1

JEE Advanced 2020 Paper 2 Offline

MCQ (More than One Correct Answer)

+4

-2

Let a and b be positive real numbers such that a > 1 and b < a. Let P be a point in the first quadrant that lies on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$. Suppose the tangent to the hyperbola at P passes through the point (1, 0), and suppose the normal to the hyperbola at P cuts off equal intercepts on the coordinate axes. Let $$\Delta $$ denote the area of the triangle formed by the tangent at P, the normal at P and the X-axis. If e denotes the eccentricity of the hyperbola, then which of the following statements is/are TRUE?

2

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 F

_{1}be the set of al pairs of circles (S_{1}, S_{2}) such that T is tangent to S_{1}at P and tangent to S_{2}at Q, and also such that S_{1}and S_{2}touch each other at a point, say M. Let E_{1}be the set representing the locus of M as the pair (S_{1}, S_{2}) varies in F_{1}. Let the set of all straight line segments joining a pair of distinct points of E_{1}and passing through the point R(1, 1) be F_{2}. Let E_{2}be the set of the mid-points of the line segments in the set F_{2}. Then, which of the following statement(s) is (are) TRUE?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?

4

JEE Advanced 2015 Paper 2 Offline

MCQ (More than One Correct Answer)

+4

-1

Consider the hyperbola $$H:{x^2} - {y^2} = 1$$ and a circle $$S$$ with center $$N\left( {{x_2},0} \right)$$. Suppose that $$H$$ and $$S$$ touch each other at a point $$P\left( {{x_1},{y_1}} \right)$$ with $${{x_1} > 1}$$ and $${{y_1} > 0}$$. The common tangent to $$H$$ and $$S$$ at $$P$$ intersects the $$x$$-axis at point $$M$$. If $$(l, m)$$ is the centroid of the triangle $$PMN$$, then the correct expressions(s) is(are)

Questions Asked from Hyperbola (MCQ (Multiple Correct Answer))

Number in Brackets after Paper Indicates No. of Questions

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