Product of any r consecutive natural numbers is always divisible

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 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


Advertisement

24.

Product of any r consecutive natural numbers is always divisible by

  • r!

  • (r + 4)!

  • (r + 1)!

  • (r + 2)!


A.

r!

The product of n consecutive natural numbers,

n + 1n + 2 ... (n + r) = n + r!n! = Crn + r . r!

Hence, it is always divisible by r!.


Advertisement
Advertisement
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


Advertisement
29.

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

  • 31

  • 12

  • 210

  • None


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


Advertisement