1
JEE Main 2022 (Online) 29th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the focal chord of the parabola $$\mathrm{P}: y^{2}=4 x$$ along the line $$\mathrm{L}: y=\mathrm{m} x+\mathrm{c}, \mathrm{m}>0$$ meet the parabola at the points M and N. Let the line L be a tangent to the hyperbola $$\mathrm{H}: x^{2}-y^{2}=4$$. If O is the vertex of P and F is the focus of H on the positive x-axis, then the area of the quadrilateral OMFN is :

A
$$2 \sqrt{6}$$
B
$$2 \sqrt{14}$$
C
$$4 \sqrt{6}$$
D
$$4 \sqrt{14}$$
2
JEE Main 2022 (Online) 29th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The number of points, where the function $$f: \mathbf{R} \rightarrow \mathbf{R}$$,

$$f(x)=|x-1| \cos |x-2| \sin |x-1|+(x-3)\left|x^{2}-5 x+4\right|$$, is NOT differentiable, is :

A
1
B
2
C
3
D
4
3
JEE Main 2022 (Online) 29th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$S=\{1,2,3, \ldots, 2022\}$$. Then the probability, that a randomly chosen number n from the set S such that $$\mathrm{HCF}\,(\mathrm{n}, 2022)=1$$, is :

A
$$\frac{128}{1011}$$
B
$$\frac{166}{1011}$$
C
$$\frac{127}{337}$$
D
$$\frac{112}{337}$$
4
JEE Main 2022 (Online) 29th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$f(x)=3^{\left(x^{2}-2\right)^{3}+4}, x \in \mathrm{R}$$. Then which of the following statements are true?

$$\mathrm{P}: x=0$$ is a point of local minima of $$f$$

$$\mathrm{Q}: x=\sqrt{2}$$ is a point of inflection of $$f$$

$$R: f^{\prime}$$ is increasing for $$x>\sqrt{2}$$

A
Only P and Q
B
Only P and R
C
Only Q and R
D
All P, Q and R
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