A sum of ₹3000 is to be given in the form of 63 prizes. If the prize money is either ₹100 or ₹25. Find the number of prizes of each type.

A sum of₹ 500 is in the form of denominations of ₹5 and ₹10. If the to tal number of notes is 90 find the num- ber of notes of each denomination: (Hint: Let the number of 5 rupee notes be 'x', then number of 10 rupee notes = 90 - x)

Find the common factors of the given terms in each :15p, 20qr, 25rp.

Represent the following situation in the form of quadratic equations. Sum of the two number is 25. We need to find the numbers, if the sum of their reciprocals is 1/6 .

A sum of Rs. 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs. 20 less than its preceding prize. Find the value of each of prizes.

If the sum of squares of two consecutive positive even numbers is 100 then find them.

(i) A pair of dice are rolled. What is the probability that they sum to 7 given that neither die shows a 2 ? (ii) A pair of dice is thrown. Find the probability that either of the dice shows 2 when their sum is 6.

The number of ways that 12 prizes can be divided among 4 students so that each may have 3 prizes is

If 3 dice are rolled, find the probability that either sum is 16 or they show different numbers.