If | cases x ^ 2 + x & x + 1 & x - 2 2 x ^ 2 + 3x - 1 & 3x & 3x - 3 x ^ 2 + 2x + 3 & 2x - 1 & 2x - 1 cases | = ax - 12 , then a is equal to:

Correct answer: B. 24 Put x = 1 on both the sides | cases 2 & 2 & - 1 4 & 3 & 0 6 & 1 & 1 cases | = a - 12 ⇒ 2(3 - 0) - 2(4 - 0) - 1(4 - 18) = a - 12 ⇒ 6 - 8 + 14 = a - 12 ⇒ 12 = a - 12 ⇒ 24 = a .

JEE Main 201511 AprilOnline

Exam: JEE Main
Year: 2015
Date: 11 April
Mode: Online
Subject: Mathematics
Chapter: Determinants

JEE Main 2015 · 11 April · Online · Mathematics · Determinants

If | cases x ^ 2 + x & x + 1 & x - 2 2 x ^ 2 + 3x - 1 & 3x & 3x - 3...

\left|

\begin{cases}{x}^{2} + x & x + 1 & x - 2 \\ 2{x}^{2} + 3x - 1 & 3x & 3x - 3 \\ {x}^{2} + 2x + 3 & 2x - 1 & 2x - 1\end{cases}

\right| = ax - 12

, then

a

is equal to:

Options

A $- 24$
B $24$
C $- 12$
D $12$

Correct answer

B. $24$

Step-by-step solution

Put

x = 1

on both the sides

\left|

\begin{cases}2 & 2 & - 1 \\ 4 & 3 & 0 \\ 6 & 1 & 1\end{cases}

\right| = a - 12

<br /><br />

⇒ 2\left(3 - 0\right) - 2\left(4 - 0\right) - 1\left(4 - 18\right) = a - 12

<br /><br />

⇒ 6 - 8 + 14 = a - 12

<br /><br />

⇒ 12 = a - 12

<br /><br />

⇒ 24 = a .

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