Practice JEE Mathematics Circles MCQs Set C provided below. The MCQ Questions for Full Syllabus Circles Mathematics with answers and follow the latest JEE (Main)/ NCERT and KVS patterns. Refer to more Chapter-wise MCQs for JEE (Main) Full Syllabus Mathematics and also download more latest study material for all subjects
MCQ for Full Syllabus Mathematics Circles
Full Syllabus Mathematics students should review the 50 questions and answers to strengthen understanding of core concepts in Circles
Circles MCQ Questions Full Syllabus Mathematics with Answers
Question. Equation of the circle passing through the origin and through the points of intersection of the circle
x2 + y2– 2x + 4y – 20 = 0 and the line x + y – 1 = 0 is
(a) x2 + y2 – 22x –16y = 0
(b) x2 + y2 - 20x +15y = 0
(c) x2 + y2 + 33x + 33y = 0
(d) None of these
Answer: A
Question. Equation of the circle concentric with the circle x2 + y2 – 3x+ 4y – c = 0 and passing through the point (–1, – 2).
(a) x2 + y2 - 3x + 4y = 0
(b) x2 + y2 – 7x + 7y = 0
(c) x2 + y2 - 3x - 4y = 0
(d) x2 + y2 + 3x + 4y = 0
Answer: A
Question. The straight line (x – 2) + (y + 3) = 0 cuts the circle (x – 2)2 + ( y – 3)2 = 11 at
(a) No points
(b) Two points
(c) One point
(d) None of these
Answer: A
Question. If the centre of a circle which passing through the points of intersection of the circle x2 + y2 – 6x + 2y + 4 = 0 and x2 + y2 + 2x – 4y – 6 = 0 is on the line y = x, then the equation of the circle is
(a) 7x2 + 7y2 -10x -10y -12 = 0
(b) x2 + y2 + 2x + 4y = 0
(c) 5x2 + 5y2 -10x -10y = 0
(d) 2x2 + 2y2 -3x -3y = 0
Answer: A
Question. Centre of the circle whose radius is 3 and which touches the circle x2 + y2 – 4x – 6y – 12 = 0 internally at the point (–1, –1) is
(a) (4/7, 7/5)
(b) (5/7, 7/5)
(c) (5/7, 2/5)
(d) none of these
Answer: A
Question. The lines 2x – 3y = 5 and 3x – 4y = 7 are diameters of a circle of area 154 sq.units.Then the equation of the circle is
(a) x2 + y2 - 2x + 2y = 47 .
(b) x2 + y2 + 2x - 2y = 62
(c) x2 + y2 - 2x + 2y = 62
(d) x2 + y2 + 2x - 2y = 47
Answer: A
Question. If the lines 2x + 3y +1 = 0 and 3x - y - 4 = 0 lie along diameter of a circle of circumference 10p, then the equation of the circle is
(a) x2 + y2 - 2x + 2y - 23 = 0
(b) x2 + y2 + 2x + 2y - 23 = 0
(c) x2 + y2 + 2x - 2 y - 23 = 0
(d) x2 + y2 - 2x - 2y - 23 = 0
Answer: A
Question. The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is
(a) (–3, –4)
(b) (3, – 4)
(c) (–3, 4)
(d) (3, 4)
Answer: A
Question. A circle of radius 5 touches another circle x2 + y2 –2x – 4y –20 = 0 at (5, 5) then its equation is
(a) x2 + y2 – 18x – 16y + 120 = 0
(b) x2 + y2 – 18x + 16y + 120 = 0
(c) x2 + y2 + 18x + 16y + 120 = 0
(d) None of these
Answer: A
Question. The circle x2 + y2 – 8x + 4y + 4 = 0 touches :
(a) y-axis only
