47
MCQ (Single Correct Answer)
If $f: R \rightarrow R$ be defined by $f(x)=2 x+\cos x$, then $f$
A
has a minimum at $x=\pi$
B
has a maximum at $x=0$
C
is a decreasing function
D
is an increasing function
48
MCQ (Single Correct Answer)
If $y=x(x-3)^2$ decreases for the values of $x$ given by
A
$1< x<3$
B
$x<0$
C
$x>0$
D
$0< x<\frac{3}{2}$
49
MCQ (Single Correct Answer)
The function $f(x)=4 \sin ^3 x-6 \sin ^2 x+12 \sin x+100$ is strictly
A
increasing in $\left(\pi, \frac{3 \pi}{2}\right)$
B
decreasing in $\left(\frac{\pi}{2}, \pi\right)$
C
decreasing in $\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$
D
decreasing in $\left[0, \frac{\pi}{2}\right]$
50
MCQ (Single Correct Answer)
Which of the following functions is decreasing on $\left(0, \frac{\pi}{2}\right)$ ?
A
$\sin 2 x$
B
$\tan x$
C
$\cos x$
D
$\cos 3 x$
51
MCQ (Single Correct Answer)
The function $f(x)=\tan x-x$
A
always increases
B
always decreases
C
never increases
D
sometimes increases and sometimes decreases