Question:
If $\, {{^n C}_{12}}$ =$\, {{^n C}_8}$ then $n$ is equal to
If $\, {{^n C}_{12}}$ =$\, {{^n C}_8}$ then $n$ is equal to
Updated On: Dec 1, 2025
- 26
- 12
- 6
- 20
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
We know that.
If ${ }^{n} C_{x}={ }^{n} C_{y}$, then
(i) $x=y$
(ii) $x + y = n $
$ \therefore { }^{n} C_{12}={ }^{n} C_{8} $
$ \Rightarrow n=12+8=20$
If ${ }^{n} C_{x}={ }^{n} C_{y}$, then
(i) $x=y$
(ii) $x + y = n $
$ \therefore { }^{n} C_{12}={ }^{n} C_{8} $
$ \Rightarrow n=12+8=20$
Was this answer helpful?
0
0
Top Questions on permutations and combinations
- Let A = \{-2, -1, 0, 1, 2, 3, 4\. Let R be a relation on A defined by xRy if and only if \(2x + y \le 2\). Let \(l\) be the number of elements in R. Let \(m\) and \(n\) be the minimum number of elements required to be added in R to make it reflexive and symmetric relations respectively. Then \(l + m + n\) is equal to :}
- JEE Main - 2026
- Mathematics
- permutations and combinations
- Let \( S=\{1,2,3,4,5,6,7,8,9\} \). Let \( x \) be the number of 9-digit numbers formed using the digits of the set \( S \) such that only one digit is repeated and it is repeated exactly twice. Let \( y \) be the number of 9-digit numbers formed using the digits of the set \( S \) such that only two digits are repeated and each of these is repeated exactly twice. Then:
- JEE Main - 2026
- Mathematics
- permutations and combinations
The number of strictly increasing functions \(f\) from the set \(\{1, 2, 3, 4, 5, 6\}\) to the set \(\{1, 2, 3, ...., 9\}\) such that \(f(i)>i\) for \(1 \le i \le 6\), is equal to:
- JEE Main - 2026
- Mathematics
- permutations and combinations
- If \( A = \{ 1, 2, 3, 4, 5, 6 \}, B = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9 \} \), then the number of strictly increasing functions from \( A \to B \) such that \( f(i) \neq i \) for \( i = 1, 2, 3, 4, 5, 6 \) is
- JEE Main - 2026
- Mathematics
- permutations and combinations
- \[ \left(\frac{1}{^{15}C_0}+\frac{1}{^{15}C_1}\right) \left(\frac{1}{^{15}C_1}+\frac{1}{^{15}C_2}\right) \cdots \left(\frac{1}{^{15}C_{12}}+\frac{1}{^{15}C_{13}}\right) = \frac{\alpha^{13}}{^{14}C_0\cdot {}^{14}C_1\cdot {}^{14}C_2\cdots {}^{14}C_{12}} \] If so, then find the value of \(30\alpha\).
- JEE Main - 2026
- Mathematics
- permutations and combinations
View More Questions
Questions Asked in KCET exam
Match the following:
In the following, \( [x] \) denotes the greatest integer less than or equal to \( x \).
Choose the correct answer from the options given below:- KCET - 2025
- Differentiability
- If \[ y = \frac{\cos x}{1 + \sin x} \] then:
- KCET - 2025
- Differentiability
- A function \( f(x) \) is given by:
\[ f(x) = \begin{cases} \frac{1}{e^x - 1}, & \text{if } x \neq 0 \\ \frac{1}{e^x + 1}, & \text{if } x = 0 \end{cases} \] Then, which of the following is true?- KCET - 2025
- Limits
- The function f(x) is given by:
For x < 0:
f(x) = ex + axFor x ≥ 0:
f(x) = b(x - 1)2
The function is differentiable at x = 0. Then,- KCET - 2025
- Differentiability
- The function \( f(x) = \tan x - x \)
- KCET - 2025
- Derivatives
View More Questions
Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.