n -1 C n -1- n - NA- n CnB- n-2 Cn-2- n-3 Cn-3D- n-1 Cn-1

The correct options are A B C D ^n+1C_n+1=(n+1)!/(n+1)!0!=1 Similarly, take each option and simplify them. ^nC_n=n!/n!0!=1 ^n+2C_n+2=(n+2)!/(n+2)!0!=1 ^n ...

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Standard XII

Mathematics

Integration

n +1 C n +1=?...

Question

$^{n + 1} C_{n + 1} = ? n \in N$

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Solution

The correct options are
A

B

C

D

$^{n + 1} C_{n + 1} = \frac{(n + 1)!}{(n + 1)! 0!} = 1$
Similarly, take each option and simplify them.
$^{n} C_{n} = \frac{n!}{n! 0!} = 1$
$^{n + 2} C_{n + 2} = \frac{(n + 2)!}{(n + 2)! 0!} = 1$
$^{n + 3} C_{n + 3} = \frac{(n + 3)!}{(n + 3)! 0!} = 1$
$^{n - 1} C_{n - 1} = \frac{(n - 1)!}{(n - 1)! 0!} = 1$

We see all the options having same value.
All A, B, C and D are correct.

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Similar questions

$^{n} C_{0} \times^{n + 1} C_{n} +^{n} C_{1}^{n} C_{n - 1} +^{n} C_{2} \times^{n - 1} C_{n - 2} + . . . . .^{n} C_{n}$ =

m \sum r = 0

^{n + r} C_{n} =

Q. The number of positive integer satisfying the inequality

^{n + 1} C_{n} -^{n + 1} C_{n - 1} \leq 100

Q. Assertion :If

x =^{n} C_{n - 1} +^{n + 1} C_{n - 1} +^{n + 2} C_{n - 1} + . . . +^{2 n} C_{n - 1}

then

\frac{x + 1}{2 n + 1}

is integer Reason:

^{n} C_{r} +^{n} C_{r - 1} =^{n + 1} C_{r} a n d^{n} C_{r}

is divisible by n if n and r are co-prime

Q. The number of positive integers satisfying the inequality

^{n + 1} C_{n - 2} -^{n + 1} C_{n - 1} \leq 100

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n+1Cn+1=? n∈N

The correct options are A B C D n+1Cn+1=(n+1)!(n+1)!0!=1 Similarly, take each option and simplify them. nCn=n!n!0!=1 n+2Cn+2=(n+2)!(n+2)!0!=1 n+3Cn+3=(n+3)!(n+3)!0!=1 n−1Cn−1=(n−1)!(n−1)!0!=1 We see all the options having same value. All A, B, C and D are correct.

$^{n + 1} C_{n + 1} = ? n \in N$