# Statistics · Mathematics · JEE Main

Start Practice## MCQ (Single Correct Answer)

JEE Main 2024 (Online) 9th April Evening Shift

If the variance of the frequency distribution
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JEE Main 2024 (Online) 9th April Morning Shift

The frequency distribution of the age of students in a class of 40 students is given below.
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JEE Main 2024 (Online) 6th April Morning Shift

The mean and standard deviation of 20 observations are found to be 10 and 2 , respectively. On rechecking, it was found that an observation by mistake...

JEE Main 2024 (Online) 4th April Morning Shift

Let $$\alpha, \beta \in \mathbf{R}$$. Let the mean and the variance of 6 observations $$-3,4,7,-6, \alpha, \beta$$ be 2 and 23, respectively. The mean...

JEE Main 2024 (Online) 1st February Evening Shift

Consider 10 observations $x_1, x_2, \ldots, x_{10}$ such that $\sum\limits_{i=1}^{10}\left(x_i-\alpha\right)=2$ and $\sum\limits_{i=1}^{10}\left(x_i-\...

JEE Main 2024 (Online) 1st February Morning Shift

Let the median and the mean deviation about the median of 7 observation $170,125,230,190,210$, a, b be 170 and $\frac{205}{7}$ respectively. Then the ...

JEE Main 2024 (Online) 31st January Evening Shift

Let the mean and the variance of 6 observations $$a, b, 68,44,48,60$$ be $$55$$ and $$194$$, respectively. If $$a>b$$, then $$a+3 b$$ is

JEE Main 2024 (Online) 30th January Morning Shift

Let M denote the median of the following frequency distribution
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JEE Main 2024 (Online) 29th January Evening Shift

If the mean and variance of five observations are $$\frac{24}{5}$$ and $$\frac{194}{25}$$ respectively and the mean of the first four observations is ...

JEE Main 2024 (Online) 27th January Morning Shift

Let $\mathrm{a}_1, \mathrm{a}_2, \ldots \mathrm{a}_{10}$ be 10 observations such that $\sum\limits_{\mathrm{k}=1}^{10} \mathrm{a}_{\mathrm{k}}=50$ and...

JEE Main 2023 (Online) 15th April Morning Shift

The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded as 50 instea...

JEE Main 2023 (Online) 11th April Evening Shift

Let the mean of 6 observations $$1,2,4,5, \mathrm{x}$$ and $$\mathrm{y}$$ be 5 and their variance be 10 .
Then their mean deviation about the mean is...

JEE Main 2023 (Online) 11th April Morning Shift

Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A...

JEE Main 2023 (Online) 10th April Evening Shift

Let $$\mu$$ be the mean and $$\sigma$$ be the standard deviation of the distribution
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JEE Main 2023 (Online) 8th April Evening Shift

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...

JEE Main 2023 (Online) 6th April Morning Shift

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 $$\sigma^{2}$$ ...

JEE Main 2023 (Online) 1st February Evening Shift

Let $$9=x_{1} ...

JEE Main 2023 (Online) 1st February Morning Shift

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 observatio...

JEE Main 2023 (Online) 31st January Evening Shift

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...

JEE Main 2023 (Online) 30th January Evening Shift

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...

JEE Main 2023 (Online) 29th January Morning Shift

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 de...

JEE Main 2023 (Online) 25th January Morning Shift

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 ...

JEE Main 2023 (Online) 24th January Evening Shift

Let the six numbers $$\mathrm{a_1,a_2,a_3,a_4,a_5,a_6}$$, be in A.P. and $$\mathrm{a_1+a_3=10}$$. If the mean of these six numbers is $$\frac{19}{2}$$...

JEE Main 2022 (Online) 25th July Evening Shift

If the mean deviation about median for the numbers 3, 5, 7, 2k, 12, 16, 21, 24, arranged in the ascending order, is 6 then the median is :

JEE Main 2022 (Online) 29th June Evening Shift

The number of values of a $$\in$$ N such that the variance of 3, 7, 12, a, 43 $$-$$ a is a natural number is :

JEE Main 2022 (Online) 29th June Morning Shift

Let the mean and the variance of 5 observations x1, x2, x3, x4, x5 be $${24 \over 5}$$ and $${194 \over 25}$$ respectively. If the mean and variance o...

