1
JEE Main 2023 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let the mean and standard deviation of marks of class A of 100 students be respectively 40 and $\alpha(>$ 0 ), and the mean and standard deviation of marks of class $B$ of $n$ students be respectively 55 and 30 $-\alpha$. If the mean and variance of the marks of the combined class of $100+\mathrm{n}$ studants are respectively 50 and 350 , then the sum of variances of classes $A$ and $B$ is :
A
450
B
900
C
650
D
500
2
JEE Main 2023 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $a_1, a_2, a_3, \ldots$ be an A.P. If $a_7=3$, the product $a_1 a_4$ is minimum and the sum of its first $n$ terms is zero, then $n !-4 a_{n(n+2)}$ is equal to :
A
24
B
$\frac{381}{4}$
C
9
D
$\frac{33}{4}$
3
JEE Main 2023 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
The number of values of $\mathrm{r} \in\{\mathrm{p}, \mathrm{q}, \sim \mathrm{p}, \sim \mathrm{q}\}$ for which $((\mathrm{p} \wedge \mathrm{q}) \Rightarrow(\mathrm{r} \vee \mathrm{q})) \wedge((\mathrm{p} \wedge \mathrm{r}) \Rightarrow \mathrm{q})$ is a tautology, is :
A
2
B
1
C
4
D
3
4
JEE Main 2023 (Online) 31st January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The complex number $z=\frac{i-1}{\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}}$ is equal to :
A
$\cos \frac{\pi}{12}-i \sin \frac{\pi}{12}$
B
$\sqrt{2}\left(\cos \frac{\pi}{12}+i \sin \frac{\pi}{12}\right)$
C
$\sqrt{2} i\left(\cos \frac{5 \pi}{12}-i \sin \frac{5 \pi}{12}\right)$
D
$\sqrt{2}\left(\cos \frac{5 \pi}{12}+i \sin \frac{5 \pi}{12}\right)$
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