Circles · JEE Main previous year questions

2020 7 questions

1. Q152020 · 6 Sept 2020 · Shift 2

   The centre of the circle passing through the point $(0,1)$ and touching the parabola $y=x^2$ at the point $(2,4)$ is :

   1. A.$\left(\frac{6}{5},\frac{53}{10}\right)$
   2. B.$\left(\frac{3}{10},\frac{16}{5}\right)$
   3. C.$\left(-\frac{53}{10},\frac{16}{5}\right)$
   4. D.$\left(-\frac{16}{5},\frac{53}{10}\right)$
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   Answer: D

2. Q232020 · 3 Sept 2020 · Shift 1· Numerical answer

   The diameter of the circle, whose centre lies on the line x + y = 2 in the first quadrant and which touches both the lines x = 3 and y = 2, is _______ .

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   Answer: 3

3. Q32020 · 3 Sept 2020 · Shift 2

   Let the latus rectum of the parabola $y^2=4x$ be the common chord to the circles ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ each of them having radius $2\sqrt{5}$. Then, the distance between the centres of the circles ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ is :

   1. A.8
   2. B.12
   3. C.$8\sqrt{5}$
   4. D.$4\sqrt{5}$
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   Answer: A

4. Q22020 · 9 Jan 2020 · Shift 1

   A spherical iron ball of $10\text{ cm}$ radius is coated with a layer of ice of uniform thickness that melts at a rate of $50{\text{ cm}}^3/\text{min}$. When the thickness of ice is $5\text{ cm}$, then the rate (in $\text{cm}/\text{min}$.) at which the thickness of ice decreases, is :

   1. A.$\frac{1}{18\pi }$
   2. B.$\frac{1}{36\pi }$
   3. C.$\frac{1}{54\pi }$
   4. D.$\frac{5}{6\pi }$
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   Answer: A

5. Q202020 · 9 Jan 2020 · Shift 1

   A circle touches the y-axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a tangent to this circle?

   1. A.3x – 4y – 24 = 0
   2. B.4x + 3y – 8 = 0
   3. C.3x + 4y – 6 = 0
   4. D.4x – 3y + 17 = 0
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   Answer: B

6. Q162020 · 8 Jan 2020 · Shift 2

   If a line, $y=mx+c$ is a tangent to the circle, $(x-3{)}^2+y^2=1$ and it is perpendicular to a line $L_1$, where $L_1$ is the tangent to the circle, $x^2+y^2=1$ at the point $\left(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}\right)$, then :

   1. A.$c^2+6c+7=0$
   2. B.$c^2-7c+6=0$
   3. C.$c^2-6c+7=0$
   4. D.$c^2+7c+6=0$
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   Answer: A

7. Q202020 · 7 Jan 2020 · Shift 2

   Let the tangents drawn from the origin to the circle, $x^2+y^2-8x-4y+16=0$ touch it at the points A and B. The $(AB{)}^2$ is equal to :

   1. A.$\frac{56}{5}$
   2. B.$\frac{32}{5}$
   3. C.$\frac{52}{5}$
   4. D.$\frac{64}{5}$
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   Answer: D