A binary sequence is an array of 0's and 1's. | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $S$ be the set of all $n$-digit binary sequences. The total number of such sequences is $2^n$.Let $E$ be the number of sequences with an even

Vedclass · Accepted Answer

$2^{n-1}$

Vedclass · Answer

(A) Let $S$ be the set of all $n$-digit binary sequences. The total number of such sequences is $2^n$.Let $E$ be the number of sequences with an even number of $0$'s and $O$ be the number of sequences with an odd number of $0$'s.We know that the sum of binomial coefficients ${}^n C_0 + {}^n C_2 + {}^n C_4 + \dots = 2^{n-1}$.This sum represents the number of ways to choose an even number of positions for $0$'s in an $n$-digit sequence.Therefore,the number of such sequences is $2^{n-1}$.

$A$ binary sequence is an array of $0$'s and $1$'s. The number of $n$-digit binary sequences which contain an even number of $0$'s is

Similar Questions

Bromine is commercially prepared from sea water by displacement reaction:
$Cl_2 + 2Br^{-}_{(aq)} \to 2Cl^{-}_{(aq)} + Br_2$
$Br_2$ gas thus formed is dissolved into a solution of $Na_2CO_3$ and then pure $Br_2$ is obtained by treatment of the solution with:

The part of the castor seed from which oil is obtained is called the .....

The $emf$ (in $V$) of a Daniell cell containing $0.1 \ M$ $ZnSO_4$ and $0.01 \ M$ $CuSO_4$ solutions at their respective electrodes is
$(E_{Cu^{2+} / Cu}^{\circ} = +0.34 \ V; E_{Zn^{2+} / Zn}^{\circ} = -0.76 \ V)$

The method of asexual reproduction in algae is -

Bond energy of covalent $O-H$ bond in water is

Vedclass Test Series

Exam Paper Generator

Online Exam Module