Let S be the set of all points in (- , ) at which the function, f… - Vidyadip

MCQ

Let $S$ be the set of all points in $(-\pi , \pi )$ at which the function, $f(x) = min\, \{sin\,x, cos\,x\}$ is non-differentiable. Then $S$ is a subset of which of the following?

A
$\left\{ { - \frac{\pi }{4},0,\frac{\pi }{4}} \right\}$
✓
$\left\{ { - \frac{{3\pi }}{4}, - \frac{\pi }{4},\frac{{3\pi }}{4},\frac{\pi }{4}} \right\}$
C
$\left\{ { - \frac{\pi }{2}, - \frac{\pi }{4},\frac{\pi }{4},\frac{\pi }{2}} \right\}$
D
$\left\{ { - \frac{{3\pi }}{4}, - \frac{\pi }{2},\frac{\pi }{2},\frac{{3\pi }}{4}} \right\}$

✓

Answer

Correct option: B.

$\left\{ { - \frac{{3\pi }}{4}, - \frac{\pi }{4},\frac{{3\pi }}{4},\frac{\pi }{4}} \right\}$

b
Hence number of points where $f(x)$ is non-differentiable are $2$

which are $\frac{{ - 3\pi }}{4}$ and $\frac{\pi }{4}$

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 $A_1, A_3, ..... A_{2n - 1}$ are $n$ skew symmetric matrices of same order then $B =$$\sum\limits_{r = 1}^n {(2r - 1){{({A_{2r - 1}})}^{2r - 1}}} $ will be

Total number of integral solution of the equation $xyz=24$ is

A point $P$ moves so that the sum of squares of its distances from the points $(1,2)$ and $(-2,1)$ is $14$ . Let $f(x, y)=0$ be the locus of $P$, which intersects the $x$-axis at the points $A , B$ and the $y-$axis at the point $C , D$. Then the area of the quadrilateral $ACBD$ is equal to.

A unit vector which is perpendicular to the vector $2\hat i - \hat j + 2\hat k$ and is coplanar with the vectors $\hat i + \hat j - \hat k$ and $2\hat i + 2\hat j - \hat k$ is

$\int {\frac{{\cos x + x\sin x}}{{x(x - \cos x)}}dx = } $

Let $P( - 1,\,0),\,$ $Q(0,\,0)$ and $R\,(3,\,3\sqrt 3 )$ be three points. Then the equation of the bisector of the angle$PQR$ is

Let $A$ be any $3 \times 3$ invertible matrix. Then which one of the following is not always true ?

The number of roots of the equation $|x{|^2} - 7|x| + 12 = 0$ is

If $\sin \theta+\cos \theta=\frac{1}{2}$, then $16(\sin (2 \theta)+\cos (4 \theta)+\sin (6 \theta))$ is equal to:

A student obtain $75\%, 80\%$ and $85\%$ in three subjects. If the marks of another subject are added, then his average cannot be less than.....$\%$