Help Please..

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

(A) $I$ and $J$ must have opposite signs.

(B) $I$ and $J$ can be both positive but not both negative.

(D) We do not have enough information to compare the signs of $I$ and $J$ .

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

(D)335

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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Comments

C and 2. B

parv mor - 5 years, 7 months ago

Could you please explain how it come through?

Anandhu Raj - 5 years, 7 months ago

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 - 5 years, 7 months ago

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 - 5 years, 7 months ago

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

Anandhu Raj - 5 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$