1
JEE Main 2023 (Online) 30th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $S$ be the set of all values of $a_1$ for which the mean deviation about the mean of 100 consecutive positive integers $a_1, a_2, a_3, \ldots ., a_{100}$ is 25 . Then $S$ is :
A
$\{9\}$
B
$\phi$
C
$\{99\}$
D
N
2
JEE Main 2023 (Online) 30th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
If a plane passes through the points $(-1, k, 0),(2, k,-1),(1,1,2)$ and is parallel to the line $\frac{x-1}{1}=\frac{2 y+1}{2}=\frac{z+1}{-1}$, then the value of $\frac{k^2+1}{(k-1)(k-2)}$ is :
A
$\frac{17}{5}$
B
$\frac{6}{13}$
C
$\frac{13}{6}$
D
$\frac{5}{17}$
3
JEE Main 2023 (Online) 30th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
$\lim\limits_{n \rightarrow \infty} \frac{3}{n}\left\{4+\left(2+\frac{1}{n}\right)^2+\left(2+\frac{2}{n}\right)^2+\ldots+\left(3-\frac{1}{n}\right)^2\right\}$ is equal to :
A
0
B
$\frac{19}{3}$
C
19
D
12
4
JEE Main 2023 (Online) 30th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Consider the following statements:

P : I have fever

Q: I will not take medicine

$\mathrm{R}$ : I will take rest.

The statement "If I have fever, then I will take medicine and I will take rest" is equivalent to :

A
$((\sim P) \vee \sim Q) \wedge((\sim P) \vee \sim R)$
B
$(P \vee \sim Q) \wedge(P \vee \sim R)$
C
$((\sim P) \vee \sim Q) \wedge((\sim P) \vee R)$
D
$(P \vee Q) \wedge((\sim P) \vee R)$
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