Question

Assertion :Statement 1: The number of solution of the equation $\left|\sin x\right|=\left|x\right|$ is only one. Reason: Statement 2: $\left|\sin x\right|\ge 0\forall xϵR$

• A. if both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1
• B. if both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1
• C. if STATEMENT 1 is TRUE and STATEMENT 2 is FALSE
• D. if STATEMENT 1 is FALSE and STATEMENT 2 is TRUE

Answer 1

The correct option is B if both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1

statement 1.
$\mid sinx\mid =\mid x\mid$, By plotting graph of $y=\mid sinx\mid$

and $y=\mid x\mid$ it can be seen that both curve intersect only at one

point $x=0$ thus it has only one solution, Hence statement 1 is correct.

statement 2.

we know for any number a $\mid a\mid \ge 0$

thus statement 2 is also correct, but it has nothing to do with solution of

statement 1.
Hence option 'B' is correct choice.