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81. Which one of the following is NOT a sum of cubes of the first n natural numbers?

1 | 23409 | 8521 | 441 |

82. Sum of first n even numbers = ?

Sum of first n odd number + n | Sum of first n natural numbers - Sum of first n odd numbers | Sum of first n odd numbers - n | Sum of first n odd numbers - Sum of first n natural numbers |

83. Among the following relationships, which one is INCORRECT?

Sum of cubes of first n natural numbers = [Sum of first n natural numbers]$^{2}$ | Sum of first n even numbers = Sum of first n odd numbers + n | Sum of first n natural numbers = 2 × Sum of first n even numbers | Sum of squares of first n natural numbers = 2 × Sum of squares of first n even numbers |

84. If you find the sum of the squares of the first n natural numbers, which n gives you a sum of 1240?

12 | 13 | 15 | 18 |

85. Which one of the following is NOT a sum of squares of the first n natural numbers?

420 | 385 | 506 | 650 |

86. The ratio of squares of first n natural numbers to square of sum of first n natural numbers is 17:325. The value of n is:

15 | 25 | 30 | 35 |

87. What is the sum of the squares of the first 20 natural numbers (1 to 20)?

2870 | 5650 | 2000 | 44100 |

88. The sum of the squares of the first 15 positive integers is equal to 1240. What is the sum of the squares of the second 15 positive integers?

2480 | 3490 | 6785 | 8215 |

89. If the sum of the first n positive integers is x, then which of the following is the sum of the first 2n even positive integers?

$2x + 2n^{2}$ | $3x + 4n^{2}$ | $4x + n^{2}$ | $4x + 2n^{2}$ |

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