The circular wire of diameter ${\rm{10}}\,\,{\rm{cm}}$ is cut and placed along the circumference of a circle of diameter ${\rm{1 m}}$. The angle subtended by the wire at the center of the circle is equal to

$\frac{\pi }{4}\,\,{\rm{rad}}\;$

$\frac{\pi }{3}\;\,\,{\rm{rad}}$

Back to CIRCLES

Your Progress

0 / 685 Answered

Correct

Incorrect

Accuracy

JEE • MATHEMATICS • CIRCLES

Circles practice · Mixed difficulty

Choose an answer to check it, or open “View answer” to study the explanation. Sign in to save progress to your account.

Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

Take a chapter quiz →

Showing 181-210 of 685 questions

Preparing practice and saved progress…

181 Easy

181 of 685

Application +4 | -1

The locus of a point, which moves such that the lengths of the tangents from it two concentric circles of radii

a

and

b

are inversely proportional to their radii is a circle with radius

View answer and explanation

Correct option: C

\sqrt{a^2+b^2}

Option C (

\sqrt{a^2+b^2}

) is correct because it represents the radius of the circle formed by the locus of points where the tangent lengths are inversely proportional to the radii of the two concentric circles.

182 Easy

182 of 685

Application +4 | -1

If the circle

(x-2)^2+(y-3)^2=a^2

lies entirely with in the circle

x^2+y^2=b^2

, then

View answer and explanation

Correct option: C

b-a > \sqrt{13}

Option C (

b-a > \sqrt{{13}}

) is correct because the distance between the centers of the circles must be less than the difference of their radii for one circle to lie entirely within the other.

183 Easy

183 of 685

Application +4 | -1

One of the diameter of the circle

{x^2} + {y^2} - 12x + 4y + 6 = 0

is given by

View answer and explanation

Correct option: B

x + 3y = 0

Option B (

x + 3y = 0

) is correct because it passes through the center of the circle, which is a necessary condition for a diameter.

184 Easy

184 of 685

Application +4 | -1

The tangent at

P

, any point on the circle

{x^2} + {y^2} = 4,

meets the coordinate axes in

A

and

B

, then

View answer and explanation

Correct option: C

The locus of the mid-point of

AB

{x^2} + {y^2} = {x^2}{y^2}

Option C (The locus of the mid-point of

AB

{x^2} + {y^2} = {x^2}{y^2}

) is correct because it's derived from finding the equation of the tangent to the circle and then determining the locus of the midpoint of the intercepts on the axes.

185 Easy

185 of 685

Application +4 | -1

The equation of the image of the circle

(x-3)^2+(y-2)^2=1

by the mirror

x+y=19

View answer and explanation

Correct option: D

(x-17)^2+(y-16)^2=1

Option D (

(x-17)^2+(y-16)^2=1

) is correct because it represents the circle with the center being the reflection of the original center across the given line.

186 Medium

186 of 685

Application +4 | -1

If two tangents from point

(3,-2)

to the circle

x^2+y^2=1

cuts

x

-axis at

A\left(x_1, 0\right)

and

B\left(x_2, 0\right)

, then

\left(\mathrm{x}_1+\mathrm{x}_2\right)

is equal to

View answer and explanation

Correct option: C

-2

Option C (-2) is correct because solving the equation

\mathrm{SS}_1=\mathrm{T}^2

with

\mathrm{y}=0

gives a quadratic equation whose sum of roots is -2.

187 Medium

187 of 685

Application +4 | -1

If two chords having lengths

{a^2} - 1

and

3\left( {a + 1} \right)

, where

a

is a constant of a circle bisect each other, then the radius of the circle is

View answer and explanation

Correct option: B

\frac{{15}}{2}

The correct answer is B (15/2) because when two chords bisect each other, they are diameters, implying equal lengths, which allows solving for 'a' and then finding the radius.

188 Easy

188 of 685

Application +4 | -1

The locus of a point which moves in a plane so that the sum of the squares of its distances from the line

a x+b y+c=0

and

b x-a y+d=0

r^2

, is a circle of radius

View answer and explanation

Correct option: A

r

Option A (

r

) is correct because the locus of the point is a circle, and its radius is found by simplifying the given equation and comparing it to the standard circle equation.

189 Easy

189 of 685

Application +4 | -1

If the locus of the mid-point of the line segment from the point (3, 2) to a point on the circle,

{x^2} + {y^2} = 1

is a circle of radius

r

, then

r

is equal to

View answer and explanation

Correct option: B

01-Feb

Option B (0.5) is correct because the radius of the locus of the midpoint is half the radius of the original circle.

