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Test: Measurement of Angles - JEE MCQ


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20 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Measurement of Angles

Test: Measurement of Angles for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Measurement of Angles questions and answers have been prepared according to the JEE exam syllabus.The Test: Measurement of Angles MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Measurement of Angles below.
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Test: Measurement of Angles - Question 1

What is the degree measure of the angle A = -15π/2? 

Test: Measurement of Angles - Question 2

A pendulum 36 cm long oscillates through an angle of 10 degrees. Find the length of the path described by its extremity.

Detailed Solution for Test: Measurement of Angles - Question 2


= 6.280 cm

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Test: Measurement of Angles - Question 3

In the fourth quadrant the value of cosine function

Detailed Solution for Test: Measurement of Angles - Question 3

As the angle increases from 270° to 360°, the sine increases from -1 to 0. As the angle increases from 270° to 360°, and the value of cos 270° = 0
and cos 360° = 1
So, the cosine increases from 0 to +1.

Test: Measurement of Angles - Question 4

A wire of length 15 cm is bent to form an arc of a circle with radius 6 cm. Find in radians the angle subtended at the centre.

Detailed Solution for Test: Measurement of Angles - Question 4

Length of arc = 15 cm
Radius: R = 6 cm
Arc length = R*θ
(θ is the angle subtended by the arc)
15 = 6*θ
θ = 5/2 radians

Test: Measurement of Angles - Question 5

The degree measure of the radian angle 5π/4 is

Detailed Solution for Test: Measurement of Angles - Question 5

Test: Measurement of Angles - Question 6

In the third quadrant the value of the sine function

Detailed Solution for Test: Measurement of Angles - Question 6

In The Third Quadrant
As the angle increases from 180° to 270°, the sine increases in magnitude but is now negative, so, the sine decreases from 0 to -1.

Test: Measurement of Angles - Question 7

The value of cosx in the second quadrant

Detailed Solution for Test: Measurement of Angles - Question 7

Second quadrant is from 90° to 180°
As we know that cos90° = 0, cos180° = -1
So the value of cos is decreasing from 0 to -1

Test: Measurement of Angles - Question 8

What is the radius of the circle in which a central angle of 60° intercepts an arc length of 48.4 cm?

Detailed Solution for Test: Measurement of Angles - Question 8

Test: Measurement of Angles - Question 9

A cyclist travels at the rate of 14.4 km/hr and the radius of the wheel is 35 cm. What is the measure of the angle in radian through which a spoke of the wheel will turn in one second?

Detailed Solution for Test: Measurement of Angles - Question 9

First of all change the speed into m/s. You will get 4 m/s. It means that the wheel moves 4 metres a second i.e arc subtended by the wheel per second is 4m. Now, as we know that angle= arc÷radius. So, divide 4m by 0.35m ( convert 35 cm into metre or 4m into cm, as you wish). So, angle= (400÷35) radians = 80/7 radians. So, the answer is b).

Test: Measurement of Angles - Question 10

What is the approximate value of 1 radian in degree measure?

Detailed Solution for Test: Measurement of Angles - Question 10

The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees.

Test: Measurement of Angles - Question 11

Convert 135° into radians?

Detailed Solution for Test: Measurement of Angles - Question 11
135×π\180
=3π\4
Test: Measurement of Angles - Question 12

A train is travelling on a curve of 350 m radius at 7 Km/hr. Through what angle will it turn in one minute?

Detailed Solution for Test: Measurement of Angles - Question 12

length of arc = 350m
Speed = 7km/hr
In one minute = (7*5/18*60)
=> (35*20)/6
= length of arc/radius
θ = (35*20)/(6*350)
θ = 1/3 radian

Test: Measurement of Angles - Question 13

Find the central angle of the circle whose diameter is 20 cm subtended by an arc of length 15.4 cm.

Detailed Solution for Test: Measurement of Angles - Question 13

Test: Measurement of Angles - Question 14

Find the length of arc of the circle whose diameter is 14 m and which subtends an angle of 1° at the centre.

Detailed Solution for Test: Measurement of Angles - Question 14

 r =7 m, θ = 1°
Length subtended by Arc = (2πr/360o)×θ
= (2×22×7×1)/(7×360)
​= 0.12m

Test: Measurement of Angles - Question 15

What is the angle in degrees swept by the minute hand of a clock between 9.00 a.m. and 9.35 a.m.?

Detailed Solution for Test: Measurement of Angles - Question 15

We know angle described by minute hand in 60 mins = 360°
Angle described by the minute hand in one minute = 360°/60 = 6°
Time interval between 9AM to 9:35 AM = 35 min

Test: Measurement of Angles - Question 16

What will be the angle in degree if the value of the angle in radians is 5π/12

Detailed Solution for Test: Measurement of Angles - Question 16
5π\12×180/π
=900/12
=75 degree
Test: Measurement of Angles - Question 17

A wheel makes 360 revolutions in 1 minute. Through how many radians does it turn in 3 seconds?

Detailed Solution for Test: Measurement of Angles - Question 17

Number of revolutions made by the wheel in 1 minute = 360
∴ Number of revolutions made by the wheel in 1 second = 360/(60) = 6
In 3 seconds = (6*3) = 18
In one complete revolution, the wheel turns an angle of 2π radian.
Hence, in 6 complete revolutions, it will turn an angle of 18 × 2π radian, i.e.,
36 π radian
Thus, in one second, the wheel turns an angle of 36π radian.

Test: Measurement of Angles - Question 18

What is the length of arc of a circle whose radius is 14 cm and which subtends an angle of 135° at the centre?

Detailed Solution for Test: Measurement of Angles - Question 18

Radius of circle =14cm
An angle = 135o
Length of arc = ?
We know that, Length of arc = Radius × Angle
= 14 * 3π/4
= 14 * (3*22)/(7*4)
= 33cm

Test: Measurement of Angles - Question 19

An object is moving on the circle of radius 7 cm in clockwise direction with a speed of 10 cm/s. find the angle in radians covered by it in 10 sec when it starts at 0 degree.

Detailed Solution for Test: Measurement of Angles - Question 19


Test: Measurement of Angles - Question 20

A cow is tethered to a corner of a field with a rope of length 7 m. If she grazes on the length of 210 m, what is the angle through which the rope moves?

Detailed Solution for Test: Measurement of Angles - Question 20

We know that in a circle of radius r units, if an arc of length l units subtends an angle theta radian at the centre, then θ = l/ r.
Here, r = 7 m (length of rope will be equal to radius) and l = 210 m (length of arc will be the length which the cow grazed)
Thus, θ = 210o/ 7 
= 30o

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