Question:
The sum
\[
\sum_{k=0}^5 \left( 5C_k \right)^2
\]
is equal to
The sum
\[
\sum_{k=0}^5 \left( 5C_k \right)^2
\]
is equal to
Show Hint
When calculating combinations and factorials, simplify expressions using combinatorial identities to reduce the complexity.
Updated On: Dec 11, 2025
- \( 25C5 \)
- \( 15C5 \)
- \( 10C5 \)
- 1
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
By simplifying the summation, we arrive at the result \( 10C5 \) as the correct value of the sum.
Was this answer helpful?
0
0
Top IPU CET Mathematics Questions
- Choose the most appropriate options.
\[ \int \frac{x^2 - 2}{x \sqrt{x^2 - 1}}\,dx \text{ equal to} \] - \[ \lim_{x \to 0} \frac{\sqrt{1+x} - \sqrt{1 - x}}{x} \]
- In how many ways can the four walls of a room be painted with three colours such that no two adjacent walls have the same colour?
- A die is thrown twice and the sum of the numbers appearing is 6. Then, the conditional probability that the number 4 has appeared at least once is
- There are 3 true coins and 1 false coin with 'head' on both sides. A coin is chosen at random and tossed 4 times. If 'head' occurs all the 4 times, then the probability that the false coin has been chosen and used is
View More Questions
Top IPU CET Binomial theorem Questions
Top IPU CET Questions
- The two kinds of main memory are:
- In computer terminology, what is the full form of RAM?
- Permanent instructions that the computer use when it is turned ON and are not changed by other instructions are contained in:
- What is the full form of PROM?
- Which of the following acts as a buffer between the CPU and the main memory?
View More Questions