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 Multiple Choice QuestionsMultiple Choice Questions

1.

If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is:

  • 46th

  • 59th

  • 52nd

  • 52nd

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2.

If the 2nd, 5th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:

  • 8/5

  • 4/3

  • 1

  • 1

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3.

If the sum of the first ten terms of the series,

open parentheses 1 3 over 5 close parentheses squared space plus open parentheses 2 2 over 5 close parentheses squared space plus open parentheses 3 1 fifth close parentheses squared space plus space 4 squared space plus space open parentheses 4 4 over 5 close parentheses squared space plus.....is 16/5 m, the m is equal to

  • 102

  • 101

  • 100

  • 100


B.

101

Let S10 be the sum of first ten terms of the series. Then, we have


S subscript 10 space equals open parentheses 1 3 over 5 close parentheses squared space plus open parentheses 2 2 over 5 close parentheses squared space plus open parentheses 3 1 fifth close parentheses squared space plus space 4 squared space plus space open parentheses 4 4 over 5 close parentheses squared space plus..... space to space 10 space terms
equals open parentheses 8 over 5 close parentheses squared space plus open parentheses 12 over 5 close parentheses squared space plus open parentheses 16 over 5 close parentheses squared space plus 4 squared space plus open parentheses 24 over 5 close parentheses squared space plus.... space to space 10 space terms
equals 4 squared over 5 squared space left parenthesis 2 squared space plus 3 squared plus 4 squared space plus 5 squared plus........ space to space 10 space terms right parenthesis
equals 4 squared over 5 squared space left parenthesis 2 squared space plus 3 squared plus 4 squared space plus 5 squared plus...11 squared right parenthesis
equals space 16 over 25 space left parenthesis 1 squared space plus 2 squared space plus..... plus 11 squared right parenthesis minus 1 squared right square bracket

equals 16 over 25 space open parentheses fraction numerator 11. left parenthesis 11 plus 1 right parenthesis left parenthesis 2.11 plus 1 right parenthesis over denominator 6 end fraction minus 1 close parentheses
space equals space 16 over 25 left parenthesis 506 minus 1 right parenthesis space equals space 16 over 25 space straight x space 505
rightwards double arrow 16 over 5 space straight m space equals space 16 over 25 space straight x space 505
straight m space equals space 101

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4.

The sum of first 9 terms of the series 1 cubed over 1 space plus fraction numerator 1 cubed plus 2 cubed over denominator 1 plus 3 end fraction space plus space fraction numerator 1 cubed plus 2 cubed plus 3 cubed over denominator 1 plus 2 plus 3 end fraction space.... is

  • 71

  • 96

  • 142

  • 142

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5.

Three positive numbers form an increasing GP. If the middle term in this GP is doubled, then new numbers are in AP. Then, the common ratio of the GP is

  • square root of 2 plus square root of 3
  • 3 plus square root of 2
  • 2 minus square root of 3
  • 2 minus square root of 3
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6.

The sum of first 20  terms of the sequence 0.7,0.77,0.777...... is

  • 7 over 81 space left parenthesis 179 minus 10 to the power of negative 20 end exponent right parenthesis
  • 7 over 9 left parenthesis 99 minus 10 to the power of negative 20 end exponent right parenthesis
  • 7 over 81 left parenthesis 179 plus 10 to the power of negative 20 end exponent right parenthesis
  • 7 over 81 left parenthesis 179 plus 10 to the power of negative 20 end exponent right parenthesis
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7.

If x, y, z are in A.P. and tan−1 x, tan−1 y and tan−1 z are also in A.P., then

  • x= y= z

  • 2x =3y = 6z

  • 6x = 3y= 2z

  • 6x = 3y= 2z

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8.

Statement 1: The sum of the series 1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + ...... + (361 + 380 +400) is 8000.
Statement 2: sum from straight k space equals 1 to straight n equals space 1 of left square bracket straight k cubed minus left parenthesis straight k minus 1 cubed right parenthesis right square bracket space equals space straight n cubed, for any natural number n.

  • Statement 1 is false, statement 2 is true

  • Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

  • Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

  • Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

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9.

If 100 times the 100th term of an AP with non zero common difference equals the 50 times its 50th term, then the 150th term of this AP is

  •  –150

  • 150

  • times its 50th term

  • times its 50th term

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10.

Let x1, x2, ......, xn be n observations, and let top enclose straight x be their arithmetic mean and σ2 be their variance.
Statement 1: Variance of 2x1, 2x2, ......, 2xn is 4 σ2.
Statement 2: Arithmetic mean of 2x1, 2x2, ......, 2xn is 4top enclose straight x.

  • Statement 1 is false, statement 2 is true

  • Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

  • Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

  • Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

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