Q195 / 270 · NDA 2016 (Phase 1) · Mathematics

Consider the equation: $k \sin x+\cos 2 x=2 k-7$ If the equation possesses solution, then what is the maximum value of k ?

  • A
    1
  • B
    2
  • C
    4
  • Correct answer
    D
    6

Solution

For maximum value of $K$, $\sin x=1$ $\begin{aligned} & \frac{K \pm \sqrt{K^2-16 K+64}}{4}=1 \\ & \Rightarrow( \pm) \sqrt{K^2-16 K+64}=(-K+4) \end{aligned}$ Squaring both sides, we get $\begin{aligned} & K^2-16 K+64=K^2+16-8 K \\ & \Rightarrow 8 K=48 \\ & \Rightarrow K=6 \end{aligned}$

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

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