190 Easy

190 of 685

Application +4 | -1

The lines

3 x-4 y+\lambda=0

and

6 x-8 y+\mu=0

are tangents to the same circle. The radius of the circle is

View answer and explanation

Correct option: A

\left|\frac{2 \lambda-\mu}{20}\right|

Option A,

\left|\frac{{2 \lambda-\mu}}{{20}}\right|

, is correct because it represents half the distance between the two parallel tangent lines, which is the radius of the circle.

191 Medium

191 of 685

Analyzing +4 | -1

The locus of the centre of the circle which touches

(y-1)^2+x^2=1

externally and also touches

x

-axis, is

View answer and explanation

Correct option: A

\left\{(x, y): x^2=4 y\right\} \cup\{(0, y): y<0\}

Option A (

\left\{(x, y): x^2=4 y\right\} \cup\{(0, y): y<0\}

) is correct because it represents the locus of the center of the circle touching the given circle externally and the x-axis.

192 Hard

192 of 685

Application +4 | -1

One of the diameters of the circle circumscribing the rectangle

ABCD

4y = x + 7.

A

and

B

are the points

\left( { - 3,4} \right)

and

\left( {5,4} \right)

respectively, then the area of the rectangle is

View answer and explanation

Correct option: C

32 sq. units

Option C (32 sq. units) is correct because it is derived from finding the center of the circle, the length of the rectangle, and the perpendicular distance to determine the width.

193 Medium

193 of 685

Analyzing +4 | -1

Choose the incorrect statement about the two circles whose equations are given below

{x^2} + {y^2} - 10x - 10y\mathrm{ } + 41\mathrm{ } = \mathrm{ }0

and

{x^2} + {y^2} - \mathrm{ }16x\mathrm{ }-\mathrm{ }10y\mathrm{ } + \mathrm{ }80\mathrm{ } = \mathrm{ }0

View answer and explanation

Correct option: B

Both circles centres lie inside region of one another

Option B (Both circles centres lie inside region of one another) is the incorrect statement because the centers of each circle lie on the circumference of the other, not inside.

194 Easy

194 of 685

Application +4 | -1

The circular wire of diameter

\mathrm{10}\,\,\mathrm{cm}

is cut and placed along the circumference of a circle of diameter

\mathrm{1 m}

. The angle subtended by the wire at the center of the circle is equal to

View answer and explanation

Correct option: C

\frac{\pi }{5}\,\,\mathrm{rad}

Option C (

\frac{\pi }{5}\,\mathrm{rad}

) is correct because the angle subtended is calculated by dividing the arc length (circumference of the small circle) by the radius of the larger circle.

195 Easy

195 of 685

Application +4 | -1

If the lines

3 x-4 y-7=0

and

2 x-3 y-5=0

are two diameters of a circle of area

49 \pi

square units, the equation of the circle is

View answer and explanation

Correct option: D

x^2+y^2-2 x+2 y-47=0

Option D (

x^2+y^2-2 x+2 y-47=0

) is correct because it represents the equation of a circle with the given area and center at the intersection of the two diameters.

Explore Other Chapters in MATHEMATICS

View All →

SEQUENCE OF SERIES 1764 MCQs DEFINITE INTEGRATION 1443 MCQs MATRICES 1363 MCQs INDEFINITE INTEGRATION 1179 MCQs PROBABILITY 1146 MCQs COMPLEX NUMBERS 980 MCQs

196 Easy

196 of 685

Understanding +4 | -1

The centre of the circle

x=2+3 \cos \theta

y=3 \sin \theta-1

, is

View answer and explanation

Correct option: B

(2,-1)

Option B (2,-1) is correct because the center can be directly identified from the parametric equations by rewriting them in the standard circle equation form.

197 Easy

197 of 685

Application +4 | -1

The equation of circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length

3 {a}

{x}^2+{y}^2={ka}^2

, where

{k}=

View answer and explanation

Correct option: A

Option A (4) is correct because the radius of the circle is 2a, and the equation of the circle is x² + y² = 4a², thus k=4.

198 Easy

198 of 685

Application +4 | -1

A line drawn through the point

\mathrm{P}(4,7)

cuts the circle

x^{2}+y^{2}=9

at the points A and

\mathrm{B}

. Then PA.PB is equal to :

View answer and explanation

Correct option: B

Option B (56) is correct because PA.PB is equal to PT², where PT is the length of the tangent from P to the circle.

199 Easy

199 of 685

Understanding +4 | -1

The curve parametrically described by the equations

x=2+3 \cos \theta, y=3+3 \sin \theta

represents a circle which touches

View answer and explanation

Correct option: A

x

-axis at

(2,0)

Option A (

x

-axis at

(2,0)

) is correct because the circle has center (2,3) and radius 3, touching the x-axis at (2,0).

