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Choose the correct alternative:If aaCaaCa2-aC2=a2-aC4 then the value of a is - Mathematics

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प्रश्न

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

पर्याय

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MCQ

उत्तर

3

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Mathematical Induction
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 4: Combinatorics and Mathematical Induction - Exercise 4.5 [पृष्ठ १९७]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 4 Combinatorics and Mathematical Induction
Exercise 4.5 | Q 9 | पृष्ठ १९७

संबंधित प्रश्‍न

By the principle of mathematical induction, prove the following:

32n – 1 is divisible by 8, 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:


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`


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 ≥ 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))`


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


Use induction to prove that 10n + 3 × 4n+2 + 5, is divisible by 9, for all natural numbers n


Prove that using the Mathematical induction
`sin(alpha) + sin (alpha + pi/6) + sin(alpha + (2pi)/6) + ... + sin(alpha + (("n" - 1)pi)/6) = (sin(alpha + (("n" - 1)pi)/12) xx sin(("n"pi)/12))/(sin (pi/12)`


Choose the correct alternative:
In 3 fingers, the number of ways four rings can be worn is · · · · · · · · · ways


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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