Xavier Aptitude Test 2015 Paper

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Question : 64 of 113

Marks: +1, -0

If f (x

^{2}

– 1) = x

^{4}

– 7x

^{2}

+

k_1

and f(x

^{3 }

– 2) = x

^{6}

– 9x

^{3}

+

k_2

then the value of

(k_2 – k_1 )

is

6
7
8
9
None of these

Solution:

(c) Given,

f\ (x^{2}-1\ )=x^{4}-7 x^{2}+k_{1}

If

x^{2}=1,

then

f(0)=-6+k_{1}

........(i)
Also,

f\ (x^{3}-2 )=x^{6}-9 x^{3}+k_{2}

If

x^{3}=2

then

f(0)=-14+k_{2}

........(ii)
Equating the values of f(0) from equation (i) and (ii),

-6+ {k}_{1}=-14+ {k}_{2}

⇒{k}_{2}- {k}_{1}=8

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