(b) None of these
(c) x-axis only
(d) both
Answer: A
Question. The line 3x – 2y = k meets the circle x2 + y2 = 4r2 at only one point then the value k2 is
(a) 52r2
(b) 32r2
(c) 50 r2
(d) none of these
Answer: A
Question. If (– 3, 2) lies on the circle x2 + y2 + 2gx + 2fy + c = 0, which is concentric with the circle x2 + y2 + 6x + 8y – 5 = 0, then c is equal to
(a) – 11
(b) 100
(c) 11
(d) 24
Answer: A
Question. The length of intercept, the circle
x2 + y2 + 10x – 6y + 9 = 0 makes on the x-axis is :
(a) 8
(b) 4
(c) 2
(d) 6
Answer: A
Question. If (xi, 1/xi =1, 2, 3, 4 are four distinct points on a circle, then the value of x1 . x2 . x3 . x4 is :
(a) 1
(b) 4
(c) – 1
(d) 0
Answer: A
Question. If the line x + 2by + 7 = 0 is a diameter of the circle x2 + y2 – 6x + 2y =0, then b =
(a) 5
(b) –5
(c) 3
(d) –1
Answer: A
Question. If the circle x2 + y2 + 2gx + 2fy + c = 0 touches x-axis, then
(a) g2 = c
(b) g2 + f2 = c
(c) g = f
(d) f2 = c
Answer: A
Question. The circle x2 + y2 + 4x – 4y + 4 = 0 touches
(a) x-axis and y-axis
(b) x-axis
(c) y-axis
(d) None of these
Answer: A
Question. If a circle S(x, y) = 0 touches the line x + y = 5 at the point (2, 3) and S (1, 2)= 0, then radius of such circle is
(a) 1/√2
(b) 4 units
(c) 2 units
(d) 1/2 units
Answer: A
Question. If (a , 0) is a point on a diameter of circle x2 + y2 = 4, then x2 – 4x – a2 = 0 has
(1) exactly one real root in (– 1,0] greater than – 1
(2) exactly one real root in [2, 5] greater than –1
(3) two distinct roots greater than – 1
(4) two distinct root greater than 5
(a) 1, 2 and 3 are correct
(b) 2 and 4 are correct
(c) 1 and 2 are correct
(d) 1 and 3 are correct
Answer: A
Question. One diagonal of a square is the portion of x-axis intercepted by the circle x2 + y2 – 4x + 6y – 12 = 0. Then the y-coordinate of the extrimity above the x-axis of the other diagonal is
(1) ( 2, 4 ) (2) (2, – 4)
(3) (– 2, – 4) (4) (–2, 4)
(a) 1 and 2 are correct
(b) 1 and 3 are correct
(c) 1, 2 and 3 are correct
(d) 2 and 4 are correct
Answer: A
Question. Statement-1 : Number of circles passing through (1, 4), (2, 3), (– 1, 6) is one. Statement-2 : Through 3 non collinear points in a plane only one circle can be drawn.
(a) Statement -1 is False, Statement-2 is True
(b) Statement -1 is True, Statement-2 is False.
(c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
(d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
Answer: A
Question. Statement-1 : The circle x2 + y2 + 2ax + c = 0 , x2 + y2 + 2by + c = 0 touches each other if 1/a2 + 1/b2 = 1/c
Statement-2 : Two circles with centre C1,C2 and radii r1, r2 touch each other, if r1 ± r2 = C1C2
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
(c) Statement -1 is False, Statement-2 is True.
(d) Statement -1 is True, Statement-2 is False.
