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Week 4 Mathematics 1 Questions | Prasnya
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34Q
01
Consider the polynomial
p
(
x
)
=
a
n
x
n
+
⋯
+
a
1
x
+
a
0
p(x)=a_nx^n+\cdots+a_1x+a_0
p
(
x
)
=
a
n
x
n
+
⋯
+
a
1
x
+
a
0
, where
a
i
∈
R
a_i \in \mathbb{R}
a
i
∈
R
and
a
n
≠
0
a_n \ne 0
a
n
=
0
. Suppose
x
0
∈
R
x_0 \in \mathbb{R}
x
0
∈
R
is the smallest root of
p
p
p
. From the options below, choose the conditions that ensure that
p
(
x
)
p(x)
p
(
x
)
is strictly decreasing in
(
−
∞
,
x
0
)
(-\infty,x_0)
(
−
∞
,
x
0
)
.
Multiple correct
HARD
4 marks
15 March 2026
02
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
EASY
4 marks
15 March 2026
03
Consider the polynomial function
p
(
x
)
=
−
(
x
2
−
16
)
(
x
−
3
)
2
(
2
−
x
)
2
(
x
+
9
)
p(x)=-(x^2-16)(x-3)^2(2-x)^2(x+9)
p
(
x
)
=
−
(
x
2
−
16
)
(
x
−
3
)
2
(
2
−
x
)
2
(
x
+
9
)
. Choose the set correct options.
Multiple correct
HARD
5 marks
15 March 2026
04
Subendu and Mohit reside at
(
4
,
−
18.9
)
(4, -18.9)
(
4
,
−
18.9
)
and
(
4
,
18.9
)
(4, 18.9)
(
4
,
18.9
)
respectively. They planned a road trip. Subendu decided to go by road
r
1
(
x
)
=
0.02
(
x
−
5
)
(
x
−
7
)
(
x
−
9
)
(
x
−
11
)
(
x
−
13
)
r_1(x) = 0.02(x-5)(x-7)(x-9)(x-11)(x-13)
r
1
(
x
)
=
0.02
(
x
−
5
)
(
x
−
7
)
(
x
−
9
)
(
x
−
11
)
(
x
−
13
)
and Mohit chose the road
r
2
(
x
)
=
0.02
(
x
−
5
)
2
(
x
−
7
)
(
x
−
9
)
(
x
−
11
)
(
x
−
13
)
r_2(x) = 0.02(x-5)^2(x-7)(x-9)(x-11)(x-13)
r
2
(
x
)
=
0.02
(
x
−
5
)
2
(
x
−
7
)
(
x
−
9
)
(
x
−
11
)
(
x
−
13
)
. They decided to meet where these roads intersect. Based on the given information, choose the correct option.
Single correct
MEDIUM
4 marks
26 October 2025
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
26 October 2025
06
A drone's vertical displacement (in meters) over time is modelled by
D
(
x
)
=
x
4
−
3
x
3
+
3
x
+
3
D(x) = x^4 - 3x^3 + 3x + 3
D
(
x
)
=
x
4
−
3
x
3
+
3
x
+
3
, where
x
x
x
is time in seconds. A wind gust's force variation is modelled by
F
(
x
)
=
x
2
+
x
−
4
F(x) = x^2 + x - 4
F
(
x
)
=
x
2
+
x
−
4
. An engineer models a control response line
R
(
x
)
R(x)
R
(
x
)
that passes through the point
(
1
,
F
(
1
)
)
(1, F(1))
(
1
,
F
(
1
))
and has a slope of
−
2
-2
−
2
. Compute the total response
D
(
x
)
+
R
(
x
)
⋅
F
(
x
)
D(x) + R(x) \cdot F(x)
D
(
x
)
+
R
(
x
)
⋅
F
(
x
)
. Choose the correct option.
