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Saturday, 31 October

JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 January 2020, Shift 2, Maths Q64

Question 64 of 75 in this shift, Maths question 14 of 25, Section A.

If a line, y=mx+cy = mx + \mathrm{c} is a tangent to the circle, (x−3)2+y2=1(x - 3)^2 + y^2 = 1 and it is perpendicular to a line L1\mathrm{L}_1, where L1\mathrm{L}_1 is the tangent to the circle, x2+y2=1x^2 + y^2 = 1 at the point (12,12)\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right); then :
  1. (1)c2−7c+6=0\mathrm{c}^2 - 7\mathrm{c} + 6 = 0
  2. (2)c2+7c+6=0\mathrm{c}^2 + 7\mathrm{c} + 6 = 0
  3. (3)c2+6c+7=0\mathrm{c}^2 + 6\mathrm{c} + 7 = 0Official answer
  4. (4)c2−6c+7=0\mathrm{c}^2 - 6\mathrm{c} + 7 = 0

Official answer

Option 3

NTA final key (Jan 2020).

Chapter
Conic Sections
Topic
Circle Tangents
Idea tested
Condition of tangency

Same idea in other shifts

Asked 11× in all
  1. 5 Apr 2024, Shift 2 · Q14Let ABCDABCD and AEFGAEFG be squares of side 4 and 2 units, respectively. The point EE is on the line segment ABAB and the point FF is on…MediumSingle correct
  2. 1 Feb 2024, Shift 1 · Q29Let the line L:2x+y=αL:\sqrt{2}x+y=\alpha pass through the point of the intersection P (in the first quadrant) of the circle x2+y2=3x^2+y^2=3 and the…HardNumerical value
  3. 29 Jan 2024, Shift 1 · Q27Equations of two diameters of a circle are 2x−3y=52x-3y=5 and 3x−4y=73x-4y=7. The line joining the points (−227,−4)\left(-\frac{22}{7},-4\right) and…MediumNumerical value
  4. 29 Jul 2022, Shift 1 · Q8Let a line L pass through the point of intersection of the lines bx+10y−8=0bx + 10y - 8 = 0 and 2x−3y=02x - 3y = 0,…HardSingle correct
  5. 30 Jun 2022, Shift 1 · Q14Consider three circles : C1:x2+y2=r2C_1 : x^2 + y^2 = r^2 C2:(x−1)2+(y−1)2=r2C_2 : (x-1)^2 + (y-1)^2 = r^2 C3:(x−2)2+(y−1)2=r2C_3 : (x-2)^2 + (y-1)^2 = r^2 If a line L :…HardSingle correct
  6. 31 Aug 2021, Shift 1 · Q86If the variable line 3x+4y=α3x+4y=\alpha lies between the two circles (x−1)2+(y−1)2=1(x-1)^2+(y-1)^2=1 and (x−9)2+(y−1)2=4(x-9)^2+(y-1)^2=4, without intercepting a chord…HardNumerical value
  7. 9 Jan 2020, Shift 1 · Q65A circle touches the yy-axis at the point (0, 4) and passes through the point (2, 0). Which of the following lines is not a tangent to…MediumSingle correct
  8. 2 Sep 2020, Shift 1 · Q74The number of integral values of k for which the line, 3x+4y=k3x+4y=k intersects the circle, x2+y2−2x−4y+4=0x^{2}+y^{2}-2x-4y+4=0 at two distinct points is…MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.