JEE Main 2022 (Online) 27th June Evening Shift

The mean and variance of the data 4, 5, 6, 6, 7, 8, x, y, where x ...

JEE Main 2022 (Online) 26th June Evening Shift

The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum ...

JEE Main 2022 (Online) 26th June Morning Shift

The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then 25 M is equal to...

JEE Main 2021 (Online) 31st August Evening Shift

The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then the variance of the remaining 5 observations ...

JEE Main 2021 (Online) 26th August Morning Shift

The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value was taken a...

JEE Main 2021 (Online) 27th July Evening Shift

Let the mean and variance of the frequency distribution$$\matrix{
{x:} & {{x_1} = 2} & {{x_2} = 6} & {{x_3} = 8} & {{x_4} = 9} \cr...

JEE Main 2021 (Online) 27th July Morning Shift

If the mean and variance of the following data : 6, 10, 7, 13, a, 12, b, 12 are 9 and $${{37} \over 4}$$ respectively, then (a $$-$$ b)2 is equal to :...

JEE Main 2021 (Online) 25th July Evening Shift

The first of the two samples in a group has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and stand...

JEE Main 2021 (Online) 20th July Evening Shift

If the mean and variance of six observations 7, 10, 11, 15, a, b are 10 and $${{20} \over 3}$$, respectively, then the value of | a $$-$$ b | is equal...

JEE Main 2021 (Online) 20th July Morning Shift

The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, then the remaining two observati...

JEE Main 2021 (Online) 18th March Evening Shift

Let in a series of 2n observations, half of them are equal to a and remaining half are equal to $$-$$a. Also by adding a constant b in each of these o...

JEE Main 2021 (Online) 16th March Morning Shift

Consider three observations a, b, and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is tru...

JEE Main 2020 (Online) 6th September Morning Slot

If $$\sum\limits_{i = 1}^n {\left( {{x_i} - a} \right)} = n$$ and $$\sum\limits_{i = 1}^n {{{\left( {{x_i} - a} \right)}^2}} = na$$
(n, a > 1) th...

JEE Main 2020 (Online) 5th September Evening Slot

If the mean and the standard deviation of the
data 3, 5, 7, a, b are 5 and 2 respectively, then
a and b are the roots of the equation :

JEE Main 2020 (Online) 5th September Morning Slot

The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14, then the absolute difference of the rem...

JEE Main 2020 (Online) 4th September Morning Slot

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations
are 5, 7, 10, 12, 14, 15, then the absolute differen...

JEE Main 2020 (Online) 3rd September Evening Slot

Let xi
(1 $$ \le $$ i $$ \le $$ 10) be ten observations of a
random variable X. If $$\sum\limits_{i = 1}^{10} {\left( {{x_i} - p} \right)} = 3$$ and...

JEE Main 2020 (Online) 3rd September Morning Slot

For the frequency distribution :
Variate (x) : x1 x2 x3
.... x15
Frequency (f) : f1
...

JEE Main 2020 (Online) 2nd September Morning Slot

Let X = {x
$$ \in $$ N : 1
$$ \le $$ x
$$ \le $$ 17} and
Y = {ax + b: x
$$ \in $$ X and a, b $$ \in $$ R, a > 0}. If mean
and variance of elements ...

JEE Main 2020 (Online) 9th January Morning Slot

Let the observations xi (1 $$ \le $$ i $$ \le $$ 10) satisfy the
equations, $$\sum\limits_{i = 1}^{10} {\left( {{x_1} - 5} \right)} $$ = 10 and $$\sum...

JEE Main 2020 (Online) 8th January Evening Slot

The mean and variance of 20 observations are
found to be 10 and 4, respectively. On
rechecking, it was found that an observation 9
was incorrect and t...

JEE Main 2020 (Online) 8th January Morning Slot

The mean and the standard deviation (s.d.) of
10 observations are 20 and 2 resepectively.
Each of these 10 observations is multiplied by
p and then re...

