| DIRECTION: Each of these questions contains two statements: Statement-1 (Assertion) and Statement-2 (Reason). Choose the correct answer (Only one option is correct) from the following - |
| Suppose\[f(x)=\frac{{{x}^{2}}}{2}+\ell n\,\,x+2\cos x\] |
| Statement-1: f is an increasing function. |
| Statement-2: Derivative off(x) with respect to x is always greater than zero. |
A) Statement-1 is false, Statement-2 is true.
B) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
C) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
D) Statement-1 is true, Statement-2 is false.
Correct Answer: B
Solution :
Statement - II is true as \[f'(x)=x+\frac{1}{x}-2\sin x\] \[\Rightarrow \] \[f'(x)>0,\forall x,\frac{1}{x}\ge 2,\forall x>0\]and \[|2\sin x|\le 2.\](domain of f is \[(0,\infty )\]) Hence, f is an increasing function.
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