1
JEE Main 2023 (Online) 31st January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

$$(\mathrm{S} 1)~(p \Rightarrow q) \vee(p \wedge(\sim q))$$ is a tautology

$$(\mathrm{S} 2)~((\sim p) \Rightarrow(\sim q)) \wedge((\sim p) \vee q)$$ is a contradiction.

Then

A
only (S2) is correct
B
both (S1) and (S2) are correct
C
only (S1) is correct
D
both (S1) and (S2) are wrong
2
JEE Main 2023 (Online) 31st January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let $$\mathrm{y}=f(x)$$ represent a parabola with focus $$\left(-\frac{1}{2}, 0\right)$$ and directrix $$y=-\frac{1}{2}$$. Then

$$S=\left\{x \in \mathbb{R}: \tan ^{-1}(\sqrt{f(x)})+\sin ^{-1}(\sqrt{f(x)+1})=\frac{\pi}{2}\right\}$$ :

A
is an empty set
B
contains exactly one element
C
contains exactly two elements
D
is an infinite set
3
JEE Main 2023 (Online) 31st January Morning Shift
Numerical
+4
-1
Change Language

The remainder on dividing $$5^{99}$$ by 11 is ____________.

Your input ____
4
JEE Main 2023 (Online) 31st January Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language

Let the line $$L: \frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-3}{1}$$ intersect the plane $$2 x+y+3 z=16$$ at the point $$P$$. Let the point $$Q$$ be the foot of perpendicular from the point $$R(1,-1,-3)$$ on the line $$L$$. If $$\alpha$$ is the area of triangle $$P Q R$$, then $$\alpha^{2}$$ is equal to __________.

Your input ____
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