Welcome to **AMBiPi (**Read as**: एम्बीपाई) (Amans Maths Blogs)**. JEE Mains and JEE Advanced exams are the engineering entrance exams for taking admission in IITs, NITs and other engineering colleges. In this article, you will get * JEE Math Previous Year Paper Complex Numbers Questions Answer Keys Solutions*.

### JEE Mains Mathematics Statistics Questions Bank

**Statistics Problems for Class 11 Questions No: 61**

If a variance of the following frequency distribution

is 50, then x is equal to

**[2020]**

**Show/Hide Answer Key**

**Correct Ans: 4**

**Statistics Problems for Class 12 Questions No: 62**

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 difference of the remaining two observations is

**[2020]**

**Option A**: 9

**Option B**: 5

**Option C**: 3

**Option D**: 7

**Show/Hide Answer Key**

**Option D: 7**

**Statistics Problems for Class 11 JEE Questions No: 63**

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 :

**[2020]**

**Option A**: x² – 10x + 18 = 0

**Option B**: 2x² – 20x + 19 = 0

**Option C**: x² – 10x + 19 = 0

**Option D**: x² – 20x + 18 = 0

**Show/Hide Answer Key**

**Option C: x² – 10x + 19 = 0**

**Statistics Problems for Class 12 JEE Questions No: 64**

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 remaining two observations is

**[2020]**

**Option A**: 1

**Option B**: 4

**Option C**: 2

**Option D**: 3

**Show/Hide Answer Key**

**Option C: 2**

**JEE Statistics Questions No : 65**

If (x_{i }– a) = n and (x_{i} – a)^{2} = na, (n, a > 1), then the standard deviation of n observations x_{1}, x_{2},…x_{n} is:

**[2020]**

**Option A**: a – 1

**Option B**: n √a – 1

**Option C**: √n (a – 1)

**Option D**: √a – 1

**Show/Hide Answer Key**

**Option D: √a – 1**

**JEE Main Statistics Questions No : 66**

Consider the data on x taking the values 0, 2, 4, 8,……, 2^{n} with frequencies ^{n}C_{0} ^{n}C_{1}, ^{n}C_{2} …….,^{n}C_{n} respectively. If the mean of this data is (728 / 2^{n}) then n is equal to

**[2020]**

**Show/Hide Answer Key**

**Correct Ans: 6**

**JEE Mathematics Statistics Questions No : 67**

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

**[2021]**

**Show/Hide Answer Key**

**Correct Ans: 11**

**JEE Main Math Statistics Questions No : 68**

Let X_{1}, X_{2},……. X_{18} be eighteen observations such that (X_{i} = α) = 36 and (X_{i} = β)² = 90, where α and β are distinct real numbers. If the standard deviation of these observations is 1, then the value of | α – β | is

**[2021]**

**Show/Hide Answer Key**

**Correct Ans: 4**

**Statistics JEE Questions No : 69**

Consider the statistics of two sets of observations as follows:

If the variance of the combined set of these two observations is 17 / 9 then the value of n is equal to

**[2021]**

**Show/Hide Answer Key**

**Correct Ans: 5**

**Statistics JEE Main Questions No : 70**

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 true?

**[2021]**

**Option A**: b^{2 }= a^{2 }+ c^{2 }+ 3d^{2}

**Option B**: b^{2 }= 3 (a^{2 }+ c^{2}) – 9d^{2}

**Option C**: b^{2 }= 3 (a^{2 }+ c^{2}) + 9d^{2}

**Option D**: b^{2 }= 3 (a^{2 }+ c^{2 }+ d^{2})

**Show/Hide Answer Key**

**Option B: b²=3 (a² + c²) – 9d²**

**Statistics Questions for JEE Mains Questions No : 71**

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 is constructed by adding 1 into each of first 2n numbers, and subtracting 1 from each of the remaining n numbers. If the variance of the new set is k, then 9k is equal to

**[2021]**

**Show/Hide Answer Key**

**Correct Ans: 68**

**Statistics Questions and Answers No : 72**

If the mean and variance of six observations 7, 10, 11, 15, a, b are 10 and (20 / 3) respectively, then the value of | a – b | is equal to :

**[2021]**

**Option A**: 9

**Option B**: 11

**Option C**: 7

**Option D**: 1

**Show/Hide Answer Key**

**Option D: 1**

**Statistics Questions with Solutions No : 73**

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 observations are

**[2021]**

**Option A**: 10, 11

**Option B**: 3, 18

**Option C**: 8, 13

**Option D**: 1, 20

**Show/Hide Answer Key**

**Option A: 10, 11**

**JEE Mains Statistics Questions No : 74**

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 standard deviation then the standard deviation of the second sample is

**[2021]**

**Option A**: 8

**Option B**: 6

**Option C**: 4

**Option D**: 5

**Show/Hide Answer Key**

**Option C: 4**

**JEE Mains Math Statistics Questions No : 75**

Let the mean and variance of the frequency distribution

be 6 and 6.8 respectively. If x_{3} is changed from 8 to 7, then the mean for the new data will be