JEE Main 2019 (Online) 12th April Morning Slot

If the data x1, x2,......., x10 is such that the mean of first four of these is 11, the mean of the remaining six is
16 and the sum of squares of all ...

JEE Main 2019 (Online) 10th April Evening Slot

If both the mean and the standard deviation of 50 observations x1, x2,..., x50 are equal to 16, then the mean of (x1 – 4)2
, (x2 – 4)2
,....., (x50 – ...

JEE Main 2019 (Online) 10th April Morning Slot

If for some x $$ \in $$ R, the frequency distribution of the marks obtained by 20 students in a test is :
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JEE Main 2019 (Online) 9th April Evening Slot

The mean and the median of the following ten
numbers in increasing order 10, 22, 26, 29, 34, x,
42, 67, 70, y are 42 and 35 respectively, then $${y \o...

JEE Main 2019 (Online) 9th April Morning Slot

If the standard deviation of the numbers
–1, 0, 1, k is $$\sqrt 5$$ where k > 0, then k is equal to

JEE Main 2019 (Online) 8th April Evening Slot

A student scores the following marks in five tests
:
45, 54, 41, 57, 43.
His score is not known for the
sixth test. If the mean score is 48 in the s...

JEE Main 2019 (Online) 8th April Morning Slot

The mean and variance of seven observations are
8 and 16, respectively. If 5 of the observations are
2, 4, 10, 12, 14, then the product of the remaini...

JEE Main 2019 (Online) 12th January Evening Slot

The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are
3, 4 and 4 ; then the absolute value of ...

JEE Main 2019 (Online) 12th January Morning Slot

If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is :

JEE Main 2019 (Online) 11th January Morning Slot

The outcome of each of 30 items was observed; 10 items gave an outcome $${1 \over 2}$$ – d each, 10 items gave outcome $${1 \over 2}$$ each and the re...

JEE Main 2019 (Online) 10th January Evening Slot

If mean and standard deviation of 5 observations x1, x2, x3, x4, x5 are 10 and 3, respectively, then the variance of 6 observations x1, x2, ….., x5 an...

JEE Main 2019 (Online) 10th January Morning Slot

The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two obser...

JEE Main 2019 (Online) 9th January Evening Slot

A data consists of n observations : x1, x2, . . . . . . ., xn.
If $$\sum\limits_{i = 1}^n {{{\left( {{x_i} ...

JEE Main 2019 (Online) 9th January Morning Slot

5 students of a class have an average height 150 cm and variance 18 cm2. A new student, whose height is 156 cm, joined them. The variance (in cm2) of ...

JEE Main 2018 (Online) 16th April Morning Slot

The mean and the standard deviation(s.d.) of five observations are9 and 0, respectively. If one of the observations is changed such that the mean of t...

JEE Main 2018 (Offline)

If $$\sum\limits_{i = 1}^9 {\left( {{x_i} - 5} \right)} = 9$$ and
$$\sum\limits_{i = 1}^9 {{{\left( {{x_i} - 5} \right)}^2}} = 45$$, then the standa...

JEE Main 2018 (Online) 15th April Evening Slot

If the mean of the data : 7, 8, 9, 7, 8, 7, $$\lambda $$, 8 is 8, then the variance of this data is :

JEE Main 2018 (Online) 15th April Morning Slot

The mean of set of 30 observations is 75. If each observation is multiplied by a non-zero number $$\lambda $$ and then each of them is decreased by 25...

JEE Main 2017 (Online) 9th April Morning Slot

The sum of 100 observations and the sum of their squares are 400 and 2475,
respectively. Later on, three observations, 3, 4 and 5, were found to be in...

JEE Main 2017 (Online) 8th April Morning Slot

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If now the...

JEE Main 2016 (Online) 10th April Morning Slot

The mean of 5 observations is 5 and their variance is 124. If three of the observations
are 1, 2 and 6 ; then the mean deviation from the mean of the ...

JEE Main 2016 (Online) 9th April Morning Slot

If the mean deviation of the numbers 1, 1 + d, ..., 1 +100d from their mean is 255, then a value of d is :

JEE Main 2016 (Offline)

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

JEE Main 2015 (Offline)

The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted
and three new observations valued 3, 4 an...