Answer: A
Question. The equation of pair of tangents drawn from the point (0,1) to the circle x2 + y2 – 2x + 4y = 0 is –
(a) 4x2 – 4y2 + 6xy – 6x + 8y –4 = 0
(b) x2 – y2 + 3xy – 3x + 2y –1 = 0
(c) x2 – y2 + 6xy – 6x + 8y –4 = 0
(d) 4x2 – 4y2 + 6xy + 6x + 8y –4 = 0
Answer: A
Question. Chord of contact with respect to point (2, 2) of circle x2 + y2 = 1 is -
(a) x + y = 1/2
(b) x + y + 1
(c) x – y = 1/2
(d) x + y = 2
Answer: A
Question. The locus of the centre of the circle which touches externally the circle x2 + y2 – 6x – 6y + 14 = 0 and also touches the y-axis, is -
(a) y2 – 10x – 6y + 14 = 0
(b) x2 – 6x – 10y + 14 = 0
(c) y2 – 6x – 10y + 14 = 0
(d) x2 – 10x – 6y + 14 = 0
Answer: A
Question. The two circles x2 + y2 = ax and x2 + y2 = c2 (with c > 0) touch each other if -
(a) c = |a|
(b) 2a = |c|
(c) 2c = a
(d) None of these
Answer: A
Question. The equation of chord of the circle x2 + y2 = 8x bisected at the point (4, 3) is
(a) y = 3
(b) None
(c) 3y = 1
(d) 4x – 3y = 9
Answer: A
Question. If lines y = x + 3 cuts the circle x2 + y2 = a2 in two points A and B, then equation of circle with AB as diameter is -
(a) x2 + y2 + 3x – 3y – a2 + 9 = 0
(b) x2 + y2 + 3x – 3y + a2 + 9 = 0
(c) x2 + y2 – 3x + 3y – a2 + 9 = 0
(d) None of these
Answer: A
Question. If the circle x2 + y2 + 4x + 22y + c = 0 bisects the circumference of the circle x2 + y2 – 2x + 8y – d = 0, then c + d =
(a) 50
(b) 56
(c) 40
(d) 60
Answer: A
Question. For what value of k the circles x2 + y2 + 5x + 3y + 7 = 0 and x2 + y2 – 8x + 6y + k = 0 cuts orthogonally ?
(a) –18
(b) 4
(c) 18
(d) – 4
Answer: A
Question. Equation of polar of point (4, 4) with respect to circle (x –1)2 + (y – 2)2 = 1 is
(a) 3x + 2y – 8 = 0
(b) 3x + 2y + 8 = 0
(c) 2x + 3y – 8 = 0
(d) 3x – 2y + 8 = 0
Answer: A
Question. The pole of the line x/a + y/b = 1 with respect to circle x2 + y2 = c2 is
(a) (c2/a, c2b)
(b) (c2/a2, c2b2)
(c) (c/a, c/b)
(d) None of these
Answer: A
Question. The radical centre of the three circles
x2 + y2 = a2,(x – c)2 + y2 = a2 and x2 + (y – b)2 = a2 is -
(a) (c/2, b/2)
(b) (a/2, b/2)
(c) (b/2, c/2)
(d) None of these
Answer: A
Question. The equation of the radical axis of two circles
x2 + y2 – x + 1 = 0 and 3(x2 + y2) + y – 1 = 0 is -
(a) 3x + y – 4 = 0
(b) 3x – y + 4 = 0
(c) 3x – y – 4 = 0
(d) None of these
Answer: A
Question. The locus of the point, the chord of contact of tangents from which to the circle x2 + y2 = a2 subtends a right angle at the centre is a circle of radius -
(a) √2a
(b) 2a
(c) a/2
(d) a2
Answer: A
Question. If a chord of the circle x2 + y2 = 8 makes equal intercepts of length a on the coordinate axes, then-
(a) | a | < 4
(b) | a | < 8
(c) | a | > 4
(d) None of these
Answer: A
Question. The equation of a normal to the circle
x2 + y2 + 6x + 8y + 1 = 0 passing through (0, 0) is -
(a) 4x – 3y = 0
(b) 3x – 4y = 0
(c) 3x + 4y = 0
(d) 4x + 3y = 0
Answer: A
Question. If the tangent to a circle x2 + y2 = 5 at point (1, –2) touches the circle x2 +y2 – 8x +6y+ 20 = 0, then its point of contact is-
(a) (3, –1)
(b) (5, 0)
(c) (–2, 1)
(d) (–1, –3)
Answer: A
Question. Length of the tangent drawn from point (1, 5) to the circle
2x2 + 2y2 = 3 is -
(a) 7 √2 / 2
(b) 7
(c) 7 √2
(d) None of these
Answer: A
Question. The pole of the straight line 9x + y – 28 = 0 with respect to the circle 2x2 + 2y2 – 3x + 5y – 7 = 0, is
(a) (3,–1)
(b) (2, – 1)
(c) (2, 1)
(d) (3,1)
Answer: A
Question. The equations of the tangents drawn from the origin to the circle x2 + y2 – 2rx – 2hy + h2 = 0, are
(1) x = 0
(2) y = 0
(3) (h2 – r2)x – 2rhy = 0
