1
JEE Main 2023 (Online) 8th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$R$$ be the focus of the parabola $$y^{2}=20 x$$ and the line $$y=m x+c$$ intersect the parabola at two points $$P$$ and $$Q$$.

Let the point $$G(10,10)$$ be the centroid of the triangle $$P Q R$$. If $$c-m=6$$, then $$(P Q)^{2}$$ is :

A
317
B
325
C
346
D
296
2
JEE Main 2023 (Online) 8th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The area of the region $$\left\{(x, y): x^{2} \leq y \leq 8-x^{2}, y \leq 7\right\}$$ is :

A
18
B
24
C
20
D
21
3
JEE Main 2023 (Online) 8th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$C(\alpha, \beta)$$ be the circumcenter of the triangle formed by the lines

$$4 x+3 y=69$$

$$4 y-3 x=17$$, and

$$x+7 y=61$$.

Then $$(\alpha-\beta)^{2}+\alpha+\beta$$ is equal to :

A
15
B
17
C
16
D
18
4
JEE Main 2023 (Online) 8th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$I(x)=\int \frac{(x+1)}{x\left(1+x e^{x}\right)^{2}} d x, x > 0$$. If $$\lim_\limits{x \rightarrow \infty} I(x)=0$$, then $$I(1)$$ is equal to :

A
$$\frac{e+1}{e+2}-\log _{e}(e+1)$$
B
$$\frac{e+1}{e+2}+\log _{e}(e+1)$$
C
$$\frac{e+2}{e+1}-\log _{e}(e+1)$$
D
$$\frac{e+2}{e+1}+\log _{e}(e+1)$$
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