Single correct
HARD
4 marks
13 July 2025
07
Consider two polynomials
p
(
x
)
=
x
4
+
3
x
3
−
9
x
+
8
p(x) = x^4 + 3x^3 - 9x + 8
p
(
x
)
=
x
4
+
3
x
3
−
9
x
+
8
and
q
(
x
)
=
(
x
2
+
x
)
(
x
+
3
)
q(x) = (x^2+x)(x+3)
q
(
x
)
=
(
x
2
+
x
)
(
x
+
3
)
. Let
r
(
x
)
r(x)
r
(
x
)
and
s
(
x
)
s(x)
s
(
x
)
be the remainder and the quotient, respectively, obtained when
p
(
x
)
p(x)
p
(
x
)
is divided by
q
(
x
)
q(x)
q
(
x
)
. Let
z
(
x
)
=
r
(
x
)
⋅
s
(
x
)
z(x) = r(x) \cdot s(x)
z
(
x
)
=
r
(
x
)
⋅
s
(
x
)
. Which of the following options is/are true?
Multiple correct
HARD
5 marks
13 July 2025
08
If
x
+
a
x + a
x
+
a
is one of the factors of
p
(
x
)
=
k
x
2
+
k
a
x
+
5
x
+
15
p(x) = kx^2 + kax + 5x + 15
p
(
x
)
=
k
x
2
+
k
a
x
+
5
x
+
15
, then find the value of
a
a
a
.
Numerical
MEDIUM
4 marks
23 February 2025
09
Consider two polynomials
p
(
x
)
=
x
4
+
3
x
3
−
9
x
+
8
p(x) = x^4 + 3x^3 - 9x + 8
p
(
x
)
=
x
4
+
3
x
3
−
9
x
+
8
and
q
(
x
)
=
(
x
2
+
x
)
(
x
+
3
)
q(x) = (x^2 + x)(x + 3)
q
(
x
)
=
(
x
2
+
x
)
(
x
+
3
)
. Let
r
(
x
)
r(x)
r
(
x
)
be the remainder obtained when
p
(
x
)
p(x)
p
(
x
)
is divided by
q
(
x
)
q(x)
q
(
x
)
. Let
l
(
x
)
l(x)
l
(
x
)
be the straight line passing through the
y
y
y
-intercept and the minimum point of
r
(
x
)
r(x)
r
(
x
)
. Which of the following options is/are true?
Multiple correct
HARD
4 marks
23 February 2025
10
Which of the following options is/are true?
Comprehension
HARD
4 marks
23 February 2025
11
Which of the following options is/are true?
Comprehension
MEDIUM
3 marks
23 February 2025
12
Consider the polynomials
p
(
x
)
=
x
3
−
3
x
2
+
100
x
−
1
p(x)=x^3-3x^2+100x-1
p
(
x
)
=
x
3
−
3
x
2
+
100
x
−
1
and
q
(
x
)
=
x
3
+
x
+
5
q(x)=x^3+x+5
q
(
x
)
=
x
3
+
x
+
5
. Then which of the following statements are correct?
Single correct
MEDIUM
4 marks
24 October 2024
13
Consider a polynomial
p
(
x
)
=
0.3
x
3
(
x
2
−
1
)
(
x
−
2
)
2
(
x
−
3
)
p(x)=0.3x^3(x^2-1)(x-2)^2(x-3)
p
(
x
)
=
0.3
x
3
(
x
2
−
1
)
(
x
−
2
)
2
(
x
−
3
)
and the following figures.Which figure represents the polynomial
p
(
x
)
p(x)
p
(
x
)
?
Single correct
HARD
4 marks
24 October 2024
14
What is the degree of
p
(
x
)
p(x)
p
(
x
)
?
Comprehension
EASY
3 marks
24 October 2024
15
Calculate the number of turning points
p
(
x
)
p(x)
p
(
x
)
can have.
Comprehension
HARD
4 marks
24 October 2024
16
Consider the following polynomial
p
(
x
)
p(x)
p
(
x
)
whose graph is given below. Which of the following options is/are correct?
