BPSC 47th Exam Prelims 2005 Solved Paper

Question : 130 of 150

Marks: +1, -0

^nC_1 +^ nC_2 + ..... ^nC_n = 255,

then the value of n is –

Solution:

{ }^{n} C_{1}+{ }^{n} C_{2}+. . . . . .+{ }^{n} C_{n}=255

∵ { }^{n} C_{0}+{ }^{n} C_{1}+{ }^{n} C_{2}+. . . . .+{ }^{n} C_{n}=2^{n}

∴ { }^{n} {C}_{1}+{ }^{n} {C}_{2}+. . . .+{ }^{n} {C}_{ {n}}=2^{ {n}}-1

⇒ 2^{n}-1=255

⇒ 2^{n}=256

⇒ 2^{n}=2^{8}

∴ n=8

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