1
JEE Main 2023 (Online) 6th April Morning Shift
+4
-1

The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of another set of 15 numbers are 14 and $$\sigma^{2}$$ respectively. If the variance of all the 30 numbers in the two sets is 13 , then $$\sigma^{2}$$ is equal to :

A
12
B
11
C
10
D
9
2
JEE Main 2023 (Online) 1st February Evening Shift
+4
-1

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
3
JEE Main 2023 (Online) 1st February Morning Shift
+4
-1

The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3, 5, then the sum of cubes of the remaining two observations is :

A
1792
B
1216
C
1456
D
1072
4
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
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