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IITM BS Week 4 Mathematics 1 Questions | Prasnya
Mathematics 1 > Week 4
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Difficulty:
All
Year:
All
7Q
01
Consider the polynomial function
f
(
x
)
=
−
(
x
+
1
)
3
(
x
−
1
)
2
(
x
−
3
)
4
f(x) = -(x + 1)^3 (x - 1)^2 (x - 3)^4
f
(
x
)
=
−
(
x
+
1
)
3
(
x
−
1
)
2
(
x
−
3
)
4
. Choose the correct statements from the following.
Multiple correct
HARD
4 marks
10 May 2026
02
Which of the following options is/are correct?
Comprehension
MEDIUM
3 marks
22 December 2024
03
Which of the following options is true?
Comprehension
EASY
3 marks
22 December 2024
04
Consider two polynomials
p
(
x
)
=
−
x
5
+
5
x
4
−
7
x
−
2
p(x) = -x^5 + 5x^4 - 7x - 2
p
(
x
)
=
−
x
5
+
5
x
4
−
7
x
−
2
and
q
(
x
)
=
−
x
5
+
5
x
4
−
x
2
−
2
q(x) = -x^5 + 5x^4 - x^2 - 2
q
(
x
)
=
−
x
5
+
5
x
4
−
x
2
−
2
. Which of the following options is/are true?
Multiple correct
MEDIUM
2 marks
01 September 2024
05
Consider two polynomials
p
(
x
)
=
−
x
5
+
5
x
4
−
7
x
−
2
p(x) = -x^5 + 5x^4 - 7x - 2
p
(
x
)
=
−
x
5
+
5
x
4
−
7
x
−
2
and
q
(
x
)
=
−
x
5
+
5
x
4
−
x
2
−
2
q(x) = -x^5 + 5x^4 - x^2 - 2
q
(
x
)
=
−
x
5
+
5
x
4
−
x
2
−
2
. Which of the following options is/are true?
Multiple correct
MEDIUM
4 marks
24 December 2023
06
The polynomial
p
(
x
)
=
a
n
x
n
+
a
n
−
1
x
n
−
1
+
⋯
+
a
0
p(x) = a_n x^n + a_{n-1} x^{n-1} + \dots + a_0
p
(
x
)
=
a
n
x
n
+
a
n
−
1
x
n
−
1
+
⋯
+
a
0
has the following properties: -
p
(
x
)
p(x)
p
(
x
)
is an odd degree polynomial with at least three distinct roots. -
p
(
x
)
p(x)
p
(
x
)
has exactly two positive real roots. -
(
x
−
5
)
2
(x - 5)^2
(
x
−
5
)
2
is a factor of
p
(
x
)
p(x)
p
(
x
)
. -
p
(
0
)
≠
0
p(0) \neq 0
p
(
0
)
=
0
Choose the best possible representations of
p
(
x
)
p(x)
p
(
x
)
.
Single correct
MEDIUM
3 marks
11 December 2022
07
The polynomial
p
(
x
)
=
a
n
x
n
+
a
n
−
1
x
n
−
1
+
⋯
+
a
0
p(x) = a_n x^n + a_{n-1} x^{n-1} + \dots + a_0
p
(
x
)
=
a
n
x
n
+
a
n
−
1
x
n
−
1
+
⋯
+
a
0
has the following properties: -
p
(
x
)
p(x)
p
(
x
)
is an even degree polynomial. -
p
(
x
)
p(x)
p
(
x
)
has at least one positive real root and at least one negative real root. - Either
(
x
−
3
)
(x - 3)
(
x
−
3
)
or
(
x
−
3
)
2
(x - 3)^2
(
x
−
3
)
2
is a factor of
p
(
x
)
p(x)
p
(
x
)
. -
p
(
0
)
≠
0
p(0) \neq 0
p
(
0
)
=
0
From the options given, choose the possible representations of
p
(
x
)
p(x)
p
(
x
)
.
Multiple correct
HARD
4 marks
07 August 2022
Showing 7 questions.
Complete question index for this section:
Question 1 (multiple):
Question 2 (comprehension):
Question 3 (comprehension):
Question 4 (multiple):
Question 5 (multiple):
Question 6 (single):
Question 7 (multiple):
