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Let (m, n) = 01 xm - 1(1 - x)n - 1 dx, m, n > 0. If 01 (1 - x10 )20 dx = a (b, c), then 100(a + b + c) equals .
(4) 2120
Put x10 = t x = t1/10, dx = 110t-9/10 dt (limits stay 0 to 1)
01 (1 - x10)20 dx = 110 01 t(1/10) - 1(1 - t)21 - 1 dt = 110 ( 110, 21 )
a = 110, b = 110, c = 21
100(a + b + c) = 10 + 10 + 2100 = 2120
Answer: (4)
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