Multiple correct
MEDIUM
4 marks
07 July 2024
17
Consider the polynomials
p
(
x
)
=
(
2
x
−
1
)
(
x
−
5
)
q
(
x
)
p(x)=(2x-1)(x-5)q(x)
p
(
x
)
=
(
2
x
−
1
)
(
x
−
5
)
q
(
x
)
where the zeros of
p
(
x
)
p(x)
p
(
x
)
with multiplicity
1
1
1
are
1
/
2
,
5
,
2
,
3
/
5
1/2,5,2,3/5
1/2
,
5
,
2
,
3/5
. Which of the following option(s) are true for
q
(
x
)
q(x)
q
(
x
)
?
Multiple correct
MEDIUM
4 marks
07 July 2024
18
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
5 marks
25 February 2024
19
Consider the following polynomial
p
(
x
)
p(x)
p
(
x
)
whose graph is given below. Which of the following options is/are correct?
Multiple correct
MEDIUM
4 marks
25 February 2024
20
Consider a polynomial
p
(
x
)
=
0.3
x
2
(
x
2
−
1
)
(
x
−
2
)
2
(
x
−
3
)
p(x)=0.3x^2(x^2-1)(x-2)^2(x-3)
p
(
x
)
=
0.3
x
2
(
x
2
−
1
)
(
x
−
2
)
2
(
x
−
3
)
. Which of the figure represents the polynomial
p
(
x
)
p(x)
p
(
x
)
?
Single correct
MEDIUM
5 marks
16 July 2023
21
Consider two polynomials
p
(
x
)
=
x
4
+
3
x
3
−
9
x
+
8
p(x)=x^4+3x^3-9x+8
p
(
x
)
=
x
4
+
3
x
3
−
9
x
+
8
and
q
(
x
)
=
(
x
2
+
x
)
(
x
+
3
)
q(x)=(x^2+x)(x+3)
q
(
x
)
=
(
x
2
+
x
)
(
x
+
3
)
. Let
r
(
x
)
r(x)
r
(
x
)
be the remainder obtained when
p
(
x
)
p(x)
p
(
x
)
is divided by
q
(
x
)
q(x)
q
(
x
)
. Let
l
(
x
)
l(x)
l
(
x
)
be the line that passes through the
y
y
y
-intercept and the minimum point in the graph of
r
(
x
)
r(x)
r
(
x
)
, for reference follow the Figure M1Q1-1. Which of the following options is/are true?
Multiple correct
HARD
5 marks
16 July 2023
22
If
m
m
m
is the number of distinct roots and
n
n
n
is the number of turning points of the polynomial
p
(
x
)
p(x)
p
(
x
)
, then find the value of
m
+
n
m+n
m
+
n
.
Comprehension
HARD
3 marks
16 July 2023
23
Which of the following options is/are true?
Comprehension
MEDIUM
4 marks
16 July 2023
24
How many times did Ritwik score exactly
40
40
40
? NOTE: Enter your answer to the nearest integer.
Comprehension
MEDIUM
2 marks
16 October 2022
25
In total, how many mock tests did Ritwik pass? NOTE: Enter your answer to the nearest integer.
Comprehension
MEDIUM
3 marks
16 October 2022
26
Figure 2 shows the graph of a polynomial
p
(
x
)
p(x)
p
(
x
)
. Choose the set of correct option(s).
Multiple correct
MEDIUM
5 marks
16 October 2022
27
The polynomial
p
(
x
)
=
a
n
x
n
+
a
n
−
1
x
n
−
1
+
⋯
+
a
0
p(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+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.
(
x
+
4
)
2
(x+4)^2
(
x
+
4
)
2
is a factor of
p
(
x
)
p(x)
p
(
x
)
.
p
(
0
)
≠
0
p(0)\ne0
p
(
0
)
=
0
. From the options given, choose the possible representations of
p
(
x
)
p(x)
p
(
x
)
.