JEE Main 2014 (Offline)

The variance of first 50 even natural numbers is

JEE Main 2013 (Offline)

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10
to each of the students. Which of the follo...

AIEEE 2012

Let x1, x2,........., xn be n observations, and let $$\overline x $$ be their arithematic mean and $${\sigma ^2}$$ be their variance.
Statement 1 : Va...

AIEEE 2011

If the mean deviation about the median of the numbers a, 2a,........., 50a is 50, then |a| equals

AIEEE 2010

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding
means are given to be 2 and 4, respectively. The varian...

AIEEE 2009

If the mean deviation of number 1, 1 + d, 1 + 2d,........, 1 + 100d from their mean is 255, then the d is
equal to

AIEEE 2009

Statement - 1 : The variance of first n even natural numbers is $${{{n^2} - 1} \over 4}$$
Statement - 2 : The sum of first n natural numbers is $${{n\...

AIEEE 2008

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following
gives possible values of a and b?

AIEEE 2007

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys
and girls combined is 50. The percentage of boys in the ...

AIEEE 2006

Suppose a population A has 100 observations 101, 102,........, 200, and another
population B has 100 observations 151, 152,......., 250. If VA and VB ...

AIEEE 2005

If in a frequency distribution, the mean and median are 21 and 22 respectively, then
its mode is approximately :

AIEEE 2005

Let x1, x2,...........,xn be n observations such that
$$\sum {x_i^2} = 400$$ and $$\sum {{x_i}} = 80$$. Then a
possible value of n among the followi...

AIEEE 2004

Consider the following statements:
(a) Mode can be computed from histogram
(b) Median is not independent of change of scale
(c) Variance is indepen...

AIEEE 2004

In a series of 2n observations, half of them equal $$a$$ and remaining half equal $$–a$$. If the
standard deviation of the observations is 2, then $$|...

AIEEE 2003

In an experiment with 15 observations on $$x$$, then following results were available:
$$\sum {{x^2}} = 2830$$, $$\sum x = 170$$
One observation tha...

AIEEE 2003

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of
the set is increased by 2, then the median of the new...

AIEEE 2002

In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is t...

## Numerical

JEE Main 2024 (Online) 8th April Evening Shift

Let $$\mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathbf{N}$$ and $$\mathrm{a}...

JEE Main 2024 (Online) 5th April Evening Shift

Let the mean and the standard deviation of the probability distribution
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JEE Main 2024 (Online) 30th January Evening Shift

The variance $$\sigma^2$$ of the data
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JEE Main 2024 (Online) 29th January Morning Shift

If the mean and variance of the data $$65,68,58,44,48,45,60, \alpha, \beta, 60$$ where $$\alpha> \beta$$, are 56 and 66.2 respectively, then $$\alpha^...

JEE Main 2024 (Online) 27th January Evening Shift

The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as ...

JEE Main 2023 (Online) 13th April Evening Shift

The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks 20 and 25 w...

JEE Main 2023 (Online) 13th April Morning Shift

Let the mean of the data
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JEE Main 2023 (Online) 12th April Morning Shift

Let the positive numbers $$a_{1}, a_{2}, a_{3}, a_{4}$$ and $$a_{5}$$ be in a G.P. Let their mean and variance be $$\frac{31}{10}$$ and $$\frac{m}{n}$...

JEE Main 2023 (Online) 10th April Morning Shift

If the mean of the frequency distribution
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JEE Main 2023 (Online) 8th April Morning Shift

Let the mean and variance of 8 numbers $$x, y, 10,12,6,12,4,8$$ be $$9$$ and $$9.25$$ respectively. If $$x > y$$, then $$3 x-2 y$$ is equal to _______...

JEE Main 2023 (Online) 6th April Evening Shift

If the mean and variance of the frequency distribution
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JEE Main 2023 (Online) 31st January Morning Shift

If the variance of the frequency distribution
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JEE Main 2023 (Online) 30th January Morning Shift

The mean and variance of 7 observations are 8 and 16 respectively. If one observation 14 is omitted and a and b are respectively mean and variance of ...