(4) (h2 – r2)x + 2rhy = 0
(a) 1 and 3 are correct
(b) 1 and 2 are correct
(c) 1, 2 and 3 are correct
(d) 2 and 4 are correct
Answer: A
Question. Consider the circle x2 + y2 – 10x – 6y + 30 = 0. Let O be the centre of the circle and tangent at A (7, 3) and B (5, 1) meet at C. Let S = 0 represents family of circles passings through A and B, then –
(1) Area of quadrilateral OACB = 4
(2) The smallest possible circle of the family of circles S = 0 is x2 + y2 – 12x – 4y + 38 = 0
(3) The coordinates of point C are (7, 1)
(4) The radical axis for the family of circles S = 0 is x + y = 10
(a) 1, 2 and 3 are correct
(b) 2 and 4 are correct
(c) 1 and 2 are correct
(d) 1 and 3 are correct
Answer: A
Question. A circle x2 + y2 = 1 cuts the line x + y = k and makes the chord with length l. The value of k is –
1. √6/2
2. -√6/2
3. √3/2
4. None of these
(a) 1 and 2 are correct
(b) 1 and 3 are correct
(c) 1, 2 and 3 are correct
(d) 2 and 4 are correct
Answer: A
Question. Statement-1 : Number of common tangents of x2 + y2 – 2x – 4y – 95 = 0 and x2 + y2 – 6x – 8y + 16 = 0 is zero.
Statement 2 : If C1C2 < | r1 – r2 |, then there will be no common tangent. (where C1, C2 are the centre and r1, r2 are radii of circles).
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
(c) Statement-1 is False, Statement-2 is True.
(d) Statement-1 is True, Statement-2 is False.
Answer: A
Question. Statement-1 : The product of slopes of all the common tangents of circles S1 = x2 + y2 – a2 = 0 and S2 = (x – 2a)2 + (y – 2a)2 – 4a2 = 0 is 1.
Statement-2 : Slope of line joining centres of S1 = x2 + y2 – a2 = 0 and S2 = (x – 2a)2 + (y – 2a)2 – 4a2 = 0 is 1. Direct common tangents make equal angles with the line joining centres of the circles.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
(c) Statement-1 is False, Statement-2 is True.
(d) Statement-1 is True, Statement-2 is False.
Answer: A
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Important Practice Resources for JEE Mathematics full syllabus Online Test
MCQs for Circles Mathematics Full Syllabus
Students can use these MCQs for Circles to quickly test their knowledge of the chapter. These multiple-choice questions have been designed as per the latest syllabus for Full Syllabus Mathematics released by JEE (Main). Our expert teachers suggest that you should practice daily and solving these objective questions of Circles to understand the important concepts and better marks in your school tests.
Circles NCERT Based Objective Questions
Our expert teachers have designed these Mathematics MCQs based on the official NCERT book for Full Syllabus. We have identified all questions from the most important topics that are always asked in exams. After solving these, please compare your choices with our provided answers. For better understanding of Circles, you should also refer to our NCERT solutions for Full Syllabus Mathematics created by our team.
Online Practice and Revision for Circles Mathematics
To prepare for your exams you should also take the Full Syllabus Mathematics MCQ Test for this chapter on our website. This will help you improve your speed and accuracy and its also free for you. Regular revision of these Mathematics topics will make you an expert in all important chapters of your course.
You can get most exhaustive JEE Mathematics Circles MCQs Set C for free on StudiesToday.com. These MCQs for Full Syllabus Mathematics are updated for the 2025-26 academic session as per JEE (Main) examination standards.
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