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Numerical

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The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 i...
JEE Main 2022 (Online) 27th July Morning Shift
The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observati...
JEE Main 2022 (Online) 26th July Evening Shift
If the mean deviation about the mean of the numbers 1, 2, 3, .........., n, where n is odd, is $${{5(n + 1)} \over n}$$,...
JEE Main 2022 (Online) 25th June Evening Shift
The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that...
JEE Main 2022 (Online) 28th June Morning Shift
Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their vari...
JEE Main 2022 (Online) 28th June Evening Shift
Let X be a random variable with distribution. .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:blac...
JEE Main 2021 (Online) 1st September 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 v...
JEE Main 2021 (Online) 27th August Evening 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) 27th August Morning 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 number...
JEE Main 2021 (Online) 26th August Evening Shift
Consider the following frequency distribution : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:bl...
JEE Main 2021 (Online) 25th July Morning Shift
Consider the following frequency distribution : Class : 0 $$ - $$ 6 6 $$ - $$ 12 12 $$ - $$ 18 1...
JEE Main 2021 (Online) 22th July Evening 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 appoi...
JEE Main 2021 (Online) 18th March Morning 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 remai...
JEE Main 2021 (Online) 17th March Evening Shift
Consider the statistics of two sets of observations as follows : Size Mean Variance Obs...
JEE Main 2021 (Online) 16th March Evening Shift
Let X1, X2, ......., X18 be eighteen observations such that $$\sum\limits_{i = 1}^{18} {({X_i} - } \alpha ) = 36$$ and $...
JEE Main 2021 (Online) 26th 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 2021 (Online) 24th February Evening Slot
Consider the data on x taking the values 0, 2, 4, 8,....., 2n with frequencies nC0 , nC1 , nC2 ,...., nCn respectively. ...
JEE Main 2020 (Online) 6th September Evening Slot
If the variance of the following frequency distribution : Class         : 10–20 ...
JEE Main 2020 (Online) 4th 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...
JEE Main 2020 (Online) 2nd September 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 Evening 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 ...
JEE Main 2020 (Online) 7th January Morning Slot

MCQ (Single Correct Answer)

