Q54 / 160 · AP EAMCET 2021 (20 Aug Shift 2) · Mathematics

If $f (10 - x) = 3 x^{2} + 4 x - 5$ and $f (x) = p x^{2} + q x + r$ then $p + q + r =$

A
$272$
Correct answer
B
$274$
C
$275$
D
$273$

Solution

Given: $f (10 - x) = 3 x^{2} + 4 x - 5$

$f (x) = p x^{2} + q x + r$

$p + q + r = f (1)$

$p + q + r = f (10 - 9)$

$\Rightarrow p + q + r = 3 \times 9^{2} + 4 \times 9 - 5$

$\Rightarrow p + q + r = 243 + 36 - 5$

$\Rightarrow p + q + r = 274$

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

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