1
JEE Main 2023 (Online) 31st January Evening Shift
+4
-1
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) 30th January Evening Shift
+4
-1
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
3
JEE Main 2023 (Online) 29th January Morning Shift
+4
-1

Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable X denote the number of rotten apples. If $$\mu$$ and $$\sigma^2$$ represent mean and variance of X, respectively, then $$10(\mu^2+\sigma^2)$$ is equal to

A
20
B
30
C
250
D
25
4
JEE Main 2023 (Online) 25th January Morning Shift
+4
-1

The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased from 8 to 12. If the new mean of the marks is 10.2, then their new variance is equal to :

A
3.92
B
4.08
C
3.96
D
4.04
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