UPSC CDS 2 2022 Math Paper

Statement 1.
x4(y−z)+y4(z−x)+z4(x−y) is positive if x>y>z.
We have to solve this by Value putting method
Here, x>y>z.
Then, x=2,y=1 or z=0
Now,
⇒24(1−0)+14(0−2)+04(2−1)
⇒16+1(−2)+0
⇒16−2=14
So, Statement 1 is positive.
Statement 2.
x4(y−z)+y4(z−x)+z4(x−y) is negative if x<y<z
Here, x<y<z
Then, x=0,y=1 or z=2
Now,
⇒04(1−2)+14(2−0)+24(0−1)
⇒0+2−16=−14
So, Statement 2 is negative.
∴ Both 1 and 2 .