The sum of 112 + 122 + .......+212 = ?  from Quantitative Apti

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 Multiple Choice QuestionsMultiple Choice Questions

31.

If 738A6A is divisible by 11, then the value of A is

  • 6

  • 3

  • 9

  • 9

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32.

The sum of 112 + 122 + .......+212 = ? 

  • 2926

  • 3017

  • 3215

  • 3215


A.

2926

1 squared space plus space 2 squared space plus space 3 squared plus space...... plus straight n squared space equals space fraction numerator straight n left parenthesis straight n plus 1 right parenthesis thin space left parenthesis 2 straight n plus 1 right parenthesis over denominator 6 end fraction
therefore space space space 11 squared space plus space 12 squared space plus space..... plus 21 squared
equals space left parenthesis 1 squared space plus space 2 squared space plus space 3 squared space plus space.... plus 21 squared right parenthesis space space minus space left parenthesis 1 squared space plus space 2 squared space plus....... plus 10 squared right parenthesis

equals space fraction numerator 21 left parenthesis 21 plus 1 right parenthesis thin space left parenthesis 42 plus 1 right parenthesis over denominator 6 end fraction space minus space fraction numerator 10 space left parenthesis 10 plus 1 right parenthesis thin space left parenthesis 20 plus 1 right parenthesis over denominator 6 end fraction
equals space fraction numerator 21 space cross times space 22 space cross times space 43 over denominator 6 end fraction space minus space fraction numerator 10 space cross times space 11 space cross times space 21 over denominator 6 end fraction space equals space 3311 space minus space 385 space equals space 2926
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33.

If m and n are positive integers and (m - n) is an even number, then (m2 - n2) will be always divisible by

  • 4

  • 6

  • 8

  • 8

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34.

n is a whole number which when divided by 4 gives the remainder 3. The remainder when 2n is divided by 4 is

  • 1

  • 2

  • 3

  • 3

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35.

If a, b are rational numbers and left parenthesis straight a minus 1 right parenthesis square root of 2 space plus space 3 space equals space straight b square root of 2 space plus space straight a, the value of (a + b) is

  • -5

  • 3

  • -3

  • -3

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36.

In four consecutive prime numbers that are in ascending order, the product of the first three is 385 and that of the last three is 1001. The largest given prime number is

  • 11

  • 13

  • 17

  • 17

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37.

Insert the missing number
3, 18, 12, 72, 66, 396 ?

  • 300

  • 380

  • 350

  • 350

156 Views

38.

A number, when divided by 296, gives 75 as the remainder. If the same number is divided by 37 then the remainder will be

  • 1

  • 2

  • 19

  • 19

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39.

The sum and product of two numbers are 12 and 35 respectively. The sum of their reciprocals will be

  • 1 third
  • 1 fifth
  • 12 over 35
  • 12 over 35
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40.

The sum of all the digits of the numbers from 1 to 100 is

  • 5050

  • 903

  • 901

  • 901

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