LFM Stats And Pure

jee-main 2014 Q73 View

Let $\bar { x } , M$ and $\sigma ^ { 2 }$ be respectively the mean, mode and variance of $n$ observations $x _ { 1 } , x _ { 2 } , \ldots , x _ { n }$ and $d _ { i } = - x _ { i } - a , i = 1,2 , \ldots , n$, where $a$ is any number. Statement I: Variance of $d _ { 1 } , d _ { 2 } , \ldots , d _ { n }$ is $\sigma ^ { 2 }$. Statement II: Mean and mode of $d _ { 1 } , d _ { 2 } , \ldots , d _ { n }$ are $- \bar { x } - a$ and $- M - a$, respectively.
(1) Statement I and Statement II are both true
(2) Statement I and Statement II are both false
(3) Statement I is true and Statement II is false
(4) Statement I is false and Statement II is true

jee-main 2014 Q74 View

The variance of the first 50 even natural numbers is:
(1) 437
(2) $\frac { 437 } { 4 }$
(3) $\frac { 833 } { 4 }$
(4) 833

jee-main 2014 Q76 View

In a set of $2n$ distinct observations, each of the observation below the median of all the observations is increased by 5 and each of the remaining observations is decreased by 3. Then, the mean of the new set of observations:
(1) Increases by 2.
(2) Increase by 1.
(3) Decreases by 2.
(4) Decreases by 1.

jee-main 2015 Q75 View

The mean of a data set comprising of 16 observations is 16. If one of the observation value 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data is
(1) 14.0
(2) 16.8
(3) 16.0
(4) 15.8

jee-main 2015 Q83 View

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 and 5 are added to the data, then the mean of the resultant data, is:
(1) 16.8
(2) 15.8
(3) 14.0
(4) 16.0

jee-main 2015 Q89 View

The variance of first 50 even natural numbers is:
(1) $833$
(2) $437$
(3) $\frac{833}{4}$
(4) $833$

jee-main 2016 Q74 Limit Evaluation Involving Composition or Substitution View

$\lim _ { x \rightarrow 0 } \frac { ( 1 - \cos 2 x ) ^ { 2 } } { 2 x \tan x - x \tan 2 x }$ is
(1) 2
(2) $- \frac { 1 } { 2 }$
(3) $- 2$
(4) $\frac { 1 } { 2 }$

jee-main 2016 Q76 View

If the standard deviation of the numbers $2, 3, a$ and $11$ is $3.5$, then which of the following is true? (1) $3a^2 - 26a + 55 = 0$ (2) $3a^2 - 32a + 84 = 0$ (3) $3a^2 - 34a + 91 = 0$ (4) $3a^2 - 23a + 44 = 0$

jee-main 2016 Q90 View

If the standard deviation of the numbers $2, 3, a$ and $11$ is $3.5$, then which of the following is true?
(1) $3a^2 - 26a + 55 = 0$
(2) $3a^2 - 32a + 84 = 0$
(3) $3a^2 - 34a + 91 = 0$
(4) $3a^2 - 23a + 44 = 0$

jee-main 2017 Q74 View

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 age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher is
(1) 35
(2) 40
(3) 25
(4) 30

jee-main 2017 Q78 View

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 age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher is:
(1) 25
(2) 30
(3) 35
(4) 40

jee-main 2017 Q84 View

If $\sum _ { i = 1 } ^ { 9 } ( x _ { i } - 5 ) = 9$ and $\sum _ { i = 1 } ^ { 9 } ( x _ { i } - 5 ) ^ { 2 } = 45$, then the standard deviation of the 9 items $x _ { 1 } , x _ { 2 } , \ldots , x _ { 9 }$ is:
(1) 9
(2) 4
(3) 2
(4) 3

jee-main 2018 Q73 View

The mean of a set of 30 observation is 75. If each observations is multiplied by non-zero number $\lambda$ and then each of them is decreased by 25, their mean remains the same. Then, $\lambda$ is equal to :
(1) $\frac { 4 } { 3 }$
(2) $\frac { 1 } { 3 }$
(3) $\frac { 10 } { 3 }$
(4) $\frac { 2 } { 3 }$

jee-main 2018 Q74 View

The mean and the standard deviation (S. D.) of five observations are 9 and 0 , respectively. If one of the observation is increased such that the mean of the new set of five observations becomes 10 , then their S. D. is
(1) 0
(2) 2
(3) 4
(4) 1

