Verified Solution • 2025–26 Session moderate

QJEEM20Ma4607: JEE Main 2020 Mathematics - Class 11 JEEM20Ma4607 Solution: If the mean and the standard deviation of the data 3, 5, 7, a,…

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 :

Multiple Choice Options

  • A x2 – 20x + 18 = 0
  • B 2x2 – 20x + 19 = 0
  • C x2 – 10x + 18 = 0
  • D x2 – 10x + 19 = 0

Step-by-Step Verified Solution

Mean = 3+5+7+a+b5{{3 + 5 + 7 + a + b} \over 5} = 5

⇒\Rightarrow aa + b = 10

Variance = 32+52+72+a2+b25{{{3^2} + {5^2} + {7^2} + {a^2} + {b^2}} \over 5} - (5)2 = 4

⇒\Rightarrow a2+b2{{a^2} + {b^2}} = 62

⇒\Rightarrow (a+b)2−2ab{\left( {a + b} \right)^2} - 2ab = 62

⇒\Rightarrow abab = 19

So aa and b are the roots of the equation

x2 – 10x + 19 = 0

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring