Question:
If n+1Cr+1: nCr: n-1Cr-1 = 55: 35: 21 then the value of n + r is _____.
If n+1Cr+1: nCr: n-1Cr-1 = 55: 35: 21 then the value of n + r is _____.
Updated On: Feb 5, 2026
Hide Solution
Verified By Collegedunia
Correct Answer: 16
Solution and Explanation
The correct answer is 16.
Was this answer helpful?
1
1
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 JEE Main exam
Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?
- JEE Main - 2026
- Organic Chemistry
- Let \( ABC \) be an equilateral triangle with orthocenter at the origin and the side \( BC \) lying on the line \( x+2\sqrt{2}\,y=4 \). If the coordinates of the vertex \( A \) are \( (\alpha,\beta) \), then the greatest integer less than or equal to \( |\alpha+\sqrt{2}\beta| \) is:
- JEE Main - 2026
- Coordinate Geometry
- Three charges $+2q$, $+3q$ and $-4q$ are situated at $(0,-3a)$, $(2a,0)$ and $(-2a,0)$ respectively in the $x$-$y$ plane. The resultant dipole moment about origin is ___.
- JEE Main - 2026
- Electromagnetic waves
Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.- JEE Main - 2026
- Complex Numbers and Quadratic Equations
- The work functions of two metals ($M_A$ and $M_B$) are in the 1 : 2 ratio. When these metals are exposed to photons of energy 6 eV, the kinetic energy of liberated electrons of $M_A$ : $M_B$ is in the ratio of 2.642 : 1. The work functions (in eV) of $M_A$ and $M_B$ are respectively.
- JEE Main - 2026
- Dual nature of matter
View More Questions