1
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$y = y(x)$$ is the solution of the differential equation

$$2{x^2}{{dy} \over {dx}} - 2xy + 3{y^2} = 0$$ such that $$y(e) = {e \over 3}$$, then y(1) is equal to :

A
$${1 \over 3}$$
B
$${2 \over 3}$$
C
$${3 \over 2}$$
D
3
2
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

If the angle made by the tangent at the point (x0, y0) on the curve $$x = 12(t + \sin t\cos t)$$, $$y = 12{(1 + \sin t)^2}$$, $$0 < t < {\pi \over 2}$$, with the positive x-axis is $${\pi \over 3}$$, then y0 is equal to:

A
$$6\left( {3 + 2\sqrt 2 } \right)$$
B
$$3\left( {7 + 4\sqrt 3 } \right)$$
C
27
D
48
3
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The value of 2sin (12$$^\circ$$) $$-$$ sin (72$$^\circ$$) is :

A
$${{\sqrt 5 (1 - \sqrt 3 )} \over 4}$$
B
$${{1 - \sqrt 5 } \over 8}$$
C
$${{\sqrt 3 (1 - \sqrt 5 )} \over 2}$$
D
$${{\sqrt 3 (1 - \sqrt 5 )} \over 4}$$
4
JEE Main 2022 (Online) 25th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is $${1 \over n}$$. If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48, is :

A
$${7 \over {{2^{11}}}}$$
B
$${7 \over {{2^{12}}}}$$
C
$${3 \over {{2^{10}}}}$$
D
$${{13} \over {{2^{12}}}}$$
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