1
JEE Main 2025 (Online) 3rd April Evening Shift
MCQ (Single Correct Answer)
+4
-1

Let $A=\{-2,-1,0,1,2,3\}$. Let R be a relation on $A$ defined by $x \mathrm{R} y$ if and only if $y=\max \{x, 1\}$. Let $l$ be the number of elements in R . Let $m$ and $n$ be the minimum number of elements required to be added in R to make it reflexive and symmetric relations, respectively. Then $l+m+n$ is equal to

A
11
B
12
C
14
D
13
2
JEE Main 2025 (Online) 3rd April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Let the Mean and Variance of five observations $x_1=1, x_2=3, x_3=a, x_4=7$ and $x_5=\mathrm{b}, a>\mathrm{b}$, be 5 and 10 respectively. Then the Variance of the observations $n+x_n, n=1,2, \ldots, 5$ is
A
17
B
16
C
16.4
D
17.4
3
JEE Main 2025 (Online) 3rd April Evening Shift
MCQ (Single Correct Answer)
+4
-1
The integral $\int_0^\pi \frac{8 x d x}{4 \cos ^2 x+\sin ^2 x}$ is equal to
A
$2 \pi^2$
B
$4 \pi^2$
C
$\pi^2$
D
$\frac{3 \pi^2}{2}$
4
JEE Main 2025 (Online) 3rd April Evening Shift
MCQ (Single Correct Answer)
+4
-1
The distance of the point $(7,10,11)$ from the line $\frac{x-4}{1}=\frac{y-4}{0}=\frac{z-2}{3}$ along the line $\frac{x-9}{2}=\frac{y-13}{3}=\frac{z-17}{6}$ is
A
16
B
12
C
18
D
14
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