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615 Questions Start JEE Mains Test
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1985 Q601 JEE Advanced Numerical
14 Mar 2026
Let ${x^2} + {y^2} - 4x - 2y - 11 = 0$ be a circle. A pair of tangentas from the point (4, 5) with a pair of radi from a quadrilateral of area............................
1985 Q602 JEE Advanced MCQ
14 Mar 2026
No tangent can be drawn from the point (5/2, 1) to the circumcircle of the triangle with vertices $\left( {1,\sqrt 3 } \right)\,\,\left( {1, - \sqrt 3 } \right),\,\,\left( {3,\sqrt 3 } \right)$.
A.
TRUE
B.
FALSE
1984 Q603 JEE Advanced MCQ
14 Mar 2026
The locus of the mid-point of a chord of the circle ${x^2} + {y^2} = 4$ which subtends a right angle at the origin is
A.
x + y = 2
B.
${x^2} + {y^2} = 1$
C.
${x^2} + {y^2} = 2$
D.
$x + y $=1
1984 Q604 JEE Advanced Numerical
14 Mar 2026
The abscissa of the two points A and B are the roots of the equation ${x^2}\, + \,2ax\, - {b^2} = 0$ and their ordinates are the roots of the equation ${x^2}\, + \,2px\, - {q^2} = 0$. Find the equation and the radius of the circle with AB as diameter.
1984 Q605 JEE Advanced Numerical
14 Mar 2026
The lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to the same circle. The radius of this circle is ........................................
1983 Q606 JEE Advanced MCQ
14 Mar 2026
The equation of the circle passing through (1, 1) and the points of intersection of ${x^2} + {y^2} + 13x - 3y = 0$ and $2{x^2} + 2{y^2} + 4x - 7y - 25 = 0$ is
A.
$4{x^2} + 4{y^2} - 30x - 10y - 25 = 0$
B.
$4{x^2} + 4{y^2} + 30x - 13y - 25 = 0$
C.
$4{x^2} + 4{y^2} - 17x - 10y + 25 = 0$
D.
none of these
1983 Q607 JEE Advanced MCQ
14 Mar 2026
The centre of the circle passing through the point (0, 1) and touching the curve $\,y = {x^2}$ at (2, 4) is
A.
$\left( {{{ - 16} \over 5},{{ - 27} \over {10}}} \right)$
B.
$\left( {{{ - 16} \over 7},{{53} \over {10}}} \right)$
C.
$\left( {{{ - 16} \over 5},{{53} \over {10}}} \right)$
D.
none of these
1983 Q608 JEE Advanced Numerical
14 Mar 2026
Through a fixed point (h, k) secants are drawn to the circle $\,{x^2}\, + \,{y^2} = \,{r^2}$. Show that the locus of the mid-points of the secants intercepted by the circle is $\,{x^2}\, + \,{y^2} $ = $hx + ky$.
1983 Q609 JEE Advanced Numerical
14 Mar 2026
The point of intersection of the line 4x - 3y - 10 = 0 and the circle ${x^2} + {y^2} - 2x + 4y - 20 = 0$ are ........................and ...................
1982 Q610 JEE Advanced Numerical
14 Mar 2026
If A and B are points in the plane such that PA/PB = k (constant) for all P on a given circle, then the value of k cannot be equal to ..........................................
1981 Q611 JEE Advanced Numerical
14 Mar 2026
Find the equations of the circle passing through (- 4, 3) and touching the lines x + y = 2 and x - y = 2.
1981 Q612 JEE Advanced Numerical
14 Mar 2026
Let A be the centre of the circle ${x^2}\, + \,{y^2}\, - \,2x\,\, - 4y\, - 20 = 0\,$. Suppose that the tangents at the points B (1, 7) and D (4. - 2) on the circle meet at the point C. Find the area of the quadrilateral ABCD.
1980 Q613 JEE Advanced MCQ
14 Mar 2026
Two circles ${x^2} + {y^2} = 6$ and ${x^2} + {y^2} - 6x + 8 = 0$ are given. Then the equation of the circle through their points of intersection and the point (1, 1) is
A.
${x^2} + {y^2} - 6x + 4 = 0$
B.
${x^2} + {y^2} - 3x + 1 = 0$
C.
${x^2} + {y^2} - 4y + 2 = 0$
D.
none of these
1980 Q614 JEE Advanced MCQ
14 Mar 2026
A square is inscribed in the circle ${x^2} + {y^2} - 2x + 4y + 3 = 0$. Its sides are parallel to the coordinate axes. The one vertex of the square is
A.
$\left( {1 + \sqrt {2,} - 2} \right)$
B.
$\,\left( {1 - \sqrt {2}, - 2} \right)$
C.
$\,\,\left( {1, - 2 + \sqrt 2 } \right)$
D.
none of these
1978 Q615 JEE Advanced Numerical
14 Mar 2026
Find the equation of the circle whose radius is 5 and which touches the circle ${x^2}\, + \,{y^2}\, - \,2x\,\, - 4y\, - 20 = 0\,$ at the point (5, 5).