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Circles - Past Year Questions

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Q1:

If the shortest distance of a given point to a given circle is 4 cm4 \, \text{cm} and the longest distance is 9 cm9 \, \text{cm}, then the radius of the circle is
Answer options
Option: 4
Correct Answer
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Q2:

If θ \theta is the angle between the pair of tangents drawn from the point (0,72)(0,\frac{7}{2}) to the circle x2+y2−14x+16y+88=0x^2 + y^2 - 14x + 16y + 88 = 0, then tan⁡θ\tan \theta equals
Answer options
Option: 4
Correct Answer
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Q3:

Which of the following straight lines are both tangent to the circle x2+y2−6x+4y−12=0x ^ 2 + y ^ 2 - 6x + 4y - 12 = 0?
Answer options
Option: 1
Correct Answer
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Q4:

The equation x2+y2−2x−4y+5=0x^2 + y^2 - 2x - 4y +5 = 0 represents
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Option: 4
Correct Answer
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Q5:

In the xy-plane let A=(−2,0),B=(2,0)A = (- 2, 0), B = (2, 0) . Define the set S as the collection of all points C on the circle x2+y2=4x ^ 2 + y ^ 2 = 4 such that the area of the triangle ABC is an integer. The number of points in the set S is
14
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Q6:

The shortest distance from the point (−4,3)(-4,3) to the circle (x2+y2=1)(x^2 + y^2 = 1) is __________.
4
Correct Answer
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Q7:

A chord is drawn inside a circle, such that the length of the chord is equal to the radius of the circle. Now, two circles are drawn, one on each side of the chord, each touching the chord at its midpoint and the original circle. Let k be the ratio of the areas of the bigger inscribed circle and the smaller inscribed circle, then k equals
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Option: 4
Correct Answer
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Q8:

On a circular path of radius 6 m a boy starts from a point AA on the circumference and walks along a chord ABAB of length 3 m. He then walks along another chord BCBC of length 2 m to reach point CC. The point BB lies on the minor arc ACAC. The distance between point CC from point AA is
Answer options
Option: 1
Correct Answer
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Q9:

The circle x2+y2−6x−10y+k=0x^2 + y^2 - 6x - 10y + k = 0 does not touch or intersect the coordinate axes. If the point (1,4)(1, 4) does not lie outside the circle, and the range of kk is (a,b](a, b], then a+ba + b is
54
Correct Answer
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Q10:

If the difference between the circumference and radius of a circle is 37 cm, using π = 22/7, what is the circumference (in cm) of the circle?

Answer options
Option: 3
Correct Answer
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Q11:

Which of the following statements are True in the context of circles?

  • A. A tangent of a circle touches it at two points.
  • B. A circle can have two parallel tangents at the most.
  • C. There is no tangent to a circle passing through a point inside the circle.

Choose the correct answer from the options given below:

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Option: 4
Correct Answer
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Q12:

The area of the circle that can be inscribed in a square of side 6 cm is:

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Option: 4
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Q13:

The equation of the circle which passes through the point (4,5)(4,5) and its centre at (2,2)(2,2) is
Answer options
Option: 2
Correct Answer
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Q14:

If the radius of each of four outer circles is rr, then the radius of the innermost circle is
Answer options
Option: 3
Correct Answer
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Q15:

The area of a circular playground is 22176 cm222176 \ cm^2. What is the cost of fencing this ground at the rate of ₹50 per metre?
Answer options
Option: 1
Correct Answer
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Q16:

The radius of two concentric circles are 13 cm and 8 cm. AB is a diameter of the bigger circle. BD is tangent to the smaller circle touching it at D. The length AD is.
Answer options
Option: 3
Correct Answer
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Q17:

What is the area of the shaded figure? Use the figure below to answer questions.
Answer options
Option: 2
Correct Answer
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Q18:

What is the ratio of the area of Circle M to the area of Circle K?
Answer options
Option: 2
Correct Answer
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Q19:

A line from center to circumference of a circle is known as
Answer options
Option: 2
Correct Answer
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Circles - Past Year Questions (Free PDF Download)

Practice with our comprehensive collection of Circles Past Year Questions (PYQs of IPMAT Indore, IPMAT Rohtak & JIPMAT) with detailed solutions. These questions are carefully curated from previous year papers to help you understand the exam pattern and improve your preparation.

Our free resources include handwritten solutions for all questions, making it easier to understand the concepts and approach. Use these PYQs to assess your preparation level and identify areas that need more focus. No login required. Compilation of IPMAT Indore, IPMAT Rohtak & JIPMAT Questions!