Find the value of n C 0- n C 1- - n C nA- 1B- 2n C- 2n-1D- 0

The correct option is B Consider the binomial expansion of (1+x)n (1+x)^n= ^n C _0 ^n C _1 .......... ^n C _n Put x = 1 ⇒ ^n C _0 + ^n C _1 + ^n C ...

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Standard XII

Mathematics

Sum of Product of Binomial Coefficients

Find the valu...

Question

Find the value of $^{n} C_{0} +^{n} C_{1} + . . . . . . . . . . . +^{n} C_{n}$

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Solution

The correct option is C

Consider the binomial expansion of (1+x)ⁿ

$(1 + x)^{n}$ = $^{n} C_{0}^{n} C_{1} . . . . . . . . . .^{n} C_{n}$

Put x = 1

⇒ $^{n} C_{0} +^{n} C_{1} +^{n} C_{2} . . . . . . . . . . . +^{n} C_{n}$

⇒ $^{n} C_{0} +^{n} C_{1} +^{n} C_{2} . . . . . . . . . . . +^{n} C_{n}$ = $2^{n}$

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Find the value of $^{n} C_{0} . (n + 1) + n .^{n} C_{1} + (n - 1)^{n} C_{2} . . . . 1.^{n} C_{n}$

Q. If

^{2 n + 1} C_{0} +^{2 n + 1} C_{1} +^{2 n + 1} C_{2} + \dots +^{2 n + 1} C_{n} = 4^{11}

then which of the following is/are correct ?

$^{n} C_{0}$ + 2. $^{n} C_{1}$ + 3. $^{n} C_{2}$ +..............(n+1) $^{n} C_{n}$ =

T h e a r i t h m e t i c m e a n o f t h e s e r i e s^{n} c_{0},^{n} c_{1},^{n} c_{2} . . . . .,^{n} c_{n} i s :

Find $\frac{1}{2}$ $^{n} C_{1}$ - $\frac{2}{3}$ $^{n} C_{2}$ + $\frac{3}{4}$ $^{n} C_{3}$ ................. $\frac{(- 1)^{n + 1} n}{n + 1}$ × $^{n} C_{n}$

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Find the value of nC0+nC1+...........+nCn

The correct option is C Consider the binomial expansion of (1+x)n (1+x)n= nC0 nC1..........nCn Put x = 1 ⇒ nC0+nC1+nC2...........+nCn ⇒ nC0+nC1+nC2...........+nCn = 2n

Find the value of $^{n} C_{0} +^{n} C_{1} + . . . . . . . . . . . +^{n} C_{n}$