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Balls are arranged in rows to form an eq...

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.

A

1600

B

1500

C

1540

D

1690

Text Solution

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The correct Answer is:
C
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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

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ML KHANNA-PROGRESSIONS -PROBLEM SET - 4 (MULTIPLE CHOICE QUESTIONS)
  1. If f : R rarr R satisfies f(x + y) = f(x) + f(y) x, y in R and f(1) = ...

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  2. If the sum of n terms of an A.P. is an(n - 1), then sum of squares of ...

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  3. Balls are arranged in rows to form an equilateral triangle. The first ...

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  4. Sum of n terms the series : 1^2-2^2+3^2-4^2+5^2-6^2+

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  5. The sum of the series: 1/((log)2 4)+1/((log)4 4)+1/((log)8 4)++1/((log...

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  6. The sum of the series (1)/(3 xx 7) + (1)/(7 xx 11) + (1)/(11 xx 15)+… ...

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  7. If (1^2-t1)+(2^2-t2)++(n^2-tn)+=(n(n^2-1))/3 , then tn is equal to n^2...

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  8. The sum of n terms of the series 1^2+2.2^2+3^2+2.4^2+5^2+2.6^2+.... is...

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  9. If the sum of n terms of an A.P is cn (n-1)where c ne 0 then the sum o...

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  10. The sum of all the products of the first n(+) ive integers taken two a...

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  11. The value of the expression (1+1/omega)(1+1/omega^(2))+(2+1/omega)(2+...

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  12. The value of the expression 2 (1 + omega) (1 + omega^(2)) + 3(2 omega ...

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  13. The value of the expression 1.(2-omega).(2-omega^2)+2.(3-omega)(3-omeg...

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  14. For and odd integer n ge 1, n^(3) - (n - 1)^(3) + …… + (- 1)^(n-1) ...

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  15. The sum of the series (1)/(3.5) + (1)/(5.7) + (1)/(7.9)+…. ad infinity...

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  16. If Sigma(r=1)^(n)t(r)=(1)/(6)n(n+1)(n+2), AA n ge 1, then the value o...

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  17. The sum of the infinite series 1 + (1+a) x + (1 + a + a^(2)) x^(2) + (...

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  18. Sum of the series 1 + 2 + 4 + 7 +…+ 67 is equal to

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  19. 99^(th) term of the series 2 + 7 + 14 + 23 + 34 +…is

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  20. Find the 50th term of the series 2+3+6+11+18+….

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