Circular Measurement of Angle

Q. If X and Y are two sets and $X^{\prime }$ denotes the complement of X, then $X\cap (X\cup Y{)}^{\prime }$ = ___.

1. X
2. Y
3. $\varphi$
4. $X\cap Y$

Q.

The circular wire of diameter 10cm is cut and placed along the circumference of a circle of diameter 1 metre. The angle subtended by the wire at the centre of the circle is equal to

1. 

2. 

3. 

4. 

Q.

The value of cosx in the second quadrant

1. increases from 0 to 1

2. increases from -1 to 0

3. decreases from 1 to 0

4. decreases from 0 to -1

Q.

$x^o=\frac{\pi }{180}\times$ x radian and $xradian=\frac{180}{\pi }\times$ degree

1. False

2. True

Q.

Find the value of other five trigonometric functions if sec x = $\frac{13}{5}$, and x lies in fourth quadrant.

Q. In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

Q. If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.

Q. The value of $\left\{\sin \frac{25\pi }{3}\right\}$ is
(where $\{.\}$ is fractional part function)

1. $0$
2. $\frac{1}{2}$
3. $\frac{\sqrt{3}}{2}$
4. $\frac{1}{\sqrt{2}}$

Q.

Solve the triangle in which $a=(\sqrt{3}+1),b=(\sqrt{3}-1)and\angle C={60}^{\circ }$

Q. If $a=\cot 5^c$, then

1. $a>0$
2. $a<0$
3. $a=0$
4. none of these

Q. If z = x + iy lies in fourth quadrant then zbar lies in

Q.

Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm $(\text{use}\pi =\frac{22}{7})$.

Q. 6. sin 765°

Q. If $(x-2{)}^{\circ }$ and $(2x+5{)}^{\circ }$ are supplementary angles, then the value of $x$ is

1. ${57}^{\circ }$
2. ${63}^{\circ }$
3. ${61}^{\circ }$
4. ${59}^{\circ }$

Q. The radius of the circle whose arc of length 15 π cm makes an angle of $\frac{3\mathrm{\pi }}{4}$ radian at the centre is
(a) 10 cm
(b) 20 cm
(c) $11\frac{1}{4}\mathrm{cm}$
(d) $22\frac{1}{2}\mathrm{cm}$

Q. 7. cosec ( 1410°)

Q. If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, find the ratio of their radii.

Q.

Which of the following is incorrect

1. 

2. 

3. 

4. 

Q.

How many of the following are matched correctly?

$\begin{array}{cc}\text{Degree measurement}& \text{Radian measurement}\\ \text{(A)}{180}^{\circ }& \text{(1)}\pi \\ \text{(B)}{60}^{\circ }& \text{(2)}\frac{\pi }{6}\\ \text{(C)}{0}^{\circ }& \text{(3)}0\\ \text{(D)}{120}^{\circ }& \text{(4)}2\frac{\pi }{6}\\ \text{(E)}{360}^{\circ }& \text{(5)}2\pi \\ \text{(F)}{30}^{\circ }& \text{(6)}\frac{\pi }{3}\\ \text{(G)}{90}^{\circ }& \text{(7)}\frac{\pi }{2}\\ \text{(H)}{45}^{\circ }& \text{(8)}\frac{\pi }{4}\\ \text{(I)}{270}^{\circ }& \text{(9)}3\pi \end{array}$
___

Q.

How many of the following are matched correctly?

Degree measurement Radian measurement

(A) ${180}^{\circ }$ (1) $\pi$
(B) ${60}^{\circ }$ (2) $\frac{\pi }{6}$
(C) $0^{\circ }$ (3) 0
(D) ${120}^{\circ }$ (4) $\frac{2\pi }{6}$
(E) ${360}^{\circ }$ (5) $2\pi$
(F) ${30}^{\circ }$ (6) $\frac{\pi }{3}$
(G) ${90}^{\circ }$ (7) $\frac{\pi }{2}$
(H) ${45}^{\circ }$ (8) $\frac{\pi }{4}$
(I) ${270}^{\circ }$ (9) $3\pi$

___

Q. If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, than the ratio of the radii of the circles is
(a) 22 : 13
(b) 11 : 13
(c) 22 : 15
(d) 21 : 13

Q. If both $\theta$ and $\varphi$ are acute angles such that $\sin \theta =\frac{1}{2}$ and $\cos \varphi =\frac{1}{3}$, then $(\theta +\varphi )$ belongs to

1. $(\frac{\pi }{3},\frac{5\pi }{12})$
2. $(\frac{\pi }{2},\frac{2\pi }{3})$
3. $(\frac{2\pi }{3},\frac{5\pi }{6})$
4. $(\frac{5\pi }{12},\frac{\pi }{2})$

Q. An angle $\theta$ in degrees can be converted to an angle in radians by multiplying $\theta$ by $\frac{180}{\pi }$.

1. True
2. False

Q.

The equation of the circle with origin as centre passing the vertices of an equilateral triangle whose median

is of length 3a is

1. 

2. 

3. 

4. 

Q.

Solve $\sqrt{3}cosx+sinx=\sqrt{2}.$

Q. $x^{\circ }=$ radian and $x$ radian $=$ degree

1. $\frac{180}{\pi }\times x$
2. $\frac{360}{\pi }\times x$
3. $\frac{\pi }{360}\times x$
4. $\frac{180}{\pi }\times \frac{1}{x}$
5. $\frac{\pi }{180}\times x$

Q. $Iftan\theta +3cot\theta =5sec\theta then\theta =$

1. 
2. 
3. 
4. 

Q.

How do you convert $\text{2π over 3}$ into degrees?

Q. Let $f:R\to R$ and $g:R\to R$ be two functions given by $f\left(x\right)=2x-3,g\left(x\right)=x^3+5.$ Then ${\left(fog\right)}^{-1}\left(x\right)$ is equal

1. ${\left(\frac{x+7}{2}\right)}^{1/3}$
2. ${\left(\frac{x-2}{7}\right)}^{1/3}$
3. ${(x-\frac{7}{2})}^{1/3}$
4. ${\left(\frac{x-2}{2}\right)}^{1/3}$

Q.

A circular wire of diameter 10cm is cut and placed along the circumference of a circle of diameter 1 metre. The angle subtended by the wire at the centre of the circle is equal to

1. $\frac{\pi }{4}$ radian

2. $\frac{\pi }{3}$ radian

3. $\frac{\pi }{5}$ radian

4. $\frac{\pi }{10}$ radian