Multiple correct
MEDIUM
4 marks
16 October 2022
28
Consider a polynomial function
p
(
x
)
=
−
0.01
(
x
−
1
)
(
x
−
2
)
2
(
x
−
3
)
2
(
x
−
4
)
x
(
x
+
1
)
(
x
+
2
)
2
p(x)=-0.01(x-1)(x-2)^2(x-3)^2(x-4)x(x+1)(x+2)^2
p
(
x
)
=
−
0.01
(
x
−
1
)
(
x
−
2
)
2
(
x
−
3
)
2
(
x
−
4
)
x
(
x
+
1
)
(
x
+
2
)
2
. Choose the correct options from the following.
Multiple correct
HARD
5 marks
05 June 2022
29
Enter the value of
a
a
a
. NOTE: Enter your answer to the nearest integer.
Comprehension
MEDIUM
3 marks
05 June 2022
30
Choose the set of correct option(s).
Comprehension
MEDIUM
3 marks
05 June 2022
31
In total how many places can they meet? NOTE: Enter your answer to the nearest integer.
Comprehension
MEDIUM
2 marks
05 June 2022
32
Sandhya launches her new company in the year 2010, which makes yearly profit in lakhs as the polynomial function
z
(
x
)
=
0.1
x
2
(
x
−
1
)
(
x
−
2
)
(
x
−
3
)
2
(
x
−
4
)
(
x
−
9
)
z(x)=0.1x^2(x-1)(x-2)(x-3)^2(x-4)(x-9)
z
(
x
)
=
0.1
x
2
(
x
−
1
)
(
x
−
2
)
(
x
−
3
)
2
(
x
−
4
)
(
x
−
9
)
for the first 12 years since the launch, where
x
x
x
is the number of years since 2010. Let the loss be represented as negative profit. Which of the following options are correct?
Multiple correct
MEDIUM
5 marks
10 July 2022
33
Using the given information, find the value of
k
k
k
. NOTE: Enter your answer to the nearest integer.
Comprehension
MEDIUM
4 marks
10 July 2022
34
Using the given information, what will be the
y
y
y
-coordinate of point
A
A
A
? NOTE: Enter your answer in one decimal place.
Comprehension
EASY
3 marks
10 July 2022
Showing 34 questions.
Mathematics 1 > Week 4
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Topic-Wise PYQs
Start Weekly Test
Mock tests
Week mock
Topic mock
Subject mock
Type:
All
Difficulty:
All
Year:
All
34Q
01
Consider the polynomial
p
(
x
)
=
a
n
x
n
+
⋯
+
a
1
x
+
a
0
p(x)=a_nx^n+\cdots+a_1x+a_0
p
(
x
)
=
a
n
x
n
+
⋯
+
a
1
x
+
a
0
, where
a
i
∈
R
a_i \in \mathbb{R}
a
i
∈
R
and
a
n
≠
0
a_n \ne 0
a
n
=
0
. Suppose
x
0
∈
R
x_0 \in \mathbb{R}
x
0
∈
R
is the smallest root of
p
p
p
. From the options below, choose the conditions that ensure that
p
(
x
)
p(x)
p
(
x
)
is strictly decreasing in
(
−
∞
,
x
0
)
(-\infty,x_0)
(
−
∞
,
x
0
)
.
Multiple correct
HARD
4 marks
15 March 2026
02
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
EASY
4 marks
15 March 2026
03
Consider the polynomial function
p
(
x
)
=
−
(
x
2
−
16
)
(
x
−
3
)
2
(
2
−
x
)
2
(
x
+
9
)
p(x)=-(x^2-16)(x-3)^2(2-x)^2(x+9)
p
(
x
)
=
−
(
x
2
−
16
)
(
x
−
3
)
2
(
2
−
x
)
2
(
x
+
9
)
. Choose the set correct options.
Multiple correct
HARD
5 marks
15 March 2026
04
Subendu and Mohit reside at
(
4
,
−
18.9
)
(4, -18.9)
(
4
,
−
18.9
)
and
(
4
,
18.9
)
(4, 18.9)
(
4
,
18.9
)
respectively. They planned a road trip. Subendu decided to go by road
r
1
(
x
)
=
0.02
(
x
−
5
)
(
x
−
7
)
(
x
−
9
)
(
x
−
11
)
(
x
−
13
)
r_1(x) = 0.02(x-5)(x-7)(x-9)(x-11)(x-13)
r
1
(
x
)
=
0.02
(
x
−
5
)
(
x
−
7
)
(
x
−
9
)
(
x
−
11
)
(
x
−
13
)
and Mohit chose the road
r
2
(
x
)
=
0.02
(
x
−
5
)
2
(
x
−
7
)
(
x
−
9
)
(
x
−
11
)
(
x
−
13
)
r_2(x) = 0.02(x-5)^2(x-7)(x-9)(x-11)(x-13)
r
2
(
x
)
=
0.02
(
x
−
5
)
2
(
x
−
7
)
(
x
−
9
)
(
x
−
11
)
(
x
−
13
)
. They decided to meet where these roads intersect. Based on the given information, choose the correct option.
Single correct
MEDIUM
4 marks
26 October 2025
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
26 October 2025
06
A drone's vertical displacement (in meters) over time is modelled by
D
(
x
)
=
x
4
−
3
x
3
+
3
x
+
3
D(x) = x^4 - 3x^3 + 3x + 3
D
(
x
)
=
x
4
−
3
x
3
+
3
x
+
3
, where
x
x
x
is time in seconds. A wind gust's force variation is modelled by
F
(
x
)
=
x
2
+
x
−
4
F(x) = x^2 + x - 4
F
(
x
)
=
x
2
+
x
−
4
. An engineer models a control response line
R
(
x
)
R(x)
R
(
x
)
that passes through the point
(
1
,
F
(
1
)
)
(1, F(1))
(
1
,
F
(
1
))
and has a slope of
−
2
-2
−
2
. Compute the total response
D
(
x
)
+
R
(
x
)
⋅
F
(
x
)
D(x) + R(x) \cdot F(x)
D
(
x
)
+
R
(
x
)
⋅
F
(
x
)
. Choose the correct option.
Single correct
HARD
4 marks
13 July 2025
07
Consider two polynomials
p
(
x
)
=
x
4
+
3
x
3
−
9
x
+
8
p(x) = x^4 + 3x^3 - 9x + 8
p
(
x
)
=
x
4
+
3
x
3
−
9
x
+
8
and
q
(
x
)
=
(
x
2
+
x
)
(
x
+
3
)
q(x) = (x^2+x)(x+3)
q
(
x
)
=
(
x
2
+
x
)
(
x
+
3
)
. Let
r
(
x
)
r(x)
r
(
x
)
and
s
(
x
)
s(x)
s
(
x
)
be the remainder and the quotient, respectively, obtained when
p
(
x
)
p(x)
p
(
x
)
is divided by
q
(
x
)
q(x)
q
(
x
)
. Let
z
(
x
)
=
r
(
x
)
⋅
s
(
x
)
z(x) = r(x) \cdot s(x)
z
(
x
)
=
r
(
x
)
⋅
s
(
x
)
. Which of the following options is/are true?
Multiple correct
HARD
5 marks
13 July 2025
08
If
x
+
a
x + a
x
+
a
is one of the factors of
p
(
x
)
=
k
x
2
+
k
a
x
+
5
x
+
15
p(x) = kx^2 + kax + 5x + 15
p
(
x
)
=
k
x
2
+
k
a
x
+
5
x
+
15
, then find the value of
a
a
a
.
Numerical
MEDIUM
4 marks
23 February 2025
09
Consider two polynomials
p
(
x
)
=
x
4
+
3
x
3
−
9
x
+
8
p(x) = x^4 + 3x^3 - 9x + 8
p
(
x
)
=
x
4
+
3
x
3
−
9
x
+
8
and
q
(
x
)
=
(
x
2
+
x
)
(
x
+
3
)
q(x) = (x^2 + x)(x + 3)
q
(
x
)
=
(
x
2
+
x
)
(
x
+
3
)
. Let
r
(
x
)
r(x)
r
(
x
)
be the remainder obtained when
p
(
x
)
p(x)
p
(
x
)
is divided by
q
(
x
)
q(x)
q
(
x
)
. Let
l
(
x
)
l(x)
l
(
x
)
be the straight line passing through the
y
y
y
-intercept and the minimum point of
r
(
x
)
r(x)
r
(
x
)
. Which of the following options is/are true?
