1
JEE Main 2022 (Online) 28th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let y = y(x) be the solution of the differential equation $$x(1 - {x^2}){{dy} \over {dx}} + (3{x^2}y - y - 4{x^3}) = 0$$, $$x > 1$$, with $$y(2) = - 2$$. Then y(3) is equal to :

A
$$-$$18
B
$$-$$12
C
$$-$$6
D
$$-$$3
2
JEE Main 2022 (Online) 28th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The number of real solutions of

$${x^7} + 5{x^3} + 3x + 1 = 0$$ is equal to ____________.

A
0
B
1
C
3
D
5
3
JEE Main 2022 (Online) 28th June Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The probability, that in a randomly selected 3-digit number at least two digits are odd, is :

A
$${{19} \over {36}}$$
B
$${{15} \over {36}}$$
C
$${{13} \over {36}}$$
D
$${{23} \over {36}}$$
4
JEE Main 2022 (Online) 28th June Morning Shift
Numerical
+4
-1
Change Language

Let R1 and R2 be relations on the set {1, 2, ......., 50} such that

R1 = {(p, pn) : p is a prime and n $$\ge$$ 0 is an integer} and

R2 = {(p, pn) : p is a prime and n = 0 or 1}.

Then, the number of elements in R1 $$-$$ R2 is _______________.

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