1
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
2
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
3
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
4
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
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