following two equations questions numbered (I) and (II) are given. You have to solve both equations and
Give answer
(a) If x > y
(b) If x ≥ y
(c) If y > x
(d) If y ≥ x
(e) If x = y or no relation can be established

$$ {I.x^{2}=81}$$
$$ {II.(y-9)^{2}}=0$$

The smallest natural number, by which 3000 must be divided to make the quotient a perfect cube, is : 

If $$ {3\sqrt{{1-a}\over{a}}}+9={19-3\sqrt{{a}\over{1-a}}}$$, then what is the value of a?

Directions: The following graph gives Sales, Expense and Capital of a company for a period of five years 1994 to 1998. Read the graph and answer the following questions.

In which year was the Sales to Expense ratio the lowest?

In ∆ABC, ∠B is a right angle, AC = 6cm, and D is the mid-point of AC. The length of BD is:

The average weight of A, B, and C is 52 kg. If the average weight of B and C is 44 kg and that of C and A is 46 kg, then what will be the weight of C?