Radians or degrees - class-X

radians or degrees

21 Questions Published

Questions

Question 1 Multiple Choice (Single Answer)

$\dfrac{\cos(90-A)\sin(90-A)}{\tan (90-A)}$=

  1. $\sin^{2}A$
  2. $\cos^{2}A$
  3. $\sin A$
  4. $1$
Question 2 Multiple Choice (Single Answer)

The value of $ \displaystyle 36^{\circ} $ in radians is 

  1. $ \displaystyle \frac{\pi }{2} $
  2. $ \displaystyle \frac{2\pi }{5} $
  3. $ \displaystyle \frac{\pi }{5} $
  4. $ 3\pi $
Question 3 Multiple Choice (Single Answer)

A unit radian is approximately equal to

  1. $57^{\circ} 17' 43"$
  2. $57^{\circ} 17' 45"$
  3. $57^{\circ} 17' 47"$
  4. $57^{\circ} 17' 49"$
Question 4 Multiple Choice (Single Answer)

The value of $\cot 15^{\circ} \cot 20^{\circ} \cot 70^{\circ} \cot 75^{\circ}$ is equal to

  1. $-1$
  2. $0$
  3. $1$
  4. $2$
Question 5 Multiple Choice (Single Answer)

Consider the following statements :
1. $1^o$ in radian measure is less than 0.02 radians.
2. 1 radian in degree measure is greater than $45^o$ 
Which of the above statements is/are correct ?

  1. 1 only
  2. 2 only
  3. Both 1 and 2
  4. Neither 1 nor 2
Question 6 Multiple Choice (Single Answer)

If $\tan 45^{\circ} = \cot \theta$, then the value of $\theta$, in radians is

  1. $\pi$
  2. $\dfrac{\pi}{9}$
  3. $\dfrac{\pi}{4}$
  4. $\dfrac{\pi}{12}$
Question 7 Multiple Choice (Single Answer)

The value of $cos^{2}30^{0}-cos^{2}60^{0}-cos 60^{0}$ is

  1. $0$
  2. $\dfrac{1}{2}$
  3. $\dfrac{3}{4}$
  4. $1$
Question 8 Multiple Choice (Multiple Answers)

If $A+B=\dfrac { \pi  }{ 3 } $ and $\cos { A } +\cos { B } =1 $, then which of the following are true: 

  1. $\cos { \left( A-B \right) =\dfrac { 1 }{ 3 } } $
  2. $\cos { \left( A-B \right) =-\dfrac { 1 }{ 3 } } $
  3. $\left| \cos { A } -\cos { B } \right| =\sqrt { 2/3 } $
  4. $\left| \cos { A } -\cos { B } \right| =\cfrac { 1 }{ \sqrt { 3 } } $
Question 9 Multiple Choice (Single Answer)

The angle subtended at the centre of circle of radius $3$ metres by an arc of length $1$ metre is equal to

  1. $20^\circ $
  2. $60^\circ $
  3. $\dfrac{1}{3}\,radian$
  4. $\,3\,radian$
Question 10 Multiple Choice (Single Answer)

The value of $\dfrac{1}{\cos 290^o}+\dfrac{1}{\sqrt{3}\sin 250^o}$ is?

  1. $\dfrac{2\sqrt{3}}{3}$
  2. $\dfrac{4\sqrt{3}}{3}$
  3. $\sqrt{3}$
  4. None
Question 11 Multiple Choice (Single Answer)

Find the degree measure corresponding to $\left(\dfrac{1}{6}\right)^C$.

  1. $9.549^\circ$
  2. $9^032$ $43.6"$
  3. $10^0$
  4. None
Question 12 Multiple Choice (Multiple Answers)

If $\cos x=\sqrt{1-\sin2x},0\le x\le \pi$, then possible  value of $x$ is 

  1. $\pi$
  2. $0$
  3. $\tan^{-1}2$
  4. $3\pi$
Question 13 Multiple Choice (Single Answer)

The area of a sector of a circle of radius $7\ cm$ and central angle $120^{o}$ is 

  1. $152\ cm^{2}$
  2. $\dfrac{154}{3}\ cm^{2}$
  3. $\dfrac{128}{3}\ cm^{2}$
  4. $128\ cm^{2}$
Question 14 Multiple Choice (Single Answer)

$\displaystyle \frac{\pi ^{c}}{5}$ in sexagesimal measure is _____

  1. $\displaystyle 18^{\circ}$
  2. $\displaystyle 36^{\circ}$
  3. $\displaystyle 54^{\circ}$
  4. $\displaystyle 72^{\circ}$
Question 15 Multiple Choice (Single Answer)

The value of $\displaystyle 144^{\circ}$ in circular measure is ___ 

  1. $\displaystyle \frac{3\pi ^{c}}{4}$
  2. $\displaystyle \frac{2\pi ^{c}}{3}$
  3. $\displaystyle \frac{4\pi ^{c}}{5}$
  4. $\displaystyle \frac{5\pi ^{c}}{6}$
Question 16 Multiple Choice (Single Answer)

Find the angle measure of $4$ radians.

  1. $114.591^{\circ}$
  2. $141.372^{\circ}$
  3. $229.183^{\circ}$
  4. $282.743^{\circ}$
  5. $458.366^{\circ}$
Question 17 Multiple Choice (Single Answer)

1 radian =

  1. $58^0.17$
  2. $65^0.17$
  3. $57^0.30$
  4. $66^0.71$
Question 18 Multiple Choice (Single Answer)

If $\displaystyle\cot  \theta+\left ( \frac{1}{\sqrt{3}} \right )\sin \theta =\frac{2}{\sqrt{3}} $ then find $\displaystyle \theta $ in circular measure

  1. $\displaystyle \frac{\pi ^{2}}{2} $
  2. $\displaystyle \frac{\pi ^{2}}{3} $
  3. $\displaystyle \frac{\pi ^{2}}{4} $
  4. $\displaystyle \frac{\pi ^{2}}{6} $
Question 19 Multiple Choice (Single Answer)

The degree measure of 1 radian (taking $\pi =\dfrac { 22 }{ 7 }$ ) is

  1. $55^o{ 61 }^{ ' }{ 22 }^{ " }$ (approx.)
  2. $57^o{ 16 }^{ ' }{ 22 }^{ " }$ (approx.)
  3. $57^o{ 22 }^{ ' }{ 16 }^{ " }$ (approx.)
  4. $57^o{ 22 }^{ ' }{ 22 }^{ " }$ (approx.)
Question 20 Multiple Choice (Single Answer)

Convert $40^\circ ,20'$ into radian measure.

  1. $\dfrac {121}{540}\pi $ radians
  2. $\dfrac {121}{570}\pi $ radians
  3. $\dfrac {120}{513}\pi $ radians
  4. None
Question 21 Multiple Choice (Single Answer)

Find the radian measure corresponding to the degree $-47^{o}30'$

  1. $\dfrac {-19\ \pi}{72}rad$
  2. $\dfrac {19\ \pi}{72}rad$
  3. $\dfrac {13\ \pi}{72}rad$
  4. $None\ of\ these$