JEE Main 2023 (Online) 29th January Evening Shift

Let $$X=\{11,12,13,....,40,41\}$$ and $$Y=\{61,62,63,....,90,91\}$$ be the two sets of observations. If $$\overline x $$ and $$\overline y $$ are thei...

JEE Main 2022 (Online) 29th July Morning Shift

Let the mean and the variance of 20 observations $$x_{1}, x_{2}, \ldots, x_{20}$$ be 15 and 9 , respectively. For $$\alpha \in \mathbf{R}$$, if the me...

JEE Main 2022 (Online) 28th July Morning Shift

Let $$x_{1}, x_{2}, x_{3}, \ldots, x_{20}$$ be in geometric progression with $$x_{1}=3$$ and the common ratio $$\frac{1}{2}$$. A new data is construct...

JEE Main 2022 (Online) 27th July Morning Shift

The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observati...

JEE Main 2022 (Online) 26th July Evening Shift

The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly rec...

JEE Main 2022 (Online) 28th June Evening Shift

Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their variance is 20. A student fails in...

JEE Main 2022 (Online) 28th June Morning Shift

The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was ...

JEE Main 2022 (Online) 25th June Evening Shift

If the mean deviation about the mean of the numbers 1, 2, 3, .........., n, where n is odd, is $${{5(n + 1)} \over n}$$, then n is equal to __________...

JEE Main 2021 (Online) 31st August Morning Shift

The mean of 10 numbers 7 $$\times$$ 8, 10 $$\times$$ 10, 13 $$\times$$ 12, 16 $$\times$$ 14, ....... is ____________.

JEE Main 2021 (Online) 27th August Evening Shift

An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2. The variance of mar...

JEE Main 2021 (Online) 27th August Morning Shift

Let n be an odd natural number such that the variance of 1, 2, 3, 4, ......, n is 14. Then n is equal to _____________.

JEE Main 2021 (Online) 26th August Evening Shift

Let the mean and variance of four numbers 3, 7, x and y(x > y) be 5 and 10 respectively. Then the mean of four numbers 3 + 2x, 7 + 2y, x + y and x ...

JEE Main 2021 (Online) 25th July Morning Shift

Consider the following frequency distribution :
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JEE Main 2021 (Online) 22th July Evening Shift

Consider the following frequency distribution :
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JEE Main 2021 (Online) 18th March Morning Shift

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean...

JEE Main 2021 (Online) 17th March Evening Shift

Consider a set of 3n numbers having variance 4. In this set, the mean of first 2n numbers is 6 and the mean of the remaining n numbers is 3. A new set...

JEE Main 2021 (Online) 16th March Evening Shift

Consider the statistics of two sets of observations as follows :
Size
Mean
Variance
Observation I
10
2
2
...

JEE Main 2021 (Online) 26th February Evening Shift

Let X1, X2, ......., X18 be eighteen observations such that $$\sum\limits_{i = 1}^{18} {({X_i} - } \alpha ) = 36$$ and $$\sum\limits_{i = 1}^{18} {({X...

JEE Main 2021 (Online) 24th February Evening Shift

If the variance of 10 natural numbers 1, 1, 1, ....., 1, k is less than 10, then the maximum possible value of k is ________.

JEE Main 2020 (Online) 6th September Evening Slot

Consider the data on x taking the values 0, 2, 4,
8,....., 2n with frequencies nC0
,
nC1
,
nC2
,....,
nCn
respectively. If the mean of this data is $$...

JEE Main 2020 (Online) 4th September Evening Slot

If the variance of the following frequency
distribution :
Class : 10–20 20–30 30–40
Frequency : ...

JEE Main 2020 (Online) 2nd September Evening Slot

If the variance of the terms in an increasing A.P., b1
, b2
, b3
,....,b11 is 90, then the common
difference of this A.P. is_______....

JEE Main 2020 (Online) 7th January Evening Slot

If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively,
then x.y is equal to _______.

JEE Main 2020 (Online) 7th January Morning Slot

If the variance of the first n natural numbers is 10 and the variance of the first m even natural
numbers is 16, then m + n is equal to_____.