NTSE Stage 2 SAT 2019 Exam Question Paper

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Question : 43 of 100

Marks: +1, -0

Let P(x) be a polynomial of degree 3 and

P(n)=1/2

for

n=1,2,3,4

. Then the value of .P(5) is

0
$1/5$
$-2/5$
$3/5$

Solution:

P(x) is a polynomial of degree 3
and

P(n)=1/n⇒nP(n)-1=0

n(P(n)) is a polynomial of degree 4

∴nP(n)-1=k(n-1)(n-2)(n-3)(n-4)

For

n=0;-1=24{k}⇒k=\;\;{-1}/{24}

For

n=5;5⋅P(5)-1=\;\;{-1}/{24}(4)(3)(2)

⇒5⋅P(5)-1=-1⇒P(5)=0

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