Q58 / 90 · JEE Main 2012 (07 May Online) · Mathematics

Let $f(x)=\sin x, g(x)=x$. Statement 1: $f(x) \leqslant g x($ for $) \mathrm{x}$ in $(0, \infty)$ Statement 2: $f(x) \leq 1$ for $x$ in $(0, \infty)$ but $g(x) \rightarrow \infty$ as $x \rightarrow \infty$.

  • A
    Statement 1 is true, Statement 2 is false.
  • B
    Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
  • Correct answer
    C
    Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
  • D
    Statement 1 is false, Statement 2 is true.

Solution

Let $f(x)=\sin x$ and $g(x)=x$ Statement-1: $f(x) \leq g \quad x(\forall x) \in 0, \infty(\quad)$ i.e., $\sin x \leq x \forall x \in(0, \infty)$ which is true Statement-2: $f(x) \leq 1 \forall x \in 0, \infty(\quad)$ i.e., $\sin x \leq 1 \forall x \in(0, \infty)$ It is true and $g(x)=x \rightarrow \infty$ as $x \rightarrow \infty$ also true.

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

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