JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 31 August 2021, Shift 1, Maths Q86

Question 86 of 90 in this shift, Maths question 26 of 30, Section B.

If the variable line

3x+4y=\alpha

lies between the two circles

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

and

(x-9)^2+(y-1)^2=4

, without intercepting a chord on either circle, then the sum of all the integral values of

\alpha

is __________.

Official answer

165

NTA final key.

Chapter: Conic Sections
Topic: Circle Tangents
Idea tested: Condition of tangency

Same idea in other shifts

Asked 11× in all

5 Apr 2024, Shift 2 · Q14Let $ABCD$ and $AEFG$ be squares of side 4 and 2 units, respectively. The point $E$ is on the line segment $AB$ and the point $F$ is on…MediumSingle correct
1 Feb 2024, Shift 1 · Q29Let the line $L:\sqrt{2}x+y=\alpha$ pass through the point of the intersection P (in the first quadrant) of the circle $x^2+y^2=3$ and the…HardNumerical value
29 Jan 2024, Shift 1 · Q27Equations of two diameters of a circle are $2x-3y=5$ and $3x-4y=7$ . The line joining the points $\left(-\frac{22}{7},-4\right)$ and…MediumNumerical value
29 Jul 2022, Shift 1 · Q8Let a line L pass through the point of intersection of the lines $bx + 10y - 8 = 0$ and $2x - 3y = 0$ ,…HardSingle correct
30 Jun 2022, Shift 1 · Q14Consider three circles : $C_1 : x^2 + y^2 = r^2$ $C_2 : (x-1)^2 + (y-1)^2 = r^2$ $C_3 : (x-2)^2 + (y-1)^2 = r^2$ If a line L :…HardSingle correct
8 Jan 2020, Shift 2 · Q64If a line, $y = mx + \mathrm{c}$ is a tangent to the circle, $(x - 3)^2 + y^2 = 1$ and it is perpendicular to a line $\mathrm{L}_1$ , where…MediumSingle correct
9 Jan 2020, Shift 1 · Q65A 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…MediumSingle correct
2 Sep 2020, Shift 1 · Q74The number of integral values of k for which the line, $3x+4y=k$ intersects the circle, $x^{2}+y^{2}-2x-4y+4=0$ 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.