1
JEE Advanced 2018 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let T be the line passing through the points P($$-$$2, 7) and Q(2, $$-$$5). Let F1 be the set of al pairs of circles (S1, S2) such that T is tangent to S1 at P and tangent to S2 at Q, and also such that S1 and S2 touch each other at a point, say M. Let E1 be the set representing the locus of M as the pair (S1, S2) varies in F1. Let the set of all straight line segments joining a pair of distinct points of E1 and passing through the point R(1, 1) be F2. Let E2 be the set of the mid-points of the line segments in the set F2. Then, which of the following statement(s) is (are) TRUE?
A
The point ($$-$$2, 7) lies in E1
B
The point $$\left( {{4 \over 5},{7 \over 5}} \right)$$ does not lie in E2
C
The point $$\left( {{1 \over 2},1} \right)$$ lies in E2
D
The point $$\left( {0,{3 \over 2}} \right)$$ does not lie in E1
2
JEE Advanced 2018 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Consider two straight lines, each of which is tangent to both the circle x2 + y2 = (1/2) and the parabola y2 = 4x. Let these lines intersect at the point Q. Consider the ellipse whose centre is at the origin O(0, 0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is $$\sqrt 2$$, then which of the following statement(s) is (are) TRUE?
A
For the ellipse, the eccentricity is 1$$\sqrt 2$$ and the length of the latus rectum is 1
B
For the ellipse, the eccentricity is 1/2 and the length of the latus rectum is 1/2
C
The area of the region bounded by the ellipse between the lines $$x = {1 \over {\sqrt 2 }}$$ and x = 1 is $${1 \over {4\sqrt 2 }}(\pi - 2)$$
D
The area of the region bounded by the ellipse between the lines $$x = {1 \over {\sqrt 2 }}$$ and x = 1 is $${1 \over {16}}(\pi - 2)$$
3
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
If $$2x - y + 1 = 0$$ is a tangent to the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {16}} = 1$$ then which of the following CANNOT be sides of a right angled triangle?
A
a, 4, 1
B
2a, 4, 1
C
a, 4, 2
D
2a, 8, 1
4
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
If a chord, which is not a tangent, of the parabola y2 = 16x has the equation 2x + y = p, and mid-point (h, k), then which of the following is(are) possible value(s) of p, h and k?
A
p = $$-$$1, h = 1, k = $$-$$3
B
p = 2, h = 3, k = $$-$$4
C
p = $$-$$2, h = 2, k = $$-$$4
D
p = 5, h = 4, k = $$-$$3
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