1
JEE Main 2023 (Online) 1st February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$9=x_{1} < x_{2} < \ldots < x_{7}$$ be in an A.P. with common difference d. If the standard deviation of $$x_{1}, x_{2}..., x_{7}$$ is 4 and the mean is $$\bar{x}$$, then $$\bar{x}+x_{6}$$ is equal to :

A
$$2\left(9+\frac{8}{\sqrt{7}}\right)$$
B
25
C
$$18\left(1+\frac{1}{\sqrt{3}}\right)$$
D
34
2
JEE Main 2023 (Online) 1st February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$P(S)$$ denote the power set of $$S=\{1,2,3, \ldots ., 10\}$$. Define the relations $$R_{1}$$ and $$R_{2}$$ on $$P(S)$$ as $$\mathrm{AR}_{1} \mathrm{~B}$$ if $$\left(\mathrm{A} \cap \mathrm{B}^{\mathrm{c}}\right) \cup\left(\mathrm{B} \cap \mathrm{A}^{\mathrm{c}}\right)=\emptyset$$ and $$\mathrm{AR}_{2} \mathrm{~B}$$ if $$\mathrm{A} \cup \mathrm{B}^{\mathrm{c}}=\mathrm{B} \cup \mathrm{A}^{\mathrm{c}}, \forall \mathrm{A}, \mathrm{B} \in \mathrm{P}(\mathrm{S})$$. Then :

A
only $$R_{2}$$ is an equivalence relation
B
both $$R_{1}$$ and $$R_{2}$$ are not equivalence relations
C
both $$R_{1}$$ and $$R_{2}$$ are equivalence relations
D
only $$R_{1}$$ is an equivalence relation
3
JEE Main 2023 (Online) 1st February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let the plane P pass through the intersection of the planes $$2x+3y-z=2$$ and $$x+2y+3z=6$$, and be perpendicular to the plane $$2x+y-z+1=0$$. If d is the distance of P from the point ($$-$$7, 1, 1), then $$\mathrm{d^{2}}$$ is equal to :

A
$$\frac{250}{83}$$
B
$$\frac{250}{82}$$
C
$$\frac{15}{53}$$
D
$$\frac{25}{83}$$
4
JEE Main 2023 (Online) 1st February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The sum of the absolute maximum and minimum values of the function $$f(x)=\left|x^{2}-5 x+6\right|-3 x+2$$ in the interval $$[-1,3]$$ is equal to :

A
13
B
24
C
10
D
12
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