If p ^4 + q ^3 + r ^2 + s + t = | , * 20 c ^2 + 3 & - 1 & + 3 + 1… - Vidyadip

MCQ

If $p{\lambda ^4} + q{\lambda ^3} + r{\lambda ^2} + s\lambda + t = $ $\left| {\,\begin{array}{*{20}{c}}{{\lambda ^2} + 3\lambda }&{\lambda - 1}&{\lambda + 3}\\{\lambda + 1}&{2 - \lambda }&{\lambda - 4}\\{\lambda - 3}&{\lambda + 4}&{3\lambda }\end{array}\,} \right|,$ the value of $t$ is

A
$16$
✓
$18$
C
$17$
D
$19$

✓

Answer

Correct option: B.

$18$

b
(b) Since it is an identity in $\lambda $ so satisfied by every value of $\lambda $.

Now put $\lambda = 0 $ in the given equation, we have $t = \left| {\,\begin{array}{*{20}{c}}0&{ - 1}&3\\1&2&{ - 4}\\{ - 3}&4&0\end{array}\,} \right|\, = - 12 + 30 = 18$.

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