Binomial Theorem
Binomial Theorem
star_batch_jee_advanced_2025
Grade None
Question:
If the coefficient of $x^t$ and $x^{t+1}$ in $\sum_{r=0}^{n}(1+x)^r$ where $t < n-2$ are equal, then :
$n$ is odd
$n$ is even
The sum of coefficients of $x^t$ and $x^{t+1} = \binom{n+1}{t+2}$
The sum of coefficients of $x^t$ and $x^{t+1} = \binom{n+2}{t+2}$
Step-by-Step Solution
Key Concept: The intersection of sets $A$ and $B$ is empty because they have no common elements satisfying both conditions simultaneously.
Observe that $3 + 3i \in A$ but $3 + 3i \notin B$ because $3 + 3i$ does not satisfy the conditions defining set $B$. Therefore $n(A \cap B) = 0$, meaning the two sets are disjoint.
Correct Answer: I need to solve this problem step by step.
**Given:** Coefficient of $x^t$ and $x^{t+1}$ in $\sum_{r=0}^{n}(1+x)^r$ are equal, where $t < n-2$.
**Step 1: Find the sum**
$$\sum_{r