The number of times the digit 5 will be written when listing the

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 Multiple Choice QuestionsShort Answer Type

21.

How many triangles can be formed by joining 6 points lying on a circle?


 Multiple Choice QuestionsMultiple Choice Questions

22.

The number of permutations by taking all letters and keeping the vowels of the word COMBINE in the odd places is

  • 96

  • 144

  • 512

  • 576


23.

If C3 n - 1+ C4n - 1 > C3n then n is just greater than integer

  • 5

  • 6

  • 4

  • 7


24.

Product of any r consecutive natural numbers is always divisible by

  • r!

  • (r + 4)!

  • (r + 1)!

  • (r + 2)!


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25.

A polygon has 44 diagonals. The number of its sides is

  • 10

  • 11

  • 12

  • 13


26.

Out of 8 given points, 3 are collinear. How many different straight lines can be drawn by joining any two points from those 8 points ?

  • 26

  • 28

  • 27

  • 25


27.

How many odd numbers of six significant digits can be formed with the digits 0, 1, 2, 5, 6, 7 when no digit is repeated ?

  • 120

  • 96

  • 360

  • 288


28.

The number of ways four boys can be seated around a round-table in four chairs of different colours is

  • 24

  • 12

  • 23

  • 64


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29.

If Cr16 = Cr + 116, then the value of Pr - 3r is

  • 31

  • 12

  • 210

  • None


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30.

The number of times the digit 5 will be written when listing the integers from 1 to 1000, is

  • 271

  • 272

  • 300

  • None of these


C.

300

Since, 5 does not occur in 1000, we have to count the number of times 5 occurs when we list the integers from 1 to 999. Any number between 1 and 999 is of the form xyz, 0  x, y, z  9.

The number in which 5 occurs exactly once

= C139 × 9 = 243

The number in which 5 occurs exactly twice

= C23 . 9 = 27

The number in which 5 occurs in all three digits = 1.

Hence, the number of times 5 occurs

      = 1 × 243 + 2 × 27 + 3 × 1= 300


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