1-12212-1B- 1-12211-1C- None of these D- 1-12211-1

The correct option is A Using ^nC_k=n/k.^n 1C_k 1 For 0 ≤ k ≤ 11 ^11C_k/k+1=^12C_k+1/12 So, given expression is ⇒1/12∑_k=0^11 ^12C_k+1⇒1/12[∑_k=0^11 ^12C_k+1 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Binomial Coefficients

1/12212-1B. 1...

Question

The value of $\frac{^{11} C_{0}}{1} + \frac{^{11} C_{1}}{2} + \frac{^{11} C_{2}}{3} + \dots + \frac{^{11} C_{11}}{12}$ will be

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
$U s i n g^{n} C_{k} = \frac{n}{k} .^{n - 1} C_{k - 1} F o r 0 \leq k \leq 11 \frac{^{11} C_{k}}{k + 1} = \frac{^{12} C_{k + 1}}{12} S o, g i v e n e x p r e s s i o n i s \Rightarrow \frac{1}{12} \sum_{k = 0}^{11}^{12} C_{k + 1} \Rightarrow \frac{1}{12} [\sum_{k = 0}^{11}^{12} C_{k + 1} -^{12} C_{0}] \Rightarrow \frac{1}{12} (2^{12} - 1)$

Suggest Corrections

Similar questions

Q. The value of

\lim_{x \to \infty} \frac{\sqrt{1 + x^{4}} + (1 + x^{2})}{x^{2}}

is

(a) −1
(b) 1
(c) 2
(d) none of these

the value of ${lim}_{x \to \infty} \frac{\sqrt{1 + x^{4}} + (1 + x^{2})}{x^{2}}$ is

Q. If

f (x) = \frac{\sin^{- 1} x}{\sqrt{1 - x^{2}}}

, then (1 − x)² f '' (x) − xf(x) =

(a) 1
(b) −1
(c) 0
(d) none of these

Q. If sin θ + sin² θ = 1, then cos² θ + cos⁴ θ =

(a) −1
(b) 1
(c) 0
(d) None of these

Q. If

z = (\frac{1 + i}{1 - i})

, then z⁴ equals
(a) 1
(b) −1
(c) 0
(d) none of these

Join BYJU'S Learning Program

The value of 11C01+11C12+11C23+⋯+11C1112 will be

The correct option is A Using nCk=nk.n−1Ck−1For 0≤k≤1111Ckk+1=12Ck+112So, given expression is⇒112∑11k=0 12Ck+1⇒112[∑11k=0 12Ck+1−12C0]⇒112(212−1)

The value of $\frac{^{11} C_{0}}{1} + \frac{^{11} C_{1}}{2} + \frac{^{11} C_{2}}{3} + \dots + \frac{^{11} C_{11}}{12}$ will be