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If the mean deviation about median for the numbers 3, 5, 7, 2k, 12, 16, 21, 24, arranged in the ascending order, is 6 th...
JEE Main 2022 (Online) 25th July Evening Shift
The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observatio...
JEE Main 2022 (Online) 26th June Evening 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 t...
JEE Main 2022 (Online) 26th June Morning Shift
Let X be a random variable having binomial distribution B(7, p). If P(X = 3) = 5P(x = 4), then the sum of the mean and t...
JEE Main 2022 (Online) 27th June Morning Shift
The mean and variance of the data 4, 5, 6, 6, 7, 8, x, y, where x ...
JEE Main 2022 (Online) 27th 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 Evening Shift
Let the mean and the variance of 5 observations x1, x2, x3, x4, x5 be $${24 \over 5}$$ and $${194 \over 25}$$ respective...
JEE Main 2022 (Online) 29th June Morning Shift
The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then the variance of...
JEE Main 2021 (Online) 31st August Evening Shift
The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mist...
JEE Main 2021 (Online) 26th August 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, t...
JEE Main 2021 (Online) 27th July Morning 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 ...
JEE Main 2021 (Online) 25th July Evening Shift
Let the mean and variance of the frequency distribution$$\matrix{ {x:} & {{x_1} = 2} & {{x_2} = 6} & {{x_...
JEE Main 2021 (Online) 27th July Evening Shift
If the mean and variance of six observations 7, 10, 11, 15, a, b are 10 and $${{20} \over 3}$$, respectively, then the v...
JEE Main 2021 (Online) 20th July Evening Shift
The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, th...
JEE Main 2021 (Online) 20th July Morning Shift
Let in a series of 2n observations, half of them are equal to a and remaining half are equal to $$-$$a. Also by adding a...
JEE Main 2021 (Online) 18th March Evening Shift
Consider three observations a, b, and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then...
JEE Main 2021 (Online) 16th March Morning Shift
If $$\sum\limits_{i = 1}^n {\left( {{x_i} - a} \right)} = n$$ and $$\sum\limits_{i = 1}^n {{{\left( {{x_i} - a} \right)...
JEE Main 2020 (Online) 6th September Morning 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...
JEE Main 2020 (Online) 5th September Evening Slot
The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14, then the ...
JEE Main 2020 (Online) 5th 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, ...
JEE Main 2020 (Online) 4th September Morning Slot
Let xi (1 $$ \le $$ i $$ \le $$ 10) be ten observations of a random variable X. If $$\sum\limits_{i = 1}^{10} {\left( {...
JEE Main 2020 (Online) 3rd September Evening Slot
For the frequency distribution : Variate (x) :      x1   x2   x3 .... &nbs...
JEE Main 2020 (Online) 3rd September Morning Slot
Let X = {x $$ \in $$ N : 1 $$ \le $$ x $$ \le $$ 17} and Y = {ax + b: x $$ \in $$ X and a, b $$ \in $$ R, a > 0}. If ...
JEE Main 2020 (Online) 2nd September Morning Slot
Let the observations xi (1 $$ \le $$ i $$ \le $$ 10) satisfy the equations, $$\sum\limits_{i = 1}^{10} {\left( {{x_1} - ...
JEE Main 2020 (Online) 9th January Morning Slot
The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an obs...
JEE Main 2020 (Online) 8th January Evening Slot
The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 resepectively. Each of these 10 observations ...
JEE Main 2020 (Online) 8th January Morning Slot
Let a random variable X have a binomial distribution with mean 8 and variance 4. If $$P\left( {X \le 2} \right) = {k \ov...
JEE Main 2019 (Online) 12th April Morning Slot
If the data x1, x2,......., x10 is such that the mean of first four of these is 11, the mean of the remaining six is 16 ...
JEE Main 2019 (Online) 12th April Morning Slot
If both the mean and the standard deviation of 50 observations x1, x2,..., x50 are equal to 16, then the mean of (x1 – 4...
JEE Main 2019 (Online) 10th April Evening Slot
If for some x $$ \in $$ R, the frequency distribution of the marks obtained by 20 students in a test is : .tg {border-...
JEE Main 2019 (Online) 10th April Morning Slot
The mean and the median of the following ten numbers in increasing order 10, 22, 26, 29, 34, x, 42, 67, 70, y are 42 and...
JEE Main 2019 (Online) 9th April Evening Slot
If the standard deviation of the numbers –1, 0, 1, k is $$\sqrt 5$$ where k > 0, then k is equal to
JEE Main 2019 (Online) 9th April Morning Slot
A student scores the following marks in five tests : 45, 54, 41, 57, 43. His score is not known for the sixth test. If...
JEE Main 2019 (Online) 8th April Evening Slot
The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are 2, 4, 10, 12, 14, t...
JEE Main 2019 (Online) 8th April Morning Slot
The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4...
JEE Main 2019 (Online) 12th January Evening Slot
If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is :
JEE Main 2019 (Online) 12th January Morning Slot
The outcome of each of 30 items was observed; 10 items gave an outcome $${1 \over 2}$$ – d each, 10 items gave outcome $...
JEE Main 2019 (Online) 11th January Morning Slot
If mean and standard deviation of 5 observations x1, x2, x3, x4, x5 are 10 and 3, respectively, then the variance of 6 o...
JEE Main 2019 (Online) 10th January Evening Slot
The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, t...
JEE Main 2019 (Online) 10th January Morning Slot
In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is...
JEE Main 2019 (Online) 10th January Morning Slot
A data consists of n observations : x1, x2, . . . . . . ., xn.     If     $$\sum\limi...
JEE Main 2019 (Online) 9th January Evening 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 t...
JEE Main 2019 (Online) 9th January Morning Slot
The mean and the standarddeviation(s.d.) of five observations are9 and 0, respectively. If one of the observations is ch...
JEE Main 2018 (Online) 16th April Morning 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 Evening Slot
The mean of set of 30 observations is 75. If each observation is multiplied by a non-zero number $$\lambda $$ and then e...
JEE Main 2018 (Online) 15th April Morning Slot
If $$\sum\limits_{i = 1}^9 {\left( {{x_i} - 5} \right)} = 9$$ and $$\sum\limits_{i = 1}^9 {{{\left( {{x_i} - 5} \right)...
JEE Main 2018 (Offline)
The sum of 100 observations and the sum of their squares are 400 and 2475, respectively. Later on, three observations, 3...
JEE Main 2017 (Online) 9th April Morning Slot
The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appo...
JEE Main 2017 (Online) 8th April Morning Slot
The mean of 5 observations is 5 and their variance is 124. If three of the observations are 1, 2 and 6 ; then the mean d...
JEE Main 2016 (Online) 10th April Morning Slot
If the mean deviation of the numbers 1, 1 + d, ..., 1 +100d from their mean is 255, then a value of d is :
JEE Main 2016 (Online) 9th April Morning Slot
If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?
JEE Main 2016 (Offline)
The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three n...
JEE Main 2015 (Offline)
The variance of first 50 even natural numbers is
JEE Main 2014 (Offline)
All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of th...
JEE Main 2013 (Offline)
Let x1, x2,........., xn be n observations, and let $$\overline x $$ be their arithematic mean and $${\sigma ^2}$$ be th...
AIEEE 2012
If the mean deviation about the median of the numbers a, 2a,........., 50a is 50, then |a| equals
AIEEE 2011
For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 a...
AIEEE 2010
Statement - 1 : The variance of first n even natural numbers is $${{{n^2} - 1} \over 4}$$ Statement - 2 : The sum of fir...
AIEEE 2009
If the mean deviation of number 1, 1 + d, 1 + 2d,........, 1 + 100d from their mean is 255, then the d is equal to
AIEEE 2009
The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible val...
AIEEE 2008
The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. ...
AIEEE 2007
Suppose a population A has 100 observations 101, 102,........, 200, and another population B has 100 observations 151, 1...
AIEEE 2006
If in a frequently distribution, the mean and median are 21 and 22 respectively, then its mode is approximately
AIEEE 2005
Let x1, x2,...........,xn be n observations such that $$\sum {x_i^2} = 400$$ and $$\sum {{x_i}} = 80$$. Then a possibl...
AIEEE 2005
In a series of 2n observations, half of them equal $$a$$ and remaining half equal $$–a$$. If the standard deviation of t...
AIEEE 2004
Consider the following statements: (a) Mode can be computed from histogram (b) Median is not independent of change of ...
AIEEE 2004
The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by...
AIEEE 2003
In an experiment with 15 observations on $$x$$, then following results were available: $$\sum {{x^2}} = 2830$$, $$\sum ...
AIEEE 2003
In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the comple...
AIEEE 2002

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