Question

Assertion :Statement 1: Equation $x=e^x$ has infinite solutions. Reason: Statement 2: $y=e^x$ is an unbounded function.

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

Answer 1

The correct option is D STATEMENT 1 is FALSE and STATEMENT 2 is TRUE

Statement 1.

$x=e^x$, By plotting graph of $y=x$ and $y=e^x$ it can be easily seen that

both curves never intersect, thus there is no solution,
Hence statement 1 is incorrect.

statement 2.

we know a function is called bounded if there exit a rel number M such that,
$\mid f\left(x\right)\mid \le M$ for all $x$ of its domain

but $y=e^x$ is not satisfying this condition, thus it is unbounded
Hence statement 2 is correct.

Therefore correct choice is 'D'.