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

If the numbers appeared on the two throws of a fair six faced die are $$\alpha$$ and $$\beta$$, then the probability that $$x^{2}+\alpha x+\beta>0$$, for all $$x \in \mathbf{R}$$, is :

A
$$\frac{17}{36}$$
B
$$ \frac{4}{9} $$
C
$$\frac{1}{2}$$
D
$$\frac{19}{36}$$
2
JEE Main 2022 (Online) 25th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

The number of solutions of $$|\cos x|=\sin x$$, such that $$-4 \pi \leq x \leq 4 \pi$$ is :

A
4
B
6
C
8
D
12
3
JEE Main 2022 (Online) 25th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

A tower PQ stands on a horizontal ground with base $$Q$$ on the ground. The point $$R$$ divides the tower in two parts such that $$Q R=15 \mathrm{~m}$$. If from a point $$A$$ on the ground the angle of elevation of $$R$$ is $$60^{\circ}$$ and the part $$P R$$ of the tower subtends an angle of $$15^{\circ}$$ at $$A$$, then the height of the tower is :

A
$$5(2 \sqrt{3}+3) \,\mathrm{m}$$
B
$$5(\sqrt{3}+3) \,\mathrm{m}$$
C
$$10(\sqrt{3}+1) \,\mathrm{m}$$
D
$$10(2 \sqrt{3}+1) \,\mathrm{m}$$
4
JEE Main 2022 (Online) 25th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Which of the following statements is a tautology ?

A
$$((\sim \mathrm{p}) \vee \mathrm{q}) \Rightarrow \mathrm{p}$$
B
$$p \Rightarrow((\sim p) \vee q)$$
C
$$((\sim p) \vee q) \Rightarrow q$$
D
$$q \Rightarrow((\sim p) \vee q)$$
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