JEE Advanced 2024 Paper 2 Online

MCQ (More than One Correct Answer)

-2

Let $A_1, B_1, C_1$ be three points in the $x y$-plane. Suppose that the lines $A_1 C_1$ and $B_1 C_1$ are tangents to the curve $y^2=8 x$ at $A_1$ and $B_1$, respectively. If $O=(0,0)$ and $C_1=(-4,0)$, then which of the following statements is (are) TRUE?

The length of the line segment $O A_1$ is $4 \sqrt{3}$

The length of the line segment $A_1 B_1$ is 16

The orthocenter of the triangle $A_1 B_1 C_1$ is $(0,0)$

The orthocenter of the triangle $A_1 B_1 C_1$ is $(1,0)$

JEE Advanced 2022 Paper 1 Online

MCQ (More than One Correct Answer)

-2

Consider the parabola $$y^{2}=4 x$$. Let $$S$$ be the focus of the parabola. A pair of tangents drawn to the parabola from the point $$P=(-2,1)$$ meet the parabola at $$P_{1}$$ and $$P_{2}$$. Let $$Q_{1}$$ and $$Q_{2}$$ be points on the lines $$S P_{1}$$ and $$S P_{2}$$ respectively such that $$P Q_{1}$$ is perpendicular to $$S P_{1}$$ and $$P Q_{2}$$ is perpendicular to $$S P_{2}$$. Then, which of the following is/are TRUE?

$$S Q_{1}=2$$

$$Q_{1} Q_{2}=\frac{3 \sqrt{10}}{5}$$

$$P Q_{1}=3$$

$$S Q_{2}=1$$

JEE Advanced 2021 Paper 2 Online

MCQ (More than One Correct Answer)

-2

Let E denote the parabola y² = 8x. Let P = ($$-$$2, 4), and let Q and Q' be two distinct points on E such that the lines PQ and PQ' are tangents to E. Let F be the focus of E. Then which of the following statements is(are) TRUE?

The triangle PFQ is a right-angled triangle

The triangle QPQ' is a right-angled triangle

The distance between P and F is 5$$\sqrt 2 $$

F lies on the line joining Q and Q'

JEE Advanced 2017 Paper 1 Offline

MCQ (More than One Correct Answer)

-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?

p = $$-$$1, h = 1, k = $$-$$3

p = 2, h = 3, k = $$-$$4

p = $$-$$2, h = 2, k = $$-$$4

p = 5, h = 4, k = $$-$$3

JEE Advanced Subjects