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Matrices and Determinants question

2011 · Shift 1 · Q45

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JEE Advanced
Mathematics
Matrices and Determinants
2011 · Shift 1 · Q45

Matrices and Determinants question

2011 · Shift 1 · Q45

JEE AdvancedMathematicsMatrices and DeterminantsMCQ+3 / −1

Let a, b and c be three real numbers satisfying

[\begin{matrix} a & b & c \\ \end{matrix} ]\left[ {\begin{matrix} 1 & 9 & 7 \\ 8 & 2 & 7 \\ 7 & 3 & 7 \\ \end{matrix} } \right] = [\begin{matrix} 0 & 0 & 0 \\ \end{matrix} ]

........ (E)Let b = 6, with a and c satisfying (E). If

\alpha

and

\beta

are the roots of the quadratic equation ax2 + bx + c = 0, then

\sum\limits_{n = 0}^\infty {{{\left( {{1 \over \alpha } + {1 \over \beta }} \right)}^n}}

is

A
6
B
7
C
${6 \over 7}$
D
$\infty$

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