TS EAMCET · Maths · Permutation Combination
A binary sequence is an array of 0's and 1's. The number of \(n\)-digit binary sequences which contain even number of 0's is
- A \(2^{n-1}\)
- B \(2^n-1\)
- C \(2^{n-1}-1\)
- D $2^n
Answer & Solution
Correct Answer
(A) \(2^{n-1}\)
Step-by-step Solution
Detailed explanation
The required number of ways \(=\) The even number of 0 's ie, \(\{0,2,4,6, \ldots\}\) \(\begin{aligned} & =\frac{n !}{n !}+\frac{n !}{2 !(n-2) !}+\frac{n !}{4 !(n-4) !} \\ & ={ }^n C_0+{ }^n C_2+{ }^n C_4+\ldots=2^{n-1} \end{aligned}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \(\mathrm{P}\left(\frac{1}{2}, 4\right)\) and \(\mathrm{Q}\) are the ends of a focal chord of the parabola \(y^2=32 x\) and \(\mathrm{S}\) is the focus of the parabola then \(\mathrm{SQ}=\)TS EAMCET 2022 Easy
- If is a matrix and thenTS EAMCET 2022 Hard
- If and then the minimum value of such isTS EAMCET 2020 Medium
- In each of the choices given below, a function and an interval are given. The correct choice having a function and the associated interval for which the Lagrange's mean value theorem is not valid isTS EAMCET 2020 Easy
- If \(\alpha, \beta, \gamma, \delta\) are the roots of the equation \(x^4+x^2+1=0\) such that \(\alpha+\beta=-1, \gamma+\delta=1, \alpha^2=\beta\) and \(\gamma^2=-\delta\), then \(\alpha^{2023}+\beta^{2023}+\gamma^{2022}+\delta^{2022}=\)TS EAMCET 2023 Hard
- In an entrance test there are multiple choice questions. There are four possible answers to each question, of which one is correct. The probability that a student know the answer to a question is \(9 / 10\). If he gets the correct answer to a question, then the probability that he was guessing isTS EAMCET 2012 Medium
More PYQs from TS EAMCET
- The differential equation of which \(x y=a e^x+b e^{-x}+x^2\) is a solution, isTS EAMCET 2020 Medium
- The work done in displacing a particle from \(y=a\) to \(y=2 a\) by a force \(-\frac{\mathrm{K}}{y^2}\) acting along \(y\)-axis isTS EAMCET 2025 Medium
- The increase in the atomic radii of the third (5d) series of transition elements is very small, which may be accounted for the filling of ' \(\mathrm{X}\) ' orbitals before ' \(\mathrm{Y}\) ' orbitals. \(\mathrm{X}\) and \(\mathrm{Y}\) are \(\mathbf{X} \quad \mathbf{Y}\)TS EAMCET 2022 Easy
- The energy associated with electron in first orbit of hydrogen atom is \(-2.18 \times 10^{-18} \mathrm{~J}\). The frequency of the light required (in Hz ) to excite the electron to fifth orbit is \(\left(\mathrm{h}=6.6 \times 10^{-34} \mathrm{Js}\right)\)TS EAMCET 2025 Medium
- \(\lim _{x \rightarrow 2}\left[\left(x^2-4 x+4\right) \cos \left(\frac{2}{x-2}\right)+\frac{x^2-4}{x^3-2 x-4}\right]=\)TS EAMCET 2022 Medium
- The equation of pair of lines passing through origin and forming an equilateral triangle with the line \(3 x+4 y-5=0\) isTS EAMCET 2018 Medium