Balls are arranged in rows to form an equilateral triangle. The first row consists of ome ball, the second row of two balls and so on. If 669 more balls are added,then all the balls can be arranged in the shape of a square and each of the sides, then contains 8 balls less than each side of the triangle. Determine the initial number of balls.

Balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If 669 more balls are added, then all the balls can be arranged in the shape of a square and each of the sides then contains 8 balls less than each side of the triangle had. The initial number of balls is (a) 1500 (b) 1540 (c) 1600 (d) 1690

Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of row balls and so on. If 99 more identical balls are added to the total number of balls used in forming the equilateral triangle, then all these balls can be arranged in a square whose each side contains exactly 2 balls less than the number of balls each side of the triangle contains. Then, the number of balls used to form the equilateral triangle is

Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of row balls and so on. If 99 more identical balls are added to the total number of balls used in forming the equilateral triangle, then all these balls can be arranged in a square whose each side contains exactly 2 balls less than the number of balls each side of the triangle contains. Then, the number of balls used to form the equilateral triangle is

If some balls are arranged in the form of an equilateral triangle with n rows such that r^(rh) row of balls has r balls in it.If 99 more balls are added to existing one and the balls can now form a square with (n-2) balls in each row.Then the number of balls that formed the equilateral triangle.

There are 3 blue balls, 4 red balls and 5 green balls. In how many ways can they be arranged in a row?

The number of ways in which 4 different red balls and 8 similar green balls can be arranged in a row so that at most 3 red balls are together is equal to

The number of ways in which 4 different red balls and 8 similar green balls can be arranged in a row so that at most 3 red balls are together is equal to