Let $\Delta \,\,\left( y \right) = \left| {\,\begin{array}{*{20}{c}} {y\,\, + \,\,a}&{y\,\, + \,\,b}&{y\,\, + \,\,a\,\, - \,\,c}\\ {y\,\, + \,\,b}&{y\,\, + \,\,c}&{y\,\, - \,\,1}\\ {y\,\, + \,\,c}&{y\,\, + \,\,d}&{y\,\, - \,\,b\,\, + \,\,d} \end{array}\,} \right|$ and, $\mathop \smallint \limits_0^2 \,\Delta \,\,\left( y \right)\,\,dy = - 16$, where $a,\;\,b,\,\,c,\,\,d$ are in A.P., then the common difference of the A.P. is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

Let

\Delta \,\,\left( y \right) = \left| {\,\begin{array}{cccccccccccccccccccc} {y\,\, + \,\,a}&{y\,\, + \,\,b}&{y\,\, + \,\,a\,\, - \,\,c}\\ {y\,\, + \,\,b}&{y\,\, + \,\,c}&{y\,\, - \,\,1}\\ {y\,\, + \,\,c}&{y\,\, + \,\,d}&{y\,\, - \,\,b\,\, + \,\,d} \end{array}\,} \right|

and,

\int \limits_0^2 \,\Delta \,\,\left( y \right)\,\,dy = - 16

, where

a,\;\,b,\,\,c,\,\,d

are in A.P., then the common difference of the A.P. is equal to

View answer and explanation

Correct option: B

\pm \,2

Option B (

\pm \,2

) is correct because the common difference of the A.P. is found by evaluating the integral and solving the resulting equation.