JEE (Advanced) 2019 Paper-2

Instructions

Answer by appropriately matching the lists based on the information given in the paragraph.
Let $$f(x) = \sin (\pi \cos x)$$ and $$g(x) = \cos (2\pi \sin x)$$ be two functions defined for $$x > 0.$$ Define the following sets whose elements are written in the increasing order:
$$X = {x : f(x) = 0}, Y = {x : f'(x) = 0},$$
$$Z = {x : g(x) = 0}, W = {x : g'(x) = 0}.$$
List —I contains the sets X, Y, Z and W. List —II contains some information regarding these sets.

Question 51

Which of the following is the only CORRECT combination?

Video Solution


Question 52

Which ofthe following is the only CORRECT combination?

Video Solution


Instructions

Answer by appropriately matching the lists based on the information given in the paragraph.
Let the circles $$C_1 : x^2 + y^2 = 9$$ and $$C_2 : (x - 3)^2 + (y - 4)^2 = 16,$$ intersect at the points X and Y. Suppose that another circle $$C_3 : (x - h)^2 + (y - k)^2 = r^2$$ satisfies the following conditions:
(i) centre of $$C_3$$ is collinear with the centres of $$C_1$$ and $$C_2$$,
(ii) $$C_1$$ and $$C_2$$ both lie inside $$C_3$$ and
(iii) $$C_3$$ touches $$C_1$$ at M and $$C_2$$ at N.
Let the line through X and Y intersect $$C_3$$ at Z and W, and let a common tangent of $$C_1$$ and $$C_3$$ be a tangent to the parabola $$x^2 = 8 \alpha y.$$
There are some expressions given in the List-I whose values are given in List-II below:

Question 53

Which of the following is the only CORRECT combination?

Video Solution


Question 54

Which of the following is the only INCORRECT combination?

Video Solution


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