Multiple correct
HARD
4 marks
23 February 2025
10
Which of the following options is/are true?
Comprehension
HARD
4 marks
23 February 2025
11
Which of the following options is/are true?
Comprehension
MEDIUM
3 marks
23 February 2025
12
Consider the polynomials
p
(
x
)
=
x
3
−
3
x
2
+
100
x
−
1
p(x)=x^3-3x^2+100x-1
p
(
x
)
=
x
3
−
3
x
2
+
100
x
−
1
and
q
(
x
)
=
x
3
+
x
+
5
q(x)=x^3+x+5
q
(
x
)
=
x
3
+
x
+
5
. Then which of the following statements are correct?
Single correct
MEDIUM
4 marks
24 October 2024
13
Consider a polynomial
p
(
x
)
=
0.3
x
3
(
x
2
−
1
)
(
x
−
2
)
2
(
x
−
3
)
p(x)=0.3x^3(x^2-1)(x-2)^2(x-3)
p
(
x
)
=
0.3
x
3
(
x
2
−
1
)
(
x
−
2
)
2
(
x
−
3
)
and the following figures.Which figure represents the polynomial
p
(
x
)
p(x)
p
(
x
)
?
Single correct
HARD
4 marks
24 October 2024
14
What is the degree of
p
(
x
)
p(x)
p
(
x
)
?
Comprehension
EASY
3 marks
24 October 2024
15
Calculate the number of turning points
p
(
x
)
p(x)
p
(
x
)
can have.
Comprehension
HARD
4 marks
24 October 2024
16
Consider the following polynomial
p
(
x
)
p(x)
p
(
x
)
whose graph is given below. Which of the following options is/are correct?
Multiple correct
MEDIUM
4 marks
07 July 2024
17
Consider the polynomials
p
(
x
)
=
(
2
x
−
1
)
(
x
−
5
)
q
(
x
)
p(x)=(2x-1)(x-5)q(x)
p
(
x
)
=
(
2
x
−
1
)
(
x
−
5
)
q
(
x
)
where the zeros of
p
(
x
)
p(x)
p
(
x
)
with multiplicity
1
1
1
are
1
/
2
,
5
,
2
,
3
/
5
1/2,5,2,3/5
1/2
,
5
,
2
,
3/5
. Which of the following option(s) are true for
q
(
x
)
q(x)
q
(
x
)
?
Multiple correct
MEDIUM
4 marks
07 July 2024
18
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
5 marks
25 February 2024
19
Consider the following polynomial
p
(
x
)
p(x)
p
(
x
)
whose graph is given below. Which of the following options is/are correct?
Multiple correct
MEDIUM
4 marks
25 February 2024
20
Consider a polynomial
p
(
x
)
=
0.3
x
2
(
x
2
−
1
)
(
x
−
2
)
2
(
x
−
3
)
p(x)=0.3x^2(x^2-1)(x-2)^2(x-3)
p
(
x
)
=
0.3
x
2
(
x
2
−
1
)
(
x
−
2
)
2
(
x
−
3
)
. Which of the figure represents the polynomial
p
(
x
)
p(x)
p
(
x
)
?
Single correct
MEDIUM
5 marks
16 July 2023
21
Consider two polynomials
p
(
x
)
=
x
4
+
3
x
3
−
9
x
+
8
p(x)=x^4+3x^3-9x+8
p
(
x
)
=
x
4
+
3
x
3
−
9
x
+
8
and
q
(
x
)
=
(
x
2
+
x
)
(
x
+
3
)
q(x)=(x^2+x)(x+3)
q
(
x
)
=
(
x
2
+
x
)
(
x
+
3
)
. Let
r
(
x
)
r(x)
r
(
x
)
be the remainder obtained when
p
(
x
)
p(x)
p
(
x
)
is divided by
q
(
x
)
q(x)
q
(
x
)
. Let
l
(
x
)
l(x)
l
(
x
)
be the line that passes through the
y
y
y
-intercept and the minimum point in the graph of
r
(
x
)
r(x)
r
(
x
)
, for reference follow the Figure M1Q1-1. Which of the following options is/are true?
