Q41 / 100 · BITSAT 2024 (Memory Based Paper 1) · Mathematics

The range of $(8 \sin \theta+6 \cos \theta)^2+2$ is

  • A
    $(0,2)$
  • Correct answer
    B
    $[2,102]$
  • C
    $(-\infty, \infty)$
  • D
    $(2,1)$

Solution

$-10 \leq 8 \sin \theta+6 \cos \theta \leq 10$ $\Rightarrow 0 \leq(8 \sin \theta+6 \cos \theta)^2 \leq 100$ $\Rightarrow 2 \leq(8 \sin \theta+6 \cos \theta)^2+2 \leq 102$

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

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