1
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
The locus of mid-points of the line segments joining ($$-$$3, $$-$$5) and the points on the ellipse $${{{x^2}} \over 4} + {{{y^2}} \over 9} = 1$$ is :
A
$$9{x^2} + 4{y^2} + 18x + 8y + 145 = 0$$
B
$$36{x^2} + 16{y^2} + 90x + 56y + 145 = 0$$
C
$$36{x^2} + 16{y^2} + 108x + 80y + 145 = 0$$
D
$$36{x^2} + 16{y^2} + 72x + 32y + 145 = 0$$
2
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
An angle of intersection of the curves, $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ and x2 + y2 = ab, a > b, is :
A
$${\tan ^{ - 1}}\left( {{{a + b} \over {\sqrt {ab} }}} \right)$$
B
$${\tan ^{ - 1}}\left( {{{a - b} \over {2\sqrt {ab} }}} \right)$$
C
$${\tan ^{ - 1}}\left( {{{a - b} \over {\sqrt {ab} }}} \right)$$
D
$${\tan ^{ - 1}}\left( {2\sqrt {ab} } \right)$$
3
JEE Main 2021 (Online) 31st August Morning Shift
+4
-1
The length of the latus rectum of a parabola, whose vertex and focus are on the positive x-axis at a distance R and S (> R) respectively from the origin, is :
A
4(S + R)
B
2(S $$-$$ R)
C
4(S $$-$$ R)
D
2(S + R)
4
JEE Main 2021 (Online) 31st August Morning Shift
+4
-1
The line $$12x\cos \theta + 5y\sin \theta = 60$$ is tangent to which of the following curves?
A
x2 + y2 = 169
B
144x2 + 25y2 = 3600
C
25x2 + 12y2 = 3600
D
x2 + y2 = 60
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