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.

(C) \(I\) and \(J\) can be both negative but not both positive.

(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

(C)330

(D)335

Note by Anandhu Raj
2 years, 11 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears 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} \( \boxed{123} \)

Comments

Sort by:

Top Newest

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 - 2 years, 11 months ago

Log in to reply

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 - 2 years, 11 months ago

Log in to reply

  1. C and 2. B

Parv Mor - 2 years, 11 months ago

Log in to reply

Could you please explain how it come through?

Anandhu Raj - 2 years, 11 months ago

Log in to reply

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 - 2 years, 11 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...