English
Tamil Nadu Board of Secondary EducationHSC Science Class 11

Choose the correct alternative:Everybody in a room shakes hands with everybody else. The total number of shake hands is 66. The number of persons in the room is ______ - Mathematics

Advertisements
Advertisements

Question

Choose the correct alternative:
Everybody in a room shakes hands with everybody else. The total number of shake hands is 66. The number of persons in the room is ______

Options

  • 11

  • 12

  • 10

  • 6

MCQ
Fill in the Blanks

Solution

12

shaalaa.com
Mathematical Induction
  Is there an error in this question or solution?
Chapter 4: Combinatorics and Mathematical Induction - Exercise 4.5 [Page 198]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board
Chapter 4 Combinatorics and Mathematical Induction
Exercise 4.5 | Q 13 | Page 198

RELATED QUESTIONS

By the principle of mathematical induction, prove the following:

13 + 23 + 33 + ….. + n3 = `("n"^2("n + 1")^2)/4` for all x ∈ N.


By the principle of mathematical induction, prove the following:

4 + 8 + 12 + ……. + 4n = 2n(n + 1), for all n ∈ N.


By the principle of mathematical induction, prove the following:

52n – 1 is divisible by 24, for all n ∈ N.


By the principle of mathematical induction, prove the following:

n(n + 1) (n + 2) is divisible by 6, for all n ∈ N.


By the principle of mathematical induction, prove the following:

2n > n, for all n ∈ N.


The term containing x3 in the expansion of (x – 2y)7 is:


Prove that the sum of the first n non-zero even numbers is n2 + n


Using the Mathematical induction, show that for any natural number n ≥ 2,
`(1 - 1/2^2)(1 - 1/3^2)(1 - 1/4^2) ... (1 - 1/"n"^2) = ("n" + 1)/2`


Using the Mathematical induction, show that for any natural number n,
`1/(1*2*3) + 1/(2*3*4) + 1/(3*4*5) + ... + 1/("n"("n" + 1)*("n" + 2)) = ("n"("n" + 3))/(4("n" + 1)("n" + 2))`


Using the Mathematical induction, show that for any natural number n,
`1/(2.5) + 1/(5.8) + 1/(8.11) + ... + 1/((3"n" - 1)(3"n" + 2)) = "n"/(6"n" + 4)`


Prove by Mathematical Induction that
1! + (2 × 2!) + (3 × 3!) + ... + (n × n!) = (n + 1)! − 1


Use induction to prove that n3 − 7n + 3, is divisible by 3, for all natural numbers n


Use induction to prove that 5n+1 + 4 × 6n when divided by 20 leaves a remainder 9, for all natural numbers n


Choose the correct alternative:
1 + 3 + 5 + 7 + · · · + 17 is equal to


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×