Multiple correct
HARD
5 marks
16 July 2023
22
If
m
m
m
is the number of distinct roots and
n
n
n
is the number of turning points of the polynomial
p
(
x
)
p(x)
p
(
x
)
, then find the value of
m
+
n
m+n
m
+
n
.
Comprehension
HARD
3 marks
16 July 2023
23
Which of the following options is/are true?
Comprehension
MEDIUM
4 marks
16 July 2023
24
How many times did Ritwik score exactly
40
40
40
? NOTE: Enter your answer to the nearest integer.
Comprehension
MEDIUM
2 marks
16 October 2022
25
In total, how many mock tests did Ritwik pass? NOTE: Enter your answer to the nearest integer.
Comprehension
MEDIUM
3 marks
16 October 2022
26
Figure 2 shows the graph of a polynomial
p
(
x
)
p(x)
p
(
x
)
. Choose the set of correct option(s).
Multiple correct
MEDIUM
5 marks
16 October 2022
27
The polynomial
p
(
x
)
=
a
n
x
n
+
a
n
−
1
x
n
−
1
+
⋯
+
a
0
p(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+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.
(
x
+
4
)
2
(x+4)^2
(
x
+
4
)
2
is a factor of
p
(
x
)
p(x)
p
(
x
)
.
p
(
0
)
≠
0
p(0)\ne0
p
(
0
)
=
0
. From the options given, choose the possible representations of
p
(
x
)
p(x)
p
(
x
)
.
Multiple correct
MEDIUM
4 marks
16 October 2022
28
Consider a polynomial function
p
(
x
)
=
−
0.01
(
x
−
1
)
(
x
−
2
)
2
(
x
−
3
)
2
(
x
−
4
)
x
(
x
+
1
)
(
x
+
2
)
2
p(x)=-0.01(x-1)(x-2)^2(x-3)^2(x-4)x(x+1)(x+2)^2
p
(
x
)
=
−
0.01
(
x
−
1
)
(
x
−
2
)
2
(
x
−
3
)
2
(
x
−
4
)
x
(
x
+
1
)
(
x
+
2
)
2
. Choose the correct options from the following.
Multiple correct
HARD
5 marks
05 June 2022
29
Enter the value of
a
a
a
. NOTE: Enter your answer to the nearest integer.
Comprehension
MEDIUM
3 marks
05 June 2022
30
Choose the set of correct option(s).
Comprehension
MEDIUM
3 marks
05 June 2022
31
In total how many places can they meet? NOTE: Enter your answer to the nearest integer.
Comprehension
MEDIUM
2 marks
05 June 2022
32
Sandhya launches her new company in the year 2010, which makes yearly profit in lakhs as the polynomial function
z
(
x
)
=
0.1
x
2
(
x
−
1
)
(
x
−
2
)
(
x
−
3
)
2
(
x
−
4
)
(
x
−
9
)
z(x)=0.1x^2(x-1)(x-2)(x-3)^2(x-4)(x-9)
z
(
x
)
=
0.1
x
2
(
x
−
1
)
(
x
−
2
)
(
x
−
3
)
2
(
x
−
4
)
(
x
−
9
)
for the first 12 years since the launch, where
x
x
x
is the number of years since 2010. Let the loss be represented as negative profit. Which of the following options are correct?
Multiple correct
MEDIUM
5 marks
10 July 2022
33
Using the given information, find the value of
k
k
k
. NOTE: Enter your answer to the nearest integer.
Comprehension
MEDIUM
4 marks
10 July 2022
34
Using the given information, what will be the
y
y
y
-coordinate of point
A
A
A
? NOTE: Enter your answer in one decimal place.
Comprehension
EASY
3 marks
10 July 2022
Showing 34 questions.
