Let the circle C1 : x2 + y2 = 9 and C2 : (x $$-$$ 3)2 + (y $$-$$ 4)2 = 16, intersect at the points X and Y. Suppose that another circle C3 : (x $$-$$ h)2 + (y $$-$$ k)2 = r2 satisfies the following conditions :
(i) centre of C3 is collinear with the centers of C1 and C2.
(ii) C1 and C2 both lie inside C3, and
(iii) C3 touches C1 at M and C2 at N.
Let the line through X and Y intersect C3 at Z and W, and let a common tangent of C1 and C3 be a tangent to the parabola x2 = 8$$\alpha $$y.
There are some expression given in the List-I whose values are given in List-II below.
Which of the following is the only CORRECT combination?
A
(II), (T)
B
(I), (S)
C
(II), (Q)
D
(I), (U)
2
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
An electric dipole with dipole moment $${{{p_0}} \over {\sqrt 2 }}(\widehat i + \widehat j)$$ is held fixed at the origin O in the presence of a uniform electric field of magnitude E0.
If the potential is constant on a circle of radius R centered at the origin as shown in figure, then the correct statement(s) is/are, ($$ \in $$0 is the permittivity of the free space, R >> dipole size)
A
The magnitude of total electric field on any two points of the circle will be same.
B
Total electric field at point B is $${\overrightarrow E _B}$$ = 0
$${\overrightarrow E _A} = \sqrt 2 {E_0}(\widehat i + \widehat j)$$
3
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
A small particle of mass m moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure.
When the distance of the piston from closed end is L = L0, the particle speed is v = v0. The piston is moved inward at a very low speed V such that $$V < < {{dL} \over L}{v_0}$$, where dL is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct?
A
After each collision with the piston, the particle speed increases by 2V.
B
If the piston moved inward by dL, the particle speed increases $$2v{{dL} \over L}$$.
C
The particle's kinetic energy increases by a factor of 4 when the piston is moved inward from L0 to 1/2 L0.
D
The rate at which the particle strikes the piston is v/L.
4
JEE Advanced 2019 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Three glass cylinders of equal height H = 30 cm and same refractive index n = 1.5 are placed on a horizontal surface as shown in figure.
Cylinder I has a flat top, cylinder II has a convex top and cylinder III has a concave top. The radii of curvature of the two curved tops are same (R = 3 m). If H1, H2, and H3 are the apparent depths of a point X on the bottom of the three cylinders, respectively, the correct statement(s) is/are
