On the interval ( 0, 2 ), the function log ,sin ,x is - Vidyadip

MCQ

On the interval $\left( {0,{\pi \over 2}} \right)$, the function $ log \,sin \,x $ is

✓
Increasing
B
Decreasing
C
Neither increasing nor decreasing
D
None of these

✓

Answer

Correct option: A.

Increasing

a
(a) Let $f(x) = \log \sin x \Rightarrow f'(x) = \cot x$

Hence function is increasing on the interval $\left( {0,\frac{\pi }{2}} \right)$.

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

More "M.C.Q (1 Marks)" from STD 12 - 6. Application of derivatives→STD 12 - 6. Application of derivatives — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If $u, v$ and $w$ are three non-coplanar vectors, then $(u + v - w)\,.\,[(u - v) \times (v - w)]$ equals

The function $f(x)=\frac{x^2+2 x-15}{x^2-4 x+9}, x \in R$ is

The differential equation of all ‘Simple Harmonic Motions’ of given period $\frac{2\pi}{\text{n}}$ is:

The corner points of the feasible region determined by the following system of linear inequalities:

$2 x+y \leq 10, x+3 y \leq 15, x, y \geq 0$ are $(0,0),(5,0),(3,4)$ and $(0,5) .$ Let $Z =p x+q y,$ where $p, q\,>\,0 .$ Condition on $p$ and $q$ so that the maximum of $Z$ occurs at both $(3,4)$ and $(0,5)$ is $....$

If $\text{y}=\text{x}^{\text{n}-1}\log\text{x}\ \text{x}^2\text{y}_2+(3-2\text{n})\text{xy}_1$ is equals to :

Let $f : R \rightarrow R$ be a function defined by $\text{f(x)}=\frac{\text{e}^{|\text{x}|}-\text{e}^{-\text{x}}}{\text{e}^\text{x}+\text{e}^{-\text{x}}}$ then $f(x)$ is:

$R$ is a relation on the set $Z$ of integers and it is given by $(x, y) \in R \Leftrightarrow | x - y | \leq 1.$ Then$, R$ is:

The maximum area (in sq. units) of a rectangle having its base on the $x-$ axis and its other two vertices on the parabola, $y = 12 -x^2$ such that the rectangle lies inside the parabola, is

What are the order and degree, respectively, of the differential equation:
$\Big(\frac{\text{d}^3\text{y}}{\text{dx}^3}\Big)^2=\text{y}^4+\Big(\frac{\text{dy}}{\text{dx}}\Big)^5?$

The value of the integral $\int\limits_0^\infty {} $ $e ^{-2x}\, (\sin\, 2x + \cos\, 2x)\, dx =$