1
JEE Advanced 2021 Paper 2 Online
Numerical
+4
-0
A number of chosen at random from the set {1, 2, 3, ....., 2000}. Let p be the probability that the chosen number is a multiple of 3 or a multiple of 7. Then the value of 500p is __________.
2
JEE Advanced 2021 Paper 2 Online
Numerical
+4
-0
Let E be the ellipse $${{{x^2}} \over {16}} + {{{y^2}} \over 9} = 1$$. For any three distinct points P, Q and Q' on E, let M(P, Q) be the mid-point of the line segment joining P and Q, and M(P, Q') be the mid-point of the line segment joining P and Q'. Then the maximum possible value of the distance between M(P, Q) and M(P, Q'), as P, Q and Q' vary on E, is _______.
3
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 __________.
4
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
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