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

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

Similar questions

If $y=y(x)$ is the solution of the equaiton $e ^{\sin y} \cos y \frac{ dy }{ dx }+ e ^{\sin y} \cos x =\cos x , y (0)=0$ then $1+ y \left(\frac{\pi}{6}\right)+\frac{\sqrt{3}}{2} y \left(\frac{\pi}{3}\right)+\frac{1}{\sqrt{2}} y \left(\frac{\pi}{4}\right)$ is equal to

For $0 \le x \le \pi ,$ the area bounded by $y = x$ and $y = x + \sin x,$ is

The distance from the point $ - i + 2j + 6k$ to the straight line through the point $(2, 3, -4)$ and parallel to the vector $6i + 3j - 4k$ is

If the value of $x$ is so small that ${x^2}$ and greater powers can be neglected, then $\frac{{\sqrt {1 + x} + \sqrt[3]{{{{(1 - x)}^2}}}}}{{1 + x + \sqrt {1 + x} }}$ is equal to

A card is drawn at random from a pack of $100$ cards numbered $1$ to $100$. The probability of drawing a number which is a square is

If a root of the equation ${x^2} + px + 12 = 0$ is $4$, while the roots of the equation ${x^2} + px + q = 0$ are same, then the value of $q$will be

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a polynomial function of degree four having extreme values at $\mathrm{x}=4$ and $\mathrm{x}=5$.
If $\lim _{x \rightarrow 0} \frac{f(\mathrm{x})}{\mathrm{x}^{2}}=5$, then $f(2)$ is equal to :

If the orthocentre of the triangle formed by the lines $\mathrm{y}=\mathrm{x}+1, \mathrm{y}=4 \mathrm{x}-8$ and $\mathrm{y}=\mathrm{mx}+\mathrm{c}$ is at $(3,-1)$, then $\mathrm{m}-\mathrm{c}$ is :

The remainder, when $7^{103}$ is divided by 23 , is equal to:

Let $T$ and $C$ respectively be the transverse and conjugate axes of the hyperbola $16 x^2-$ $y^2+64 x+4 y+44=0$. Then the area of the region above the parabola $x^2=y+4$, below the transverse axis $T$ and on the right of the conjugate axis $C$ is: