1
JEE Main 2023 (Online) 10th April Evening Shift
+4
-1 Let $$\mu$$ be the mean and $$\sigma$$ be the standard deviation of the distribution

$${x_i}$$ 0 1 2 3 4 5
$${f_i}$$ $$k + 2$$ $$2k$$ $${k^2} - 1$$ $${k^2} - 1$$ $${k^2} + 1$$ $$k - 3$$

where $$\sum f_{i}=62$$. If $$[x]$$ denotes the greatest integer $$\leq x$$, then $$\left[\mu^{2}+\sigma^{2}\right]$$ is equal to

A
9
B
8
C
6
D
7
2
JEE Main 2023 (Online) 8th April Evening Shift
+4
-1 Let the mean and variance of 12 observations be $$\frac{9}{2}$$ and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is $$\frac{m}{n}$$, where $$\mathrm{m}$$ and $$\mathrm{n}$$ are coprime, then $$\mathrm{m}+\mathrm{n}$$ is equal to :

A
317
B
316
C
314
D
315
3
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
4
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
JEE Main Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination