Help Please..

1) A polynomial p(x)=x4+ax3+bx2+cx+dp(x)={ x }^{ 4 }+a{ x }^{ 3 }+b{ x }^{ 2 }+cx+d has roots 2,e\sqrt { 2 } ,e and π\pi and no other roots. Let I=2ep(x)dxI=\int _{ \sqrt { 2 } }^{ e }{ p(x)dx } and J=eπp(x)dx.J=\int _{ e }^{ \pi }{ p(x)dx. } Then,

(A) II and JJ must have opposite signs.

(B) II and JJ can be both positive but not both negative.

(C) II and JJ can be both negative but not both positive.

(D) We do not have enough information to compare the signs of II and JJ.

2) All the inner angles of a -7 gon are obtuse , their sizes in degree being distinct integers divisible by 9. What is the sum(in degree) of the largest two angles?

(A) 300

(B)315

(C)330

(D)335

Note by Anandhu Raj
4 years ago

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1 vote

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  1. C and 2. B

parv mor - 4 years ago

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Could you please explain how it come through?

Anandhu Raj - 4 years ago

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For the first ques as it has three roots and no other root and also the function is bi quadratic so there must be a repeated root. Considering three different cases just plot the graph and check the sign of integral.

parv mor - 4 years ago

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1.C we can verify it by graph

2.B because the angles would be 99,108,117,126,135,153,162 as all angles are obtuse and divisible by 9 so sum of 2 largest angles =153+162=315

Btw U too preparing for kvpy??

Naman Kapoor - 4 years ago

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Yup!! By the way could you please help with these also? The positive integer k for which 101k2k!\frac { { 101 }^{ \frac { k }{ 2 } } }{ k! } is a maximum is?

Anandhu Raj - 4 years ago

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