MCQ

MCQ 11 Mark

The angle between the minute and hour hands of a clock at 8 : 30 is:

A
80°
✓
75°
C
60°
D
105°

Answer

Correct option: B.

75°

We know that the hour of a clock completes one rotation in 12 hours.
Angle traced by the hour hand in 12 hours = 360°
Now,
Angle traced by the hour hand in 8 hours 30 minutes, i.e.
We also know that the minute hand of a clock completes one rotation in 60 minutes.
Angle traced by the minute hade in 30 minutes $=\Big(\frac{360}{60}\times30^{\circ}\Big)=180^{\circ}$
Required angle between the two hands of the clock = 255° - 180° = 75°

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MCQ 21 Mark

If the angles of a triangle are in $A.P.$ then the measures of one of the angles in radians is:

A
$\frac{\pi}{6}$
✓
$\frac{\pi}{3}$
C
$\frac{\pi}{2}$
D
$\frac{2\pi}{3}$

Answer

Correct option: B.

$\frac{\pi}{3}$

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MCQ 31 Mark

The radius of the circle whose arc of length $15\pi$ makes an angle of $\frac{3\pi}{4}$ radian at the centre is:

A
$10\text{cm}$
✓
$20\text{cm}$
C
$11\frac{1}{4}\ \text{cm}$
D
$22\frac{1}{2}\ \text{cm}$

Answer

Correct option: B.

$20\text{cm}$

$20\text{cm}$

Solution:
$\theta=\frac{\text{Arc}}{\text{Radius}}$
$\Rightarrow\frac{3\pi}{4}=\frac{15\pi}{\text{Radius}}$
$\Rightarrow\frac{60}{3}$
$\Rightarrow20\text{cm}$

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MCQ 41 Mark

If the arac of the same langth in two circles subtend angles 65° and 110° at the center, the ratio of the circle is:

✓
22 : 13
B
11 : 13
C
22 : 15
D
21 : 13

Answer

Correct option: A.

22 : 13

Let the angle subtended at the by the arec and radii of the first second circle $\theta_{1}$ and $\text{r}_{1}$ and $\theta_{2}$ and $\text{r}_{2}.$
We have,
$\theta_{1}=65^{\circ}=\Big(65\times\frac{\pi}{180}\Big)\ \text{radian}$
$\theta_{2}=65^{\circ}=\Big(110\times\frac{\pi}{180}\Big)\ \text{radian}$
$\theta_{1}=\frac{1}{\text{r}_{1}}$
$\Rightarrow \text{r}_{1}=\frac{1}{\big(65\times\frac{\pi}{180}\big)}$
$\Rightarrow \text{r}_{2}=\frac{1}{\big(110\times\frac{\pi}{180}\big)}$
$\frac{\text{r}_{1}}{\text{r}_{2}}=\frac{\frac{l}{\big(65\times\frac{\pi}{180}\big)}}{\frac{i}{\big(110\times\frac{\pi}{180}\big)}} $
$=\frac{110}{65}=\frac{22}{13}$
$\text{r}_{1}:\text{r}_{2}=22:13$

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MCQ 51 Mark

If OP makes 4 revolutions in on second the angular velocity in radians per seconds is:

A
$\pi$
B
$2\pi$
C
$4\pi$
✓
$8\pi$

Answer

Correct option: D.

$8\pi$

$\text{Angular velocity}=\frac{\text{Distance}}{\text{Time}}$
$=\frac{4\times2\pi}{1}$
$=8\pi\ \text{radians}$

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MCQ 61 Mark

If D, G and R denote respectively the number of degrees, grades and radians in an angle, then:

A
$\frac{\text{D}}{100}=\frac{\text{G}}{90}=\frac{2\text{R}}{\pi}$
B
$\frac{\text{D}}{90}=\frac{\text{G}}{100}=\frac{\text{R}}{\pi}$
✓
$\frac{\text{D}}{100}=\frac{\text{G}}{100}=\frac{2\text{R}}{\pi}$
D
$\frac{\text{D}}{90}=\frac{\text{G}}{100}=\frac{\text{R}}{\pi}$

Answer

Correct option: C.

$\frac{\text{D}}{100}=\frac{\text{G}}{100}=\frac{2\text{R}}{\pi}$

It is the relation between degree, grade and radian.

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MCQ 71 Mark

At 3 : 40, the hour and minute hands of a clock are inclined at:

A
$\frac{2\pi^{\text{c}}}{3}$
B
$\frac{7\pi^{\text{c}}}{12}$
✓
$\frac{13\pi^{\text{c}}}{18}$
D
$\frac{13\pi^{\text{c}}}{4}$

Answer

Correct option: C.

$\frac{13\pi^{\text{c}}}{18}$

We know that the hour of a clock completes one rotation in 12 hours = 360°
Angle traced by the hour hand in 12 hours = 360°
Now,
Angle traced by the hour hand in 8 hours 30 minutes, i.e.
We also know that the minute hand of a clock completes one rotation in 60 minutes.
Angle traced by the minute hade in 30 minutes $=\Big(\frac{360}{60}\times40^{\circ}\Big)=240^{\circ}$
Required angle between the two hands of the clock = 240° - 110° = 130°
Value of the angle (in radians) between the two hands of the clock $\Big(130\times\frac{\pi}{180}\Big)^{\text{c}}=\frac{13\pi^{\text{c}}}{18}$

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