200 Easy

200 of 685

Application +4 | -1

The radius of the circle

{x^2} + {y^2} + 4x + 6y + 13 = 0

View answer and explanation

Correct option: D

Option D (0) is correct because the equation represents a point circle, where the radius is zero.

201 Easy

201 of 685

Understanding +4 | -1

The centre of the circ le

x = 2 + 3\cos \mathrm{\theta },y = 3\sin \theta - 1

View answer and explanation

Correct option: B

\left( {2, - 1} \right)

The correct answer is B (

\left( {2, - 1} \right)

) because the parametric equations directly provide the center of the circle in the form

x = h + r\cos{\theta}

y = k + r\sin{\theta}

, where

(h, k)

is the center.

202 Easy

202 of 685

Understanding +4 | -1

Assertion: Centre of the circle

x^2+y^2-6 x+4 y-12=0

(3,-2)

.

Reason: The coordinates of the centre of the circle

x^2+y^2+2 g x+2 f y+c=0

are

\left(-\frac{1}{2} \text{ coefficient of } x,-\frac{1}{2} \text{ coefficient of } y\right)

View answer and explanation

Correct option: A

Assertion is correct, reason is correct; reason is a correct explanation for assertion

Option A is correct because the assertion is correct, the reason is correct, and the reason correctly explains the assertion. The center of the circle can be found using the coefficients of x and y.

203 Easy

203 of 685

Application +4 | -1

If the circle

x^{2}+y^{2}-6 x-8 y+\left(25-a^{2}\right)=0

touches the axis of

y

, then

a

equals.

View answer and explanation

Correct option: D

\pm 3

The correct answer is D (

\pm 3

) because if the circle touches the y-axis, the absolute value of the x-coordinate of the center equals the radius.

204 Easy

204 of 685

Application +4 | -1

The equation of the circle of radius 5 and touching the coordinate axes in third quadrant, is

View answer and explanation

Correct option: D

(x+5)^2+(y+5)^2=25

Option D (

(x+5)^2+(y+5)^2=25

) is correct because the center is at (-5, -5) and the radius is 5, touching the axes in the third quadrant.

205 Easy

205 of 685

Analyzing +4 | -1

The maximum number of points with rational coordinates on a circle whose centre is

\left( {\sqrt 3 ,0} \right)

View answer and explanation

Correct option: B

Two

Option B (Two) is correct because a circle centered at

(\sqrt{3}, 0)

can have at most two points with rational coordinates.

206 Easy

206 of 685

Application +4 | -1

C_1

is a circle with centre at the origin and radius equal to

r

and

C_2

is a circle with centre at

(3 r, 0)

and radius equal to

2 r

. The number of common tangents that can be drawn to the two circles are

View answer and explanation

Correct option: C

Option C (3) is correct because the circles touch each other externally, resulting in three common tangents.

207 Medium

207 of 685

Application +4 | -1

The farthest point on the circle

x^2+y^2-2 x-4 y-11=0

from the origin is

View answer and explanation

Correct option: B

\left(1+\frac{4}{\sqrt{5}}, 2+\frac{8}{\sqrt{5}}\right)

Option B (1+4/sqrt(5), 2+8/sqrt(5)) is correct because it represents the point on the circle farthest from the origin, found by moving along the line connecting the origin and the circle's center.

208 Easy

208 of 685

Application +4 | -1

\left( {3, - 2} \right)

is the centre of a circle and

4x + 3y + 19 = 0

is a tangent to the circle, then the equation of the circle is

View answer and explanation

Correct option: C

{x^2} + {y^2} - 6x + 4y - 12 = 0

Option C (

{x^2} + {y^2} - 6x + 4y - 12 = 0

) is correct because it represents the circle with the given center and tangent.

209 Medium

209 of 685

Application +4 | -1

The locus of the point from where tangents are drawn to the circle

x^2+y^2=16

and the product of the slopes of these tangents is 2, is

View answer and explanation

Correct option: B

2 x^2-y^2=16

Option B (

2 x^2-y^2=16

) is correct because the locus is found by using the equation of the tangent to the circle and the condition on the product of the slopes.

210 Easy

210 of 685

Understanding +4 | -1

The equation

\left(x-x_1\right)\left(x-x_2\right)+\left(y-y_1\right)\left(y-y_2\right)=0

represents a circle whose centre is

View answer and explanation

Correct option: B

\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)

Option B is correct because the equation represents a circle with the given line segment as a diameter, and the center is the midpoint of that diameter.

Revision notes and key takeaways

Review CIRCLES in your textbook or class notes, then use this set to check your understanding.

Showing 181-210 of 685 questions

Your Progress

Circles practice · Mixed difficulty

Explore Other Chapters in MATHEMATICS

Continue Your Practice

Your practice