Download App

STD 12 - 6. Application of derivatives — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 6. Application of derivatives4 Marks
MCQ
Consider two statements $S_1$ and $S_2$ .

$S_1$ : If $f(x)$ is a differentiable function with $f'(x)$ = $0$ in $(a, b)$ and $f(x)$ is increasing in $(a, b)$ , then $\frac {f(x)}{f\ '(x)}$ is also increasing in $(a, b).$

$ S_2$ : Both $sin\ x$ and $tan\ x$ are increasing function in $(0,\frac{\pi}{2})$. Which of the following is true 

  • A
    both $S_1$ and $S_2$ are wrong
  • B
    $S_1$ is correct and implies $S_2$.
  • ✓
    $S_1$ is wrong and $S_2$ is right.
  • D
    both $S_1$ and $S_2$ are right.
✓

Answer

Correct option: C.
$S_1$ is wrong and $S_2$ is right.
c
$S_1$ is wrong and $S_2$ is right

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $\vec{a}=\hat{i}+\hat{j}-\hat{k}$ and $\vec{c}=2 \hat{i}-3 \hat{j}+2 \hat{k}$. Then the number of vectors $\vec{b}$ such that $\vec{b} \times \vec{c}=\vec{a}$ and $|\vec{b}| \in\{1,2, \ldots ., 10\}$ is
→
Let $a _{ n }$ be the $n ^{\text {th }}$ term of the series $5+8+14+23$ $+35+50+\ldots$ and $S _{ n }=\sum \limits_{ k =1}^{ n } a _{ k }$. Then $S _{30}- a _{40}$ is equal to
→
The probability, that in a randomly selected $3-$digit number at least two digits are odd, is
→
If $I = {\kern 1pt} \int\limits_0^{\frac{\pi }{6}} {\frac{{\cos x}}{x}dx,J = \int\limits_{\frac{\pi }{3}}^{\frac{\pi }{2}} {\frac{{\cos x}}{x}dx.} } $ Which of the following is CORRECT ?
→
The sum of infinite terms of the geometric progression $\frac{{\sqrt 2 + 1}}{{\sqrt 2 - 1}},\frac{1}{{2 - \sqrt 2 }},\frac{1}{2}.....$ is
→
If variable point $(x, y)$ satisfies the equation $x^2 + y^2 -8x -6y + 9 = 0$ , then range of $\frac{y}{x}$ is
→
$\int_{\,\pi }^{\,10\pi } {\,|\sin x|dx} $ is
→
Let $f(x)$ be $a$ quadratic expression which is positive for all real $x$ . If $g(x) = f(x) + f' (x) + f'' (x)$, then for any real $x$, which one is correct .
→
Let $f$ and $g$ be two differentiable functions on $R$ such that $f'(x) > 0$ and $g'(x) < 0$ for all $x\in R$ .Then for all $x$
→
Let $f:[0, \infty) \rightarrow[0, \infty)$ be defined as

$\mathrm{f}(\mathrm{x})= \int_{0}^{x}[y] \,d y$

Where $[x]$ is the greatest integer less than or equal to $x$. Which of the following is true?

→