In the expansion of \( (1 + x)^{43} \), if the coefficients of \( (2r + 1)^{th} \) and \( (r + 2)^{th} \) terms are equal, then what is the value of r (r ≠1)?
Let \( \alpha \) and \( \beta \) be real numbers and z be a complex number. If \( z^{2} + \alpha z + \beta = 0 \) has two distinct non-real roots with \( Re(z) = 1 \), then it is necessary that
Let A and B be subsets of X and \( C = (A \cap B') \cup (A' \cap B) \), where A′ and B′ are complements of A and B respectively in X. What is C equal to?
If the coefficients of \( a^{m} \) and \( a^{n} \) in the expansion of \( (1 + a)^{m+n} \) are \( \alpha \) and \( \beta \), then which one of the following is correct?
