CDS MATHEMATICS QUIZ 1

Question 1:

The maximum value of $\sin \theta+\cos \theta$ is:

1

$\sqrt{2} $

2

3

Question 2:

An arc in a circle makes an angle of $45^{\circ}$ at the centre. If the length of the arc is 11 cm, then find the radius of the circle.

$12 \mathrm{~cm}$

$21 \mathrm{~cm}$

$14 \mathrm{~cm}$

$7 \mathrm{~cm}$

Question 3:

Length of the arc of the sector-

$\frac{2 \pi r}{360} \times \theta$

$\frac{\pi r}{360^{\circ}} \times \theta$

$\frac{2 r \theta}{360^{\circ}}$

$\frac{ r \theta}{360^{\circ}}$

Question 4:

IF arcs of equal length of two circles subtend angles of $60^{\circ}$ and $75^{\circ}$ respectively at their centers, then find the ratio of their radii.

$4: 5$

$5: 4$

$3: 4$

$4: 3$

Question 5:

What is the simplified value of $\operatorname{cosec} 2 A+\cot 2 A$ ?

$\sec A $

$\sec\frac{\mathrm{A}}{2}$

$\cot A $

$\cot ^{2} A$

Question 6:

IF $A=30^{\circ}, B=60^{\circ}$ and $C=135^{\circ}$, then what is the value of $\sin ^{3} A+\cos ^{3} B+\tan ^{3} C-$ $3 \sin A \cos B \tan C$.

0

1

8

9

Question 7:

If $\theta$ be acute angle and $\tan \left(4 \theta-50^{\circ}\right)=\cot \left(50^{\circ}-\theta\right)$, then the value of $\theta$ in degrees is.

$20^{\circ}$

$50^{\circ}$

$40^{\circ}$

$30^{\circ}$

Question 8:

IF the sum and difference of two angles are $145^{\circ}$ and $\frac{\pi}{12}$ respectively, then the value of the angles in degree measure are.

$70^{\circ}, 65^{\circ}$

$75^{\circ}, 60^{\circ}$

$45^{\circ}, 90^{\circ}$

$80^{\circ}, 65^{\circ}$

Question 9:

$\left(\frac{3 \pi}{5}\right)$ radians is equal to:

$118^{\circ}$

$180^{\circ}$

$110^{\circ}$

$108^{\circ}$

Question 10:

The degree measure of 2 radian. $ use (\pi=22 / 7)$

$114^{\circ} 51^{\prime} 22^{\prime \prime}$ (approx.)

$114^{\circ} 36^{\prime} 22^{\prime \prime}$ (approx.)

$114^{\circ} 42^{\prime} 16^{\prime \prime}$ (approx.)

$114^{\circ} 32^{\prime} 43^{\prime \prime}$ (approx.)