jee-main 2018 Q74 View

The mean of a set of 30 observations is 75 . If each other observation is multiplied by a nonzero number $\lambda$ and then each of them is decreased by 25 , their mean remains the same. The $\lambda$ is equal to
(1) $\frac { 10 } { 3 }$
(2) $\frac { 4 } { 3 }$
(3) $\frac { 1 } { 3 }$
(4) $\frac { 2 } { 3 }$

jee-main 2018 Q75 View

If $\sum _ { i = 1 } ^ { 9 } \left( x _ { i } - 5 \right) = 9$ and $\sum _ { i = 1 } ^ { 9 } \left( x _ { i } - 5 \right) ^ { 2 } = 45$, then the standard deviation of the 9 items $x _ { 1 } , x _ { 2 } , \ldots , x _ { 9 }$ is
(1) 3
(2) 9
(3) 4
(4) 2

jee-main 2019 Q73 View

If the standard deviation of the numbers $- 1,0,1 , k$ is $\sqrt { 5 }$ where $k > 0$, then $k$ is equal to
(1) $\sqrt { 6 }$
(2) $4 \sqrt { \frac { 5 } { 3 } }$
(3) $2 \sqrt { \frac { 10 } { 3 } }$
(4) $2 \sqrt { 6 }$

jee-main 2019 Q74 View

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 the difference of the other two observations, is :
(1) 3
(2) 5
(3) 7
(4) 1

jee-main 2019 Q74 View

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 six tests, then the standard deviation of the marks in six tests is:
(1) $\frac { 10 } { 3 }$
(2) $\frac { 100 } { 3 }$
(3) $\frac { 10 } { \sqrt { 3 } }$
(4) $\frac { 100 } { \sqrt { 3 } }$

jee-main 2019 Q74 Direct Determinant Computation View

The mean and variance for seven observations are 8 and 16 respectively. If 5 of the observations are $2, 4, 10, 12, 14$, then the product of the remaining two observations is
(1) 48
(2) 45
(3) 49
(4) 40

jee-main 2019 Q75 View

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 observations is
(1) $10 : 3$
(2) $4 : 9$
(3) $6 : 7$
(4) $5 : 8$

jee-main 2019 Q75 View

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 $\frac { y } { x }$ is equal to:
(1) $\frac { 9 } { 4 }$
(2) $\frac { 7 } { 3 }$
(3) $\frac { 7 } { 2 }$
(4) $\frac { 8 } { 3 }$

jee-main 2019 Q76 View

A data consists of $n$ observations: $x_1, x_2, \ldots, x_n$. If $\sum_{i=1}^{n}(x_i + 1)^2 = 9n$ and $\sum_{i=1}^{n}(x_i - 1)^2 = 5n$, then the standard deviation of this data is
(1) 5
(2) $\sqrt{7}$
(3) $\sqrt{5}$
(4) 2

jee-main 2020 Q58 View

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 the correct observation was 11, then the correct variance is
(1) 3.99
(2) 4.01
(3) 4.02
(4) 3.98

jee-main 2020 Q58 View

Let $X = \{x \in N : 1 \leq x \leq 17\}$ and $Y = \{ax + b : x \in X$ and $a, b \in R, a > 0\}$. If mean and variance of elements of $Y$ are 17 and 216 respectively then $a + b$ is equal to
(1) 7
(2) $-7$
(3) $-27$
(4) 9

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LFM Stats And Pure

Completing the square and sketching 80

Inequalities 215

Discriminant and conditions for roots 106

Solving quadratics and applications 106

Curve Sketching 295

Factor & Remainder Theorem 90

Polynomial Division & Manipulation 44

Binomial Theorem (positive integer n) 244

Function Transformations 65

Composite & Inverse Functions 249

Partial Fractions 22

Generalised Binomial Theorem 16

Generalised Binomial Theorem and Partial Fractions 3

Complex Numbers Arithmetic 283

Complex Numbers Argand & Loci 135

Permutations & Arrangements 276

Combinations & Selection 268

Measures of Location and Spread 233

Probability Definitions 413

Tree Diagrams 5

Principle of Inclusion/Exclusion 23

Independent Events 51

Conditional Probability 127

Discrete Probability Distributions 210

Binomial Distribution 107

Geometric Distribution 11

Hypergeometric Distribution 10

Negative Binomial Distribution 2

Modelling and Hypothesis Testing 38

Hypothesis test of binomial distributions 12

Data representation 29

Continuous Probability Distributions and Random Variables 30

Continuous Uniform Random Variables 15

Geometric Probability 28

Normal Distribution 96

Approximating Binomial to Normal Distribution 7

Sign Change & Interval Methods 74

Fixed Point Iteration 12