Question:
If \(\sum_{r=0}^{n} \binom{n}{r} \frac{r + 3}{r} = \frac{3}{a+3}\), then \(a - n\) is equal to
If \(\sum_{r=0}^{n} \binom{n}{r} \frac{r + 3}{r} = \frac{3}{a+3}\), then \(a - n\) is equal to
Show Hint
Match the closed form after simplifying binomial ratios.
Updated On: Mar 23, 2026
- 0
- 1
- 2
- None of these
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Using \(\frac{\binom{n}{r} (r + 3)!}{(n-r)! (r+3)!}\) and summing gives \(\frac{3}{n+3}\).
Thus \(a = n \implies a - n = 0\).
Was this answer helpful?
0
0
Top BITSAT Mathematics Questions
- The solution of $\sin^{-1}\,x-\sin^{-1}\,2x=\pm\frac{\pi}{3}$ is
- If one root of the quadratic equation $a x^{2}+b x+c=0$ is equal to $n^{\text {th }}$ power of the other root, then the value of: $a^{\frac{n}{n-1}} C^{\frac{1}{n-1}}+c^{\frac{n}{n-1}} a^{\frac{1}{n-1}}$ is equal to
- $(x -1) (x^2 - 5x + 7) < (x -,1),$ then $x$ belongs to
- An ellipse has $OB$ as semi-minor axis, $F$ and $F$ are its foci and the $\angle FBF$, is a right angle. Then, the eccentricity of the ellipse is
- $2^{1/4}. 2^{2/8}. 2^{3/16}. 2^{4/32}......\infty$ is equal to-
View More Questions
Top BITSAT permutations and combinations Questions
- Number of words from the letters of the word BHARAT in which B and H will never come together is:
- How many different 4-letter words can be formed from the letters of the word "BINARY" without repetition?
- In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70, then the number of diagonals of the polygon is
- With 17 consonants and 5 vowels, the number of words of four letters that can be formed having two different vowels in the middle and one consonant, repeated or different at each end is
- If ²⁰Cᵣ = ²⁰Cᵣ-₁₀, then ¹⁵Cᵣ is equal to:
View More Questions
Top BITSAT Questions
- Two point charges $-q$ and $+ q$ are located at point's $(0, 0, - a)$ and, $(0, 0, a)$ respectively. The electric potential at a point $(0, 9, z)$, where $z > a$ is
- Which of the following must be known in order to determine the power output of an automobile?
- A large drop of oil (density $0.8 \,g / cm ^{3}$ and viscosity $\eta_{0}$ ) floats up through a column of another liquid (density $1.2\, g / cm ^{3}$ and viscosity $\eta_{L}$ ). Assuming that the two liquids do not mix, the velocity with which the oil drop rises will depend on :
- A body is projected vertically upwards at time $ t = 0$ and it is seen at a height $H$ at time $t_1$ and $t_2$ second during its flight. The maximum height attained is ($g$ is acceleration due to gravity)
- At what point of a projectile motion, acceleration and velocity are perpendicular to each other ?
View More Questions