The sum of the squares of two positive integers is 100 and the difference of their squares is 28. The sum of the numbers is: 

The average of marks scored by the students of a class is 68. The average of marks of the girls in the class is 80 and that of the boys is 60. What is the percentage of boys in the class? 

The present age of father and son are in the ratio 3: 1. After 20 years the ratio becomes 2 : 1 . Find the present age of the father. 

The speed of three cars in the ratio 4 : 5 : 8 . What is the ratio among the time taken by these cars to travel the same distance ? 

The radius of a circular wheel is 1.75 m. The number of revolutions it will make in travelling 11 km is (use  );

Find the value of $$\left({sin 35°\over cos55°} \right)^2+\left({cos55°\over sin 35°} \right)^2 \ -2 sin^{3}30°$$

In equation $$ {x^{2}-24x+k=0}$$ the first root is x=2 then find out  the second root of equation.

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

$$ {I.2x^{2}-7x-60=0}$$
$$ {II.3y^{2}+13y+4=0}$$