1
JEE Main 2022 (Online) 28th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$C$$ be the centre of the circle $$x^{2}+y^{2}-x+2 y=\frac{11}{4}$$ and $$P$$ be a point on the circle. A line passes through the point $$\mathrm{C}$$, makes an angle of $$\frac{\pi}{4}$$ with the line $$\mathrm{CP}$$ and intersects the circle at the points $$Q$$ and $$R$$. Then the area of the triangle $$P Q R$$ (in unit $$^{2}$$ ) is :

A
2
B
2$$\sqrt2$$
C
$$8 \sin \left(\frac{\pi}{8}\right)$$
D
$$8 \cos \left(\frac{\pi}{8}\right)$$
2
JEE Main 2022 (Online) 28th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The remainder when $$7^{2022}+3^{2022}$$ is divided by 5 is :

A
0
B
2
C
3
D
4
3
JEE Main 2022 (Online) 28th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$S_{1}=\left\{z_{1} \in \mathbf{C}:\left|z_{1}-3\right|=\frac{1}{2}\right\}$$ and $$S_{2}=\left\{z_{2} \in \mathbf{C}:\left|z_{2}-\right| z_{2}+1||=\left|z_{2}+\right| z_{2}-1||\right\}$$. Then, for $$z_{1} \in S_{1}$$ and $$z_{2} \in S_{2}$$, the least value of $$\left|z_{2}-z_{1}\right|$$ is :

A
0
B
$$\frac{1}{2}$$
C
$$\frac{3}{2}$$
D
$$\frac{5}{2}$$
4
JEE Main 2022 (Online) 28th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the minimum value of $$f(x)=\frac{5 x^{2}}{2}+\frac{\alpha}{x^{5}}, x>0$$, is 14 , then the value of $$\alpha$$ is equal to :

A
32
B
64
C
128
D
256
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