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Saturday, 31 October

JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 10 April 2023, Shift 2, Maths Q19

Question 19 of 90 in this shift, Maths question 19 of 30, Section A.

Let μ\mu be the mean and σ\sigma be the standard deviation of the distribution xix_i: 00, 11, 22, 33, 44, 55 fif_i: k+2k+2, 2k2k, k2−1k^2-1, k2−1k^2-1, k2+1k^2+1, k−3k-3 where ∑fi=62\sum f_i = 62. If [x][x] denotes the greatest integer ≤x\leq x, then [μ2+σ2][\mu^2 + \sigma^2] is equal to

The figure, in words

Frequency table: x_i = 0,1,2,3,4,5 with f_i = k+2, 2k, k^2-1, k^2-1, k^2+1, k-3 respectively.
  1. (1)66
  2. (2)77
  3. (3)88Official answer
  4. (4)99

Official answer

Option 3

NTA final key.

Chapter
Statistics
Topic
Variance and SD
Idea tested
Variance of Discrete Frequency Distribution

Same idea in other shifts

Asked 3× in all
  1. 9 Apr 2024, Shift 2 · Q19If the variance of the frequency distribution | xx | cc | 2c2c | 3c3c | 4c4c | 5c5c | 6c6c | |---|---|---|---|---|---|---| | ff | 2 | 1…MediumSingle correct
  2. 30 Jan 2024, Shift 2 · Q30The variance σ2\sigma^2 of the data | xix_i | 0 | 1 | 5 | 6 | 10 | 12 | 17 | |---|---|---|---|---|---|---|---| | fif_i | 3 | 2 | 3 | 2 | 6…EasyNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. This question needs a figure we do not reproduce; it is described in words above. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.