KEAM 2012 Math Paper

Let the other two numbers be x and y.
∴ Mean =‌

−1+1+2+x+y

5

⇒‌‌0=‌

2+x+y

5

⇒‌‌x+y=−2.....(i)
and variance =‌

Σ(xi−x)2

n

⇒‌‌10=1+1+4+x2+y2
⇒‌‌x2+y2=4......(ii)
On squaring Eq. (i), we get
x2+y2+2xy=4
⇒‌‌4+2xy=4  [From Eq. (ii)]
⇒‌‌xy=0
Now, x−y=√(x+y)2−4xy
=√(−2)2−4×0=2  [From Eq. (i)]
⇒‌‌x−y=2.....(iii)
On solving Eqs. (i) and (iii), we get
2x=0⇒x=0
and y=−2