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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 ______

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प्रश्न

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 ______

पर्याय

  • 11

  • 12

  • 10

  • 6

MCQ
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उत्तर

12

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Mathematical Induction
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 4: Combinatorics and Mathematical Induction - Exercise 4.5 [पृष्ठ १९८]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 4 Combinatorics and Mathematical Induction
Exercise 4.5 | Q 13 | पृष्ठ १९८

संबंधित प्रश्‍न

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:

1.2 + 2.3 + 3.4 + … + n(n + 1) = `(n(n + 1)(n + 2))/3` 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:


By the principle of mathematical induction, prove that, for n ≥ 1
13 + 23 + 33 + ... + n3 = `(("n"("n" + 1))/2)^2`


By the principle of mathematical induction, prove that, for n ≥ 1
12 + 32 + 52 + ... + (2n − 1)2 = `("n"(2"n" - 1)(2"n" + 1))/3`


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


By the principle of Mathematical induction, prove that, for n ≥ 1
1.2 + 2.3 + 3.4 + ... + n.(n + 1) = `("n"("n" + 1)("n" + 2))/3`


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))`


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 10n + 3 × 4n+2 + 5, is divisible by 9, for all natural numbers n


Choose the correct alternative:
If `""^("a"^2 - "a")"C"_2 = ""^("a"^2 - "a")"C"_4` then the value of a is


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


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