1
JEE Main 2022 (Online) 24th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The number of distinct real roots of the equation

x7 $$-$$ 7x $$-$$ 2 = 0 is

A
5
B
7
C
1
D
3
2
JEE Main 2022 (Online) 24th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A random variable X has the following probability distribution :

X 0 1 2 3 4
P(X) k 2k 4k 6k 8k

The value of P(1 < X < 4 | X $$\le$$ 2) is equal to :

A
$${4 \over 7}$$
B
$${2 \over 3}$$
C
$${3 \over 7}$$
D
$${4 \over 5}$$
3
JEE Main 2022 (Online) 24th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

The number of solutions of the equation

$$\cos \left( {x + {\pi \over 3}} \right)\cos \left( {{\pi \over 3} - x} \right) = {1 \over 4}{\cos ^2}2x$$, $$x \in [ - 3\pi ,3\pi ]$$ is :

A
8
B
5
C
6
D
7
4
JEE Main 2022 (Online) 24th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the shortest distance between the lines $${{x - 1} \over 2} = {{y - 2} \over 3} = {{z - 3} \over \lambda }$$ and $${{x - 2} \over 1} = {{y - 4} \over 4} = {{z - 5} \over 5}$$ is $${1 \over {\sqrt 3 }}$$, then the sum of all possible value of $$\lambda$$ is :

A
16
B
6
C
12
D
15
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