**[2021]**

**Option A**: 4

**Option B**: 5

**Option C**: 17 / 3

**Option D**: 16 / 3

**Show/Hide Answer Key**

**Option C: 17 / 3**

**Statistics Questions for JEE Questions No : 76**

If the mean and variance of the following data: 6, 10, 7, 13, a, 12, b, 12 are 9 and respectively, then (a – b)² is equal to:

**[2021]**

**Option A**: 24

**Option B**: 12

**Option C**: 32

**Option D**: 16

**Show/Hide Answer Key**

**Option D: 16**

**Statistics Problems for Class 11 Questions No : 77**

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 – y is

**[2021]**

**Show/Hide Answer Key**

**Correct Ans: 12**

**Statistics Problems for Class 12 Questions No : 78**

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 as 25 instead of 35. If α and √β are the mean and standard deviation respectively for correct data, then (α, β) is

**[2021]**

**Option A**: (11, 26)

**Option B**: (10.5, 25)

**Option C**: (11, 25)

**Option D**: (10.5, 26)

**Show/Hide Answer Key**

**Option D: (10.5, 26)**

**Statistics Problems for Class 11 JEE Questions No : 79**

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 marks obtained by 30 girls is also 2. The average marks of all 50 candidates is 15. If μ is the average marks of girls and σ² is the variance of marks of 50 candidates, then μ + σ² is equal to

**[2021]**

**Show/Hide Answer Key**

**Correct Ans:25**

**Statistics Problems for Class 12 JEE Questions No : 80**

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 is

**[2021]**

**Option A**: 92 / 5

**Option B**: 134 / 5

**Option C**: 536 / 25

**Option D**: 112 / 5

**Show/Hide Answer Key**

**Option C: 536 / 25**

**JEE Statistics Questions No : 81**

Let X be a random variable with distribution.

If the mean of X is 2.3 and variance of X is σ², then 100 σ² is equal to :

**[2021]**

**Show/Hide Answer Key**

**Correct Ans: 781**

**JEE Main Statistics Questions No : 82**

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

**[2021]**

**Show/Hide Answer Key**

**Correct Ans: 35**

**JEE Mathematics Statistics Questions No : 83**

Consider the following frequency distribution:

If Mean (309 / 22) and median = 14, then the value (a – b)^{2} is

**[2021]**

**Show/Hide Answer Key**

**Correct Ans: 4**

**JEE Main Math Statistics Questions No : 84**

Consider the following frequency distribution:

If the sum of all frequencies is 584 and median is 45, then | α – β | is equal to

**[2021]**

**Show/Hide Answer Key**

**Correct Ans: 164**

**Statistics JEE Questions No : 85**

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

**[2021]**

**Show/Hide Answer Key**

**Correct Ans: 13**

**Statistics JEE Main Questions No : 86**

The mean of 10 numbers 7 × 8, 10 × 10, 13 × 12, 16 × 14,….. is

**[2021]**

**Show/Hide Answer Key**

**Correct Ans: 398**

JEE Main Mathematics Previous Year Questions with Solutions: Algebra |

JEE Main Previous Year Mathematics Questions Set, Relations & Functions | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Complex Numbers | 1 to 30 | 31 to 60 | 61 to 81 | |

JEE Main Previous Year Mathematics Questions Sequence & Series| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Quadratic Equations| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Permutations & Combinations| 1 to 30 | 31 to 60 | 61 to 94 | |

JEE Main Previous Year Mathematics Questions Binomial Theorems| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Determinants & Matrices| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Trigonometry |

JEE Main Previous Year Mathematics Questions Trigonometry Ratios Identities| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Properties of Triangles| 1 to 31 | |

JEE Main Previous Year Mathematics Questions Trigonometrical Equations| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Inverse Trigonometrical Functions| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Height & Distance| 1 to 27 | |

JEE Main Mathematics Previous Year Questions with Solutions: Coordinate Geometry |

JEE Main Previous Year Mathematics Questions Cartesian System & Straight Lines | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Circles | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Parabola | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Ellipse | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Hyperbola | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Differential Equations |

JEE Main Previous Year Mathematics Questions Limit, Continuity & Differentiability | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Differentiations | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Application of Derivative | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Integral Calculus |

JEE Main Previous Year Mathematics Questions Indefinite Integrals | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Definite Integrals | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Area By Integration | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Differential Equations |

JEE Main Previous Year Mathematics Questions Differential Equations | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Vector & 3D Geometry |

JEE Main Previous Year Mathematics Questions Vectors | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 139 | |

JEE Main Previous Year Mathematics Questions 3D Geometry | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Statistics & Probability |

JEE Main Previous Year Mathematics Questions Statistics | 1 to 30 | 31 to 60 | 61 to 86 | |

JEE Main Previous Year Mathematics Questions Probability | 1 to 30 | 31 to 60 | 61 to 95 | |

JEE Main Mathematics Previous Year Questions with Solutions: Miscellaneous |

JEE Main Previous Year Mathematics Questions Mathematical Induction | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Mathematical Reasoning | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |