Verified Solution • 2025–26 Session moderate

QJEEM19Ma9cf1: JEE Main 2019 Mathematics - Class 11 JEEM19Ma9cf1 Solution: If for some x R, the frequency distribution of the marks…

If for some x ∈\in R, the frequency distribution of the marks obtained by 20 students in a test is :

Marks 2 3 5 7
Frequency (x + 1)2 2x - 5 x2 - 3x x

then the mean of the marks is

Multiple Choice Options

  • A 3
  • B 2.8
  • C 2.5
  • D 3.2

Step-by-Step Verified Solution

Number of students

⇒(x+1)2+(2x−5)+(x2−3x)+x=20\Rightarrow {\left( {x + 1} \right)^2} + (2x - 5) + \left( {{x^2} - 3x} \right) + x = 20

⇒2x2+2x−4=20\Rightarrow 2{x^2} + 2x - 4 = 20

⇒x2+x−12=0\Rightarrow {x^2} + x - 12 = 0

⇒(x+4)(x−3)=0\Rightarrow (x + 4)(x - 3) = 0

x=3x = 3

Marks 2 3 5 7
No. of students 16 1 0 3

Average marks = 32+3+2120=5620=2.8{{32 + 3 + 21} \over {20}} = {{56} \over {20}} = 2.8

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