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

Let $$\widehat a$$ and $$\widehat b$$ be two unit vectors such that $$|(\widehat a + \widehat b) + 2(\widehat a \times \widehat b)| = 2$$. If $$\theta$$ $$\in$$ (0, $$\pi$$) is the angle between $$\widehat a$$ and $$\widehat b$$, then among the statements :

(S1) : $$2|\widehat a \times \widehat b| = |\widehat a - \widehat b|$$

(S2) : The projection of $$\widehat a$$ on ($$\widehat a$$ + $$\widehat b$$) is $${1 \over 2}$$

A
Only (S1) is true.
B
Only (S2) is true.
C
Both (S1) and (S2) are true.
D
Both (S1) and (S2) are false.
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