1
JEE Main 2022 (Online) 26th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$\tan \left(2 \tan ^{-1} \frac{1}{5}+\sec ^{-1} \frac{\sqrt{5}}{2}+2 \tan ^{-1} \frac{1}{8}\right)$$ is equal to :

A
1
B
2
C
$$\frac{1}{4}$$
D
$$\frac{5}{4}$$
2
JEE Main 2022 (Online) 26th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

The statement $$(\sim(\mathrm{p} \Leftrightarrow \,\sim \mathrm{q})) \wedge \mathrm{q}$$ is :

A
a tautology
B
a contradiction
C
equivalent to $$(p \Rightarrow q) \wedge q$$
D
equivalent to $$(p \Rightarrow q) \wedge p$$
3
JEE Main 2022 (Online) 26th July Morning Shift
Numerical
+4
-1
Change Language

If for some $$\mathrm{p}, \mathrm{q}, \mathrm{r} \in \mathbf{R}$$, not all have same sign, one of the roots of the equation $$\left(\mathrm{p}^{2}+\mathrm{q}^{2}\right) x^{2}-2 \mathrm{q}(\mathrm{p}+\mathrm{r}) x+\mathrm{q}^{2}+\mathrm{r}^{2}=0$$ is also a root of the equation $$x^{2}+2 x-8=0$$, then $$\frac{\mathrm{q}^{2}+\mathrm{r}^{2}}{\mathrm{p}^{2}}$$ is equal to ____________,

Your input ____
4
JEE Main 2022 (Online) 26th July Morning Shift
Numerical
+4
-1
Change Language

The number of 5-digit natural numbers, such that the product of their digits is 36 , is __________.

Your input ____
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