Q72.Statement-1 : The variance of first n even natural numbers is n2−14 Statement-2 : The sum of first n natural numbers is n(n+1) 2 and the sum of squares of first n natural numbers is n(n+1)(2n+1)6 (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-2 is not a correct explanation for Statement-1 Statement-1 (3) Statement-1 is true, Statement-2 is false (4) Statement-1 is false, Statement-2 is true
What This Question Tests
This question assesses the understanding of the variance formula and the application of standard sum formulas for the first n natural numbers and their squares to derive the variance of the first n even natural numbers.
Concepts Tested
Formulas Used
Variance σ^2 = (Σx_i^2 / N) - (x̄)^2
Σn = n(n+1)/2
Σn^2 = n(n+1)(2n+1)/6
📚 NCERT Sections This Tests
14.1 — In An N-Type Silicon, Which Of The Following Statement Is True:
Physics Class 12 · Chapter 14
14.1 In an n-type silicon, which of the following statement is true: (a) Electrons are majority carriers and trivalent atoms are the dopants. (b) Electrons are minority carriers and pentavalent atoms are the dopants. (c) Holes are minority carriers and pentavalent atoms are the dopants. (d) Holes are majority carriers and trivalent atoms are the dopants.
14.2 — Which Of The Statements Given In Exercise 14.1 Is True For P-Type
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14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
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Chemistry Class 11 · Chapter 4
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📋 Question Details
- Chapter
- Statistics
- Topic
- Variance of natural numbers
- Year
- 2009
- Shift
- Unknown
- Q Number
- Q72
- Type
- Assertion Reasoning
- NCERT Ref
- Class 11 Mathematics Ch 15: Statistics
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