Let a-2b+c=1. If fx= x+a x+2 x+1 x+b x+3 x+2 x+c x+4 x+3 , then:

Correct answer: (D) f50=1. Apply R_1=R_1+R_3-2R_2 ⇒fx=a-2b+c 1 0 0 x+b x+3 x+2 x+c x+4 x+3 ⇒fx=1x+3^2-x+2x+4 ⇒fx=1 ⇒f50=1

Q37 / 75 · JEE Main 2020 (09 Jan Shift 2) · Mathematics

Let $a - 2 b + c = 1 .$
If $f (x) = |\begin{matrix} x + a & x + 2 & x + 1 \\ x + b & x + 3 & x + 2 \\ x + c & x + 4 & x + 3 \end{matrix}|,$ then:

A
$f (- 50) = 501$
B
$f (- 50) = - 1$
C
$f (50) = - 501$
Correct answer
D
$f (50) = 1$

Solution

Apply $R_{1} = R_{1} + R_{3} - 2 R_{2}$
$\Rightarrow f (x) = (a - 2 b + c) |\begin{matrix} 1 & 0 & 0 \\ x + b & x + 3 & x + 2 \\ x + c & x + 4 & x + 3 \end{matrix}|$

$\Rightarrow f (x) = 1 [{(x + 3)}^{2} - (x + 2) (x + 4)]$

$\Rightarrow f (x) = 1$

$\Rightarrow f (50) = 1$

Hence, the correct answer is option: 'D'.

Let a-2b+c=1.If fx=x+ax+2x+1x+bx+3x+2x+cx+4x+3, then:

Solution

Relevant Questions

Let $a - 2 b + c = 1 .$
If $f (x) = |\begin{matrix} x + a & x + 2 & x + 1 \\ x + b & x + 3 & x + 2 \\ x + c & x + 4 & x + 3 \end{matrix}|,$ then: