Week 4 Mathematics 1 Questions | Prasnya
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Topic wise questions
Q1
Consider the polynomial
p
(
x
)
=
a
n
x
n
+
⋯
+
a
1
x
+
a
0
p(x)=a_nx^n+\cdots+a_1x+a_0
, where
a
i
∈
R
a_i \in \mathbb{R}
and
a
n
≠
0
a_n \ne 0
. Suppose
x
0
∈
R
x_0 \in \mathbb{R}
is the smallest root of
p
p
. From the options below, choose the conditions that ensure that
p
(
x
)
p(x)
is strictly decreasing in
(
−
∞
,
x
0
)
(-\infty,x_0)
.
Multiple correct
MARCH 15, 2026
MARCH 15, 2026
Q2
Consider two polynomials
p
(
x
)
=
−
x
5
+
5
x
4
−
7
x
−
2
p(x)=-x^5+5x^4-7x-2
and
q
(
x
)
=
−
x
5
+
5
x
4
−
x
2
−
2
q(x)=-x^5+5x^4-x^2-2
. Which of the following options is/are true?
Multiple correct
MARCH 15, 2026
MARCH 15, 2026
Q3
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)
. Choose the set correct options.
Multiple correct
MARCH 15, 2026
MARCH 15, 2026
Q4
Subendu and Mohit reside at
(
4
,
−
18.9
)
(4, -18.9)
and
(
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)
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)
. They decided to meet where these roads intersect. Based on the given information, choose the correct option.
Single correct
OCTOBER 26, 2025
OCTOBER 26, 2025
Q5
Consider two polynomials
p
(
x
)
=
−
x
5
+
5
x
4
−
7
x
−
2
p(x) = -x^5 + 5x^4 - 7x - 2
and
q
(
x
)
=
−
x
5
+
5
x
4
−
x
2
−
2
q(x) = -x^5 + 5x^4 - x^2 - 2
. Which of the following options is/are true?
Multiple correct
OCTOBER 26, 2025
OCTOBER 26, 2025
Q6
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
, where
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
. An engineer models a control response line
R
(
x
)
R(x)
that passes through the point
(
1
,
F
(
1
)
)
(1, F(1))
and has a slope of
−
2
-2
. Compute the total response
D
(
x
)
+
R
(
x
)
⋅
F
(
x
)
D(x) + R(x) \cdot F(x)
. Choose the correct option.
Single correct
JULY 13, 2025
JULY 13, 2025
Q7
Consider two polynomials
p
(
x
)
=
x
4
+
3
x
3
−
9
x
+
8
p(x) = x^4 + 3x^3 - 9x + 8
and
q
(
x
)
=
(
x
2
+
x
)
(
x
+
3
)
q(x) = (x^2+x)(x+3)
. Let
r
(
x
)
r(x)
and
s
(
x
)
s(x)
be the remainder and the quotient, respectively, obtained when
p
(
x
)
p(x)
is divided by
q
(
x
)
q(x)
. Let
z
(
x
)
=
r
(
x
)
⋅
s
(
x
)
z(x) = r(x) \cdot s(x)
. Which of the following options is/are true?
Multiple correct
JULY 13, 2025
JULY 13, 2025
Q8
If
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
, then find the value of
a
a
.
Integer answer
FEBRUARY 23, 2025
FEBRUARY 23, 2025
Q9
Consider two polynomials
p
(
x
)
=
x
4
+
3
x
3
−
9
x
+
8
p(x) = x^4 + 3x^3 - 9x + 8
and
q
(
x
)
=
(
x
2
+
x
)
(
x
+
3
)
q(x) = (x^2 + x)(x + 3)
. Let
r
(
x
)
r(x)
be the remainder obtained when
p
(
x
)
p(x)
is divided by
q
(
x
)
q(x)
. Let
l
(
x
)
l(x)
be the straight line passing through the
y
y
-intercept and the minimum point of
r
(
x
)
r(x)
. Which of the following options is/are true?
Multiple correct
FEBRUARY 23, 2025
FEBRUARY 23, 2025
Q10
Which of the following options is/are true?
Comprehension
FEBRUARY 23, 2025
FEBRUARY 23, 2025
Q11
Which of the following options is/are true?
Comprehension
FEBRUARY 23, 2025
FEBRUARY 23, 2025
