Angle and its Measurement - Maharashtra Board STD 11 Maths Questions

Q 1MCQ1 Mark

The central angle of a sector of circle of area 9π sq.cm is 60°, the perimeter of the sector is

A
π
B
3 + π
✓
6 + π
D
6

Answer: C.

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Q 2MCQ1 Mark

Find the measure of the angle between hour- hand and the minute hand of a clock at twenty minutes past two.

✓
50°
B
60°
C
54°
D
65°

Answer: A.

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Q 3MCQ1 Mark

20 metres of wire is available for fencing off a flower-bed in the form of a circular sector of radius 5 metres, then .the maximum area (in sq. m.) of the flower-bed is

A
15
B
20
✓
25
D
30

Answer: C.

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Q 4MCQ1 Mark

Angle between hands of a clock when it shows the time 9 :45 is

A
(7.5)°
B
(12.5)°
C
(17.5)°
✓
(22.5)°

Answer: D.

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Q 5MCQ1 Mark

A pendulum 14 cm long oscillates through an angle of 12°, then the angle of the path described by its extremities is

A
$\frac{13 \pi}{14}$
B
$\frac{14 \pi}{13}$
C
$\frac{15 \pi}{14}$
✓
$\frac{14 \pi}{15}$

Answer: D.

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Q 6Solve the following Question.(1 Marks)1 Mark

Show that minute-hand of a clock gains 5° 30′ on the hour-hand in one minute.

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Q 7Solve the following Question.(1 Marks)1 Mark

A wire of length 10 cm is bent so as to form an arc of a circle of radius 4 cm. What is the angle subtended at the centre in degrees ?

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Q 8Solve the following Question.(1 Marks)1 Mark

Find the number of sides of a regular polygon if each of its interior angle is
$
\left(\frac{4 \pi}{5}\right)^c
$

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Q 9Solve the following Question.(1 Marks)1 Mark

ABCDEFGH is a regular octagon inscribed in a circle of radius 9cm. Find the length of minor arc AB.

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Q 10Solve the following Question.(1 Marks)1 Mark

A pendulum of length 21cm oscillates through an angle of 36°. Find the length of its path.

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Q 11Solve the Following Question.(2 Marks)2 Marks

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

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Q 12Solve the Following Question.(2 Marks)2 Marks

The area of a circle is $81$ TH sq.cm. Find the length of the arc subtending an angle of $300^\circ$ at the centre and also the area of corresponding sector.

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Q 13Solve the Following Question.(2 Marks)2 Marks

Find the radius of the circle in which a central angle of $60^\circ$ intercepts an arc of length $37.4\ cm.$

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Q 14Solve the Following Question.(2 Marks)2 Marks

Find the number of sides of a regular polygon, if each of its interior angles is $\frac{3 \pi^c}{4}$.

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Q 15Solve the Following Question.(2 Marks)2 Marks

One angle of a quadrilateral is $\frac{2 \pi}{9}$ radian and the measures of the other three angles are in the ratio $3: 5: 8$, find their measures in degree.

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Q 16Solve the Following Question.(3 Marks)3 Marks

A train is running on a circular track of radius 1 km at the rate of 36 km per hour. Find the angle to the nearest minute, through which it will turn in 30 seconds.

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Q 17Solve the Following Question.(3 Marks)3 Marks

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

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Q 18Solve the Following Question.(3 Marks)3 Marks

∆PQR is an equilateral triangle with side 18 cm. A circle is drawn on segment QR as diameter. Find the length of the arc of this circle within the triangle.

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Q 19Solve the Following Question.(3 Marks)3 Marks

The measures of the angles of the triangle are in A. P. The smallest angle is 40. Find the angles of the triangle in degree and in radian.

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Q 20Solve the Following Question.(3 Marks)3 Marks

In a circle of radius 12 cms, an arc PQ subtends an angle of 30° at the centre. Find the area between the arc PQ and chord PQ.

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Q 21Complete the following activities and rewrite it : (3M)3 Marks

Draw the angle ABC of measure 40°

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Q 22Solve the Following Question.(4 Marks)4 Marks

The angles of a quadrilateral are in A.P. and the greatest angle is double the least. Find angles of the quadrilateral in radians.

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Q 23Solve the Following Question.(4 Marks)4 Marks

Two circles each of radius 7 cm, intersect each other. The distance between their centres is 7√2 cm. Find the area common to both the circles.

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Q 24Solve the Following Question.(4 Marks)4 Marks

Find the angle between hour hand and minute hand of a clock at
i) Quarter past five
ii) Quarter to twelve

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Q 25Solve the Following Question.(4 Marks)4 Marks

OPQ is the sector of a circle having centre at O and radius 15 cm. If m∠POQ = 30°, find the area enclosed by arc PQ and chord PQ.

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Q 26Solve the Following Question.(4 Marks)4 Marks

One angle of a quadrilateral has measure $\frac{2π^C}{5}$ and the measures of other three angles are in the ratio $2:3:4.$ Find their measures in degrees and radians.

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Angle and its Measurement question types

Angle and its Measurement questions

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Angle and its Measurement Maths - Angle and its Measurement

Angle and its Measurement question types

Angle and its Measurement questions

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