jee-main 2014 Q78

jee-main · India · 06apr Matrices Determinant and Rank Computation

If $\alpha , \beta \neq 0 , f ( n ) = \alpha ^ { n } + \beta ^ { n }$ 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) 1
(2) - 1
(3) $\alpha \beta$
(4) $\frac { 1 } { \alpha \beta }$

If $\alpha , \beta \neq 0 , f ( n ) = \alpha ^ { n } + \beta ^ { n }$ 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) 1\\
(2) - 1\\
(3) $\alpha \beta$\\
(4) $\frac { 1 } { \alpha \beta }$

Paper Questions

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