Question:
If sumᵣ=0ⁿ(-1)ʳfracⁿCᵣⁿ+3Cᵣ=(3)/(a+3), then a-n is equal to
If sumᵣ=0ⁿ(-1)ʳfracⁿCᵣⁿ+3Cᵣ=(3)/(a+3), then a-n is equal to
Show Hint
Such sums often simplify to rational expressions independent of r.
Updated On: Mar 19, 2026
- 0
- 1
- 2
- None of these
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Using the identity:
sumᵣ=0ⁿ(-1)ʳfracⁿCᵣⁿ+kCᵣ=(k)/(n+k)
Here k=3, so:
(3)/(n+3)=(3)/(a+3)⟹ a=n+1
Thus a-n=1.
Was this answer helpful?
0
0
Top Questions on permutations and combinations
- The number of ways 16 oranges distributed to 4 children, each gets at least one.
- 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 all the letters of the word 'UDAYPUR' are arranged in all possible permutations and these permutations are listed in dictionary order, then the rank of the word 'UDAYPUR' is
- JEE Main - 2026
- Mathematics
- 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
View More Questions
Questions Asked in BITSAT exam
- The 5th term of an AP is 20 and the 12th term is 41. Find the first term.
- BITSAT - 2025
- Arithmetic Progression
- A dust particle of mass 4 × 10⁻¹² mg is suspended in air under the influence of an electric field of 50 N/C directed vertically upwards. How many electrons were removed from the neutral dust particle? (g = 10 m/s²)
- BITSAT - 2025
- Electrostatics
- Calculate the electric field at a point due to a uniformly charged spherical shell.
- BITSAT - 2025
- Electrostatics
- What is the dot product of the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \)?
- BITSAT - 2025
- Vector Algebra
- Calculate the de Broglie wavelength of an electron moving with a given velocity.
- BITSAT - 2025
- Wave Optics
View More Questions