A set contains $(2n + 1)$ elements. The number of sub-sets of the set which contains at most $n$ elements is :-
A set contains $(2n + 1)$ elements. The number of sub-sets of the set which contains at most $n$ elements is :-
- A
$2^{n-1}$
- B
$2^{n+1}$
- C
$2^{2n}$
- D
$2^n$
Similar Questions
If $\alpha { = ^m}{C_2}$, then $^\alpha {C_2}$is equal to
If $\alpha { = ^m}{C_2}$, then $^\alpha {C_2}$is equal to
A group of students comprises of $5$ boys and $n$ girls. If the number of ways, in which a team of $3$ students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is $1750$, then $n$ is equal to
A group of students comprises of $5$ boys and $n$ girls. If the number of ways, in which a team of $3$ students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is $1750$, then $n$ is equal to
- [JEE MAIN 2019]
The total number of natural numbers of six digits that can be made with digits $1, 2, 3, 4$, if all digits are to appear in the same number at least once, is
The total number of natural numbers of six digits that can be made with digits $1, 2, 3, 4$, if all digits are to appear in the same number at least once, is
A boy needs to select five courses from $12$ available courses, out of which $5$ courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is
A boy needs to select five courses from $12$ available courses, out of which $5$ courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is
- [JEE MAIN 2023]
${ }^{n-1} C_r=\left(k^2-8\right){ }^n C_{r+1}$ if and only if:
${ }^{n-1} C_r=\left(k^2-8\right){ }^n C_{r+1}$ if and only if:
- [JEE MAIN 2024]