Q32 / 66 · JEE Advanced 2007 (Paper 2) · Mathematics

Let $f(x)=2+\cos x$ for all real $x$. Statement I For each real $t$, there exists a point $c$ in $[t, t+\pi]$ such that $f^{\prime}(c)=0$. Statement II $f(t)=f(t+2 \pi)$ for each real $t$.

  • A
    Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I
  • Correct answer
    B
    Statement I is True, Statement II is true; Statement II is not a correct explanation for Statement I
  • C
    Statement I is true, Statement II is false
  • D
    Statement I is false, Statement II is true

Solution

$f(x)=2+\cos x \forall x \in R$ Statement I There exists a point $c \in[t, t+\pi]$, where $f^{\prime}(c)=0$ Hence, Statement 1 is true. Statement II $f(t)=f(t+2 \pi)$ is true. But Statement II is not a correct explanation for Statement I.

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

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