Teaching DSSSB TGT Mock Test 2025 Mathematical Science Complex Analysis Schwarz Lemma

Let f:D → D be holomorphic with f(0) = 0 and f(\(\frac12\)) = 0 where D = {z: |z| < 1}. Which of the following is false

1
|f'(1/2)| ≤ 4/3
2
|f'(0)| ≤ 1
3
|f'(0)| ≤ 1 and |f'(1/2)| ≤ 4/3
4
f(z) = z for all z ∈ D
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