JEE Main 2016 · 3 Apr · Shift 1 · Mathematics Q86

MathematicsSingle correct+4 / -1Question 86 of 90

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true ?

3a^2-26a+55=0

3a^2-32a+84=0

3a^2-34a+91=0

3a^2-23a+44=0

Answer and worked solution

Official answer: B

$\sigma^2=\dfrac{134+a^2}4-\left(\dfrac{16+a}4\right)^2=\dfrac{49}4$ . Multiplying by 16: $536+4a^2-256-32a-a^2=196$ , i.e. $3a^2-32a+84=0$ .

JEE Main 2016 · 3 Apr · Shift 1, Mathematics question 86