Question:
The number of subsets of $\{1, 2, 3, ..., 9\} $containing at least one odd number is
The number of subsets of $\{1, 2, 3, ..., 9\} $containing at least one odd number is
Updated On: Jun 17, 2022
- 324
- 396
- 496
- 512
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
The total number of subsets of given set is $2^{9}=512$
Even numbers are $\{2,4,6,8\}$
Case I: When selecting only one even number $={ }^{4} C_{1}=4$
Case II: When selecting only two even numbers $={ }^{4} C_{2}=6$
Case III: When selecting only three even numbers $={ }^{4} C_{3}=4$
Case IV : When selecting only four even numbers $={ }^{4} C_{4}=1$
$\therefore$ Required number of ways
$=512-(4+6+4+1)-1=496$
[Here, we subtract 1 for due to the null set]
Even numbers are $\{2,4,6,8\}$
Case I: When selecting only one even number $={ }^{4} C_{1}=4$
Case II: When selecting only two even numbers $={ }^{4} C_{2}=6$
Case III: When selecting only three even numbers $={ }^{4} C_{3}=4$
Case IV : When selecting only four even numbers $={ }^{4} C_{4}=1$
$\therefore$ Required number of ways
$=512-(4+6+4+1)-1=496$
[Here, we subtract 1 for due to the null set]
Was this answer helpful?
0
0
Top Questions on Sets
- Let \[f(x) =\begin{cases} x-1, & x \text{ is even, } \, x \in \mathbb{N}, \\2x, & x \text{ is odd, } \, x \in \mathbb{N}.\end{cases}\]If for some $a \in \mathbb{N}$, $f(f(f(a))) = 21$, then \[\lim_{x \to a^-} \left\{ \frac{|x|^3}{a} - \left\lfloor \frac{x}{a} \right\rfloor \right\},\]where $\lfloor t \rfloor$ denotes the greatest integer less than or equal to $t$, is equal to:
- Let \( \alpha \beta \gamma = 45 \); \( \alpha, \beta, \gamma \in \mathbb{R} \). If \( x(\alpha, 1, 2) + y(1, \beta, 2) + z(2, 3, \gamma) = (0, 0, 0) \) for some \( x, y, z \in \mathbb{R} \), \( xyz \neq 0 \), then \( 6\alpha + 4\beta + \gamma \) is equal to ______.
- Let \( A = \{ n \in [100, 700] \cap \mathbb{N} : n \text{ is neither a multiple of 3 nor a multiple of 4} \} \).
Then the number of elements in \( A \) is: - If \[ S(x) = (1 + x) + 2(1 + x)^2 + 3(1 + x)^3 + \ldots + 60(1 + x)^{60}, \, x \neq 0, \] and \[ (60)^2 S(60) = a(b)^b + b, \] where $a, b \in \mathbb{N}$, then $(a + b)$ is equal to ________.
- If \( f(x) = \frac{4x + 5}{6x - 4}, \, x \neq \frac{2}{3} \) and \( (fof)(x) = g(x) \), where \( g : \mathbb{R} - \left\{ \frac{2}{3} \right\} \rightarrow \mathbb{R} - \left\{ \frac{2}{3} \right\} \), then \( (gogogog)(4) \) is equal to
View More Questions
Questions Asked in VITEEE exam
- Two identical blocks A and B, each of mass 'm' resting on a smooth floor are connected by a light spring of natural length L and spring constant K, with the spring at its natural length. A third identical block 'C' (mass m) moving with a speed v along the line joining A and B collides with A. the maximum compression in the spring is
- VITEEE - 2023
- work, energy and power
- Assertion :
The binding energy of the nucleus increases with the increase in atomic number.
Reason :
Heavier elements have a greater number of non-radioactive isotopes than radioactive isotopes. - The half-life of radioactive radon is 3.8 days. The time at the end of which \(\frac{1}{20}th\) of the Radon sample will remain undecayed is (given log10e=0.4343)
- Which element has more electron gain enthalpy among chalcogen group?
- VITEEE - 2022
- sulphur
- Coin is tossed till heads is obtained what is expectation of no. of coin tosses
- VITEEE - 2022
- Random Variables
View More Questions
Concepts Used:
Sets
Set is the collection of well defined objects. Sets are represented by capital letters, eg. A={}. Sets are composed of elements which could be numbers, letters, shapes, etc.
Example of set: Set of vowels A={a,e,i,o,u}
Representation of Sets
There are three basic notation or representation of sets are as follows:
Statement Form: The statement representation describes a statement to show what are the elements of a set.
- For example, Set A is the list of the first five odd numbers.
Roster Form: The form in which elements are listed in set. Elements in the set is seperatrd by comma and enclosed within the curly braces.
- For example represent the set of vowels in roster form.
A={a,e,i,o,u}
Set Builder Form:
- The set builder representation has a certain rule or a statement that specifically describes the common feature of all the elements of a set.
- The set builder form uses a vertical bar in its representation, with a text describing the character of the elements of the set.
- For example, A = { k | k is an even number, k ≤ 20}. The statement says, all the elements of set A are even numbers that are less than or equal to 20.
- Sometimes a ":" is used in the place of the "|".