Suppose a class has 9 boys & 1 girl. The average marks of these students in the mathematics exam is 60 & their variance is 82.2. A student fails in the exam if he/she gets less than 50 marks. Given that highest marks = 83 which are secured by the girl & the marks of no 2 students are the same & all marks $\in N$ . Worst case is when maximum no. of students fail.

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

In the worst case, the no. of students that can fail is 2

In the worst case, the minimum marks a student can get is 48

In the worst case, the standard deviation of the boys that have passed = 2

In the worst case, the average of 3^rd best & 7^th best is 61

answer is A, B, D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Soddy $σ^{2} = \frac{{(x_{1} - 60)}^{2} + {(x_{2} - 60)}^{2} + \dots {(x_{9} - 60)}^{2} + 23^{2}}{10} = 82.2$
$\Rightarrow_{i = 1}^{9} {(x_{i} - 60)}^{2} = 822 - 529 = 293$
Now in the worst case $\to 2$ students have failed
$∵ {(48 - 60)}^{2} + {(49 - 60)}^{2} +_{i = 3}^{q} {(x_{i} - 60)}^{2} = 293 \Rightarrow_{i = 3}^{9} {(x_{i} - 60)}^{2} = 28$
Now: Cheek if 28 con be broken into sum of 7 distinct sq's
$28 \to 0 + 1^{2} + {(- 1)}^{2} + 2^{2} + {(- 2)}^{2} + 3^{2} + {(- 3)}^{2}$

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th