1
JEE Main 2020 (Online) 7th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value of k when k consecutive heads are obtained for k = 3, 4, 5, otherwise X takes the value -1. Then the expected value of X, is :
A
$$ - {3 \over {16}}$$
B
$$ - {1 \over 8}$$
C
$${1 \over 8}$$
D
$${3 \over {16}}$$
2
JEE Main 2020 (Online) 7th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
The area of the region, enclosed by the circle x2 + y2 = 2 which is not common to the region bounded by the parabola y2 = x and the straight line y = x, is:
A
$${1 \over 6}\left( {24\pi - 1} \right)$$
B
$${1 \over 3}\left( {12\pi - 1} \right)$$
C
$${1 \over 3}\left( {6\pi - 1} \right)$$
D
$${1 \over 6}\left( {12\pi - 1} \right)$$
3
JEE Main 2020 (Online) 7th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is :
A
$$\sqrt 3 $$
B
$$3\sqrt 2 $$
C
$${3 \over {\sqrt 2 }}$$
D
$$2\sqrt 3 $$
4
JEE Main 2020 (Online) 7th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the earth. After it reaches height R (R = radius of the earth), it ejects a rocket of mass $${m \over {10}}$$ so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is (G is the gravitational constant; M is the mass of the earth) :
A
$${{3m} \over 8}{\left( {u + \sqrt {{{5GM} \over {6R}}} } \right)^2}$$
B
$${m \over {20}}\left( {{u^2} + {{113} \over {100}}{{GM} \over R}} \right)$$
C
$$5m\left( {{u^2} - {{119} \over {100}}{{GM} \over R}} \right)$$
D
$${m \over {20}}{\left( {u - \sqrt {{{2GM} \over {3R}}} } \right)^2}$$
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