1
JEE Advanced 2021 Paper 2 Online
Numerical
+4
-0
For any real number x, let [ x ] denote the largest integer less than or equal to x. If $$I = \int\limits_0^{10} {\left[ {\sqrt {{{10x} \over {x + 1}}} } \right]dx}$$, then the value of 9I is __________.
2
JEE Advanced 2021 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
One end of a horizontal uniform beam of weight W and length L is hinged on a vertical wall at point O and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point Q, at a height L above the hinge at point O. A block of weight $$\alpha$$W is attached at the point P of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of (2$$\sqrt 2$$)W. Which of the following statement(s) is(are) correct?

A
The vertical component of reaction force at O does not depend on $$\alpha$$
B
The horizontal component of reaction force at O is equal to W for $$\alpha$$ = 0.5
C
The tension in the rope is 2W for $$\alpha$$ = 0.5
D
The rope breaks if $$\alpha$$ > 1.5
3
JEE Advanced 2021 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
A source, approaching with speed u towards the open end of a stationary pipe of length L, is emitting a sound of frequency fs. The farther end of the pipe is closed. The speed of sound in air is v and f0 is the fundamental frequency of the pipe. For which of the following combination(s) of u and fs, will the sound reaching the pipe lead to a resonance?
A
u = 0.8v and fs = f0
B
u = 0.8v and fs = 2f0
C
u = 0.8v and fs = 0.5f0
D
u = 0.5v and fs = 1.5f0
4
JEE Advanced 2021 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
For a prism of prism angle $$\theta$$ = 60$$^\circ$$, the refractive indices of the left half and the right half are, respectively, n1 and n2 (n2 $$\ge$$ n1) as shown in the figure. The angle of incidence i is chosen such that the incident light rays will have minimum deviation if n1 = n2 = n = 1.5. For the case of unequal refractive indices, n1 = n and n2 = n + $$\Delta$$n (where $$\Delta$$n << n), the angle of emergence e = i + $$\Delta$$e. Which of the following statement(s) is(are) correct?

A
The value of $$\Delta$$e (in radians) is greater than that of $$\Delta$$n
B
$$\Delta$$e is proportional to $$\Delta$$n
C
$$\Delta$$e lies between 2.0 and 3.0 milliradians, if $$\Delta$$n = 2.8 $$\times$$ 10$$-$$3
D
$$\Delta$$e lies between1.0 and 1.6 milliradians, if $$\Delta$$n = 2.8 $$\times$$ 10$$-$$3
EXAM MAP
Medical
NEET