Graph of Trigonometric Ratios

Q. The number of roots of the equation $x+2\tan x=\frac{\pi }{2}$ in the interval $[0,2\pi ]$ is

1. $1$
2. $2$
3. $3$
4. infinite

Q.

The function which is neither decreasing nor increasing in $\left(\frac{\mathrm{\pi }}{2},\frac{3\mathrm{\pi }}{2}\right)$ is:

1. $\cos ecx$

2. $\tan x$

3. $x^2$

4. $\left|x-1\right|$

Q.

If y = 2/(sin theta + √3 cos theta), then find the minimum value of y

Q. The number of solution(s) of the equation $\cos x=|x|$ in $[-\frac{3\pi }{2},\frac{3\pi }{2}]$ is

Q. The area (in sq. units) bounded by curves $y=\text{cosec}x,$ $y=\sec x,$ $y=\cos x$ and $y=\sin x$ on interval $(0,\frac{\pi }{2})$ is equal to

1. $1+\ln (\sqrt{2}+1)$
2. $2\ln (\sqrt{2}+1)$
3. $2\ln (\sqrt{2}+1)-\sqrt{2}$
4. $\ln (\sqrt{2}+1)-\frac{1}{\sqrt{2}}$

Q.

Sketch the graph of the following functions:
y= tan 2x

Q.

Sketch the following graphs :
(i) y=2 sin 2x
(ii) y= 3 sin x
(iii) $y=2sin(x-\frac{\pi }{4})$
(iv) y=2 sin (2x-1)
(v) y=3 sin(3x+1)
(vi) $y=3sin(2x-\frac{\pi }{4})$

Q. The intervals for which $\tan x>\cot x$, where $x\in (0,\pi )-\left\{\frac{\pi }{2}\right\}$ is

1. $(0,\frac{\pi }{4})\cup (\frac{3\pi }{4},\pi )$
2. $(0,\frac{\pi }{4})\cup (\frac{\pi }{2},\frac{3\pi }{4})$
3. $(\frac{\pi }{4},\frac{\pi }{2})\cup (\frac{\pi }{2},\frac{3\pi }{4})$
4. $(\frac{\pi }{4},\frac{\pi }{2})\cup (\frac{3\pi }{4},\pi )$

Q. The graph of the function $y=2\cos x+1$ is

1. 
2. 
3. 
4. 

Q. The area bounded by curve $y=x\sin x$ and $x-$axis, between $x=0$ and $x=2\pi ,$ is equal to

1. $2\pi$ sq. units
2. $3\pi$ sq. units
3. $4\pi$ sq. units
4. $6\pi$ sq. units

Q. The area (in sq. units) of the smaller region bounded by the curves $x^2+y^2=5$ and $y^2=4x$ is

1. $\frac{\pi }{4}+\frac{1}{6}$
2. $\frac{\pi }{4}-\frac{1}{6}$
3. $\frac{1}{3}+\frac{5\pi }{4}-\frac{5}{2}{\sin }^{-1}\frac{1}{\sqrt{5}}$
4. $\frac{2}{3}+\frac{5\pi }{2}-5{\sin }^{-1}\frac{1}{\sqrt{5}}$

Q.

Evaluate the determinants in Exercises 1 and 2.

(i) (ii)

Q. Let $f\left(x\right)$ be a $\text{sine}$ function with fundamental period $3\pi$ and it passes through the origin. If the maximum value of $f\left(x\right)$ is $10$, then $f\left(x\right)$ is

1. $f\left(x\right)=\pm 10\sin \left(\frac{3x}{2}\right)$
2. $f\left(x\right)=10\sin \left(\frac{2x}{3}\right)$
3. $f\left(x\right)=\pm 10\sin \left(\frac{2x}{3}\right)$
4. $f\left(x\right)=10\sin \left(\frac{3x}{2}\right)$

Q.

what is the value of θ if tanθ=0.51

Q. The area bounded in the first quadrant by the normal at $(1,2)$ on the curve $y^2=4x,x-$ axis and the curve is equal to

1. $\frac{10}{3}$ sq. units
2. $\frac{7}{3}$ sq. units
3. $\frac{4}{3}$ sq. units
4. $\frac{9}{2}$ sq. units

Q. The number of points of intersection of the curve $y=\sin 3x$ with $x$-axis in the interval $(0,\pi )$ is

1. $1$
2. $2$
3. $4$
4. $3$

Q.

Sketch the graph of the following functions :
$y=co{s}^{2}x$

Q. $\mathrm{The}\mathrm{function}f\left(x\right)=\tan x\mathrm{is}\mathrm{defined}\mathrm{for}x\in R~(2n+1)\frac{\pi }{2},n\in Z$

1. True
2. False

Q. The number of point(s) of intersection of curves $y=\sin x$ and $y=\cos x$ in $[0,2\pi ]$ is

Q.

Sketch the graph of the following functions:
y=2 tan 3x

Q. Which of the following is possible?

1. 
   $\sin \theta =\frac{5}{3}$
2. 
   $\tan \theta =1002$
3. 
   $\mathrm{cosec}\theta =\frac{1}{2}$
4. 
   $\cos \theta =\frac{3}{5}$

Q. The graph of $y=e^{x^2}$ is

1. 
2. 
3. 
4. None of these

Q. If $A=\tan 1,B=\tan 2$ and $C=\tan 3,$ then the descending order of $A,B$ and $C$ is

1. $A,B,C$
2. $C,B,A$
3. $A,C,B$
4. $B,C,A$

Q. If $f\left(x\right)=\sin \left(\log x\right)$ and $g\left(x\right)=\cos \left(\sin x\right)$ are two functions such that $\left(f\right(x){)}^2+(g\left(x\right){)}^2=1,$ then the number of maximum possible real values of $x$ is

Q.

Sketch the graph of the following pairs of functions on the same axes:
(i) y=sin x, y = sin $(x+\frac{\pi }{4})$
(ii) y=sin x, y = sin 3x

Q. Which of the following is the least?

1. 
   $\sin 3$
2. 
   $\sin 2$
3. 
   $\sin 1$
4. 
   $\sin 7$

Q. If $x=\sin 1+\cos 1,y=\sqrt{\sin 1}+\sqrt{\cos 1}$ and $z=\sin 1-\cos 1,$ then which among the following relation between $x,y,z$ is correct ?

1. $x>y>z$
2. $z>y>x$
3. $y>x>z$
4. $z>x>y$

Q.

Convert the given complex number in polar form: 1 – i

Q. If the area bounded by the curves(lies above the $x-$axis) $x^2+y^2=25$ and $4y=|4-x^2|$ is $a{\sin }^{-1}\frac{b}{5}+b\text{sq.units}$. Then the value of $(\sqrt{a}+b)=$

Q.

Sketch the graph of the following functions:
y= 2 cot 2x