CUET and UG exam TS EAMCET Engineering Mock Test Series 2025 Mathematics Determinants Evaluation of Determinants
If \( \alpha, \beta \neq 0 \), and \( f(n)=\alpha ^{n}+\beta ^{n} \) and \( \begin{vmatrix}3 & 1+f(1) & 1+f(2)\\ 1+f(1) & 1+f(2) & 1+f(3)\\ 1+f(2) & 1+f(3) & 1+f(4) \end{vmatrix} =K(1-\alpha )^{2}(1-\beta )^{2}(\alpha -\beta )^{2} \), then \( K \) is equal to
1
\( \alpha \beta \)
2
\( \displaystyle \dfrac{1}{\alpha \beta } \)
3
\( 1 \)
4
\( -1 \)