Circles · JEE Main previous year questions

211 questions asked across 20 exam years, newest first

2024 29 questions

Q232024 · 29 Jan 2024 · Shift 1· Numerical answer
Equations of two diameters of a circle are $2 x - 3 y = 5$ and $3 x - 4 y = 7$ . The line joining the points $(- \frac{22}{7}, - 4)$ and $(- \frac{1}{7}, 3)$ intersects the circle at only one point $P (α, β)$ . Then, $17 β - α$ is equal to _______.
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Answer: 2
Q42024 · 27 Jan 2024 · Shift 1
If the shortest distance of the parabola $y^{2} = 4 x$ from the centre of the circle $x^{2} + y^{2} - 4 x - 16 y + 64 = 0$ is $d$ , then $d^{2}$ is equal to :
1. A.16
2. B.24
3. C.20
4. D.36
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Answer: C
Q122024 · 27 Jan 2024 · Shift 1
Four distinct points $(2 k, 3 k), (1, 0), (0, 1)$ and $(0, 0)$ lie on a circle for $k$ equal to :
1. A. $\frac{3}{13}$
2. B. $\frac{2}{13}$
3. C. $\frac{5}{13}$
4. D. $\frac{1}{13}$
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Answer: C
Q282024 · 27 Jan 2024 · Shift 2· Numerical answer
Consider a circle $(x - α)^{2} + (y - β)^{2} = 50$ , where $α, β > 0$ . If the circle touches the line $y + x = 0$ at the point $P$ , whose distance from the origin is $42$ , then $(α + β)^{2}$ is equal to _______.
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Answer: 100