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Week 3 Mathematics 1 Questions | Prasnya
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Type:
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Difficulty:
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Year:
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29Q
01
If the product of two consecutive positive integers is
182
182
182
, find the smaller integer.
Numerical
EASY
4 marks
15 March 2026
02
Consider the two quadratic functions
f
(
x
)
=
x
2
−
4
x
+
c
,
g
(
x
)
=
−
x
2
+
3
x
+
c
,
f(x)=x^2-4x+c, \qquad g(x)=-x^2+3x+c,
f
(
x
)
=
x
2
−
4
x
+
c
,
g
(
x
)
=
−
x
2
+
3
x
+
c
,
where
c
∈
R
c \in \mathbb{R}
c
∈
R
. Which of the following statements are true?
Multiple correct
MEDIUM
5 marks
15 March 2026
03
Consider the two quadratic functions
y
1
=
x
2
−
4
x
+
1
y_1 = x^2 - 4x + 1
y
1
=
x
2
−
4
x
+
1
and
y
2
=
x
2
−
6
x
−
3
y_2 = x^2 - 6x - 3
y
2
=
x
2
−
6
x
−
3
. A quadratic function
f
(
x
)
=
a
x
2
+
b
x
+
c
f(x) = ax^2 + bx + c
f
(
x
)
=
a
x
2
+
b
x
+
c
has its vertex at the intersection point of
y
1
y_1
y
1
and
y
2
y_2
y
2
, its
y
y
y
-intercept is 2, and its axis of symmetry is parallel to the
y
y
y
-axis. What is the equation of
f
(
x
)
f(x)
f
(
x
)
?
Single correct
MEDIUM
4 marks
26 October 2025
04
Which of the following statements is/are true?
Multiple correct
MEDIUM
4 marks
26 October 2025
05
A quadratic equation of the form
a
x
2
+
b
x
+
c
=
0
ax^2 + bx + c = 0
a
x
2
+
b
x
+
c
=
0
has its vertex at
(
3
,
−
2
)
(3, -2)
(
3
,
−
2
)
and its
y
y
y
-intercept at 4. Due to a recording error, the coefficient
b
b
b
was written as 5 instead of its correct value. Find the absolute difference between the sum of the roots of the incorrectly recorded quadratic equation and that of the correct quadratic equation.
Numerical
HARD
4 marks
26 October 2025
06
The polynomial
p
(
x
)
=
a
(
x
−
4
)
(
x
−
6
)
(
x
−
8
)
(
x
−
10
)
p(x) = a(x-4)(x-6)(x-8)(x-10)
p
(
x
)
=
a
(
x
−
4
)
(
x
−
6
)
(
x
−
8
)
(
x
−
10
)
passes through the vertex of the quadratic function
q
(
x
)
=
−
(
x
−
7
)
2
−
9
q(x) = -(x-7)^2 - 9
q
(
x
)
=
−
(
x
−
7
)
2
−
9
. Based on this information, calculate the value of
a
a
a
.
Numerical
MEDIUM
5 marks
26 October 2025
07
What is the minimum value of
f
(
x
)
f(x)
f
(
x
)
?
Comprehension
MEDIUM
3 marks
13 July 2025
08
Which of the following graphs can represent
q
(
x
)
q(x)
q
(
x
)
?
Comprehension
EASY
4 marks
13 July 2025
09
If
x
=
2
x = 2
x
=
2
is a root of
q
(
x
)
q(x)
q
(
x
)
, then which of the following options can be the expression for
q
(
x
)
q(x)
q
(
x
)
?
Comprehension
MEDIUM
4 marks
13 July 2025
10
Aman and Prakash want to solve a quadratic equation. Aman made a mistake in writing down the constant term and ended up getting roots as 3 and 4. Prakash made a mistake in writing down the coefficient of
x
x
x
and got the roots as 2 and 3. What are the roots of the correct equation?
Single correct
MEDIUM
4 marks
23 February 2025
11
If
α
\alpha
α
and
β
\beta
β
are the roots of the equation
x
2
+
4
x
+
1
=
0
x^2+4x+1=0
x
2
+
4
x
+
1
=
0
, then the equation whose roots are
α
2
\alpha^2
α
2
and
β
2
\beta^2
β
2
is:
Single correct
MEDIUM
5 marks
24 October 2024
12
Consider the parabola
y
=
x
2
+
4
x
+
12
y=x^2+4x+12
y
=
x
2
+
4
x
+
12
. Which of the following option(s) are true?
Multiple correct
EASY
4 marks
07 July 2024
13
Consider the quadratic equation
a
x
2
+
b
x
+
c
=
0
ax^2+bx+c=0
a
x
2
+
b
x
+
c
=
0
where
a
,
b
,
c
a,b,c
a
,
b
,
c
are integers with
a
≠
0
a\ne 0
a
=
0
. Which of the following option(s) are true?
Single correct
EASY
4 marks
07 July 2024
14
Which of the following options is/are true?
Multiple correct
MEDIUM
4 marks
25 February 2024
15
Calculate the value of
A
A
A
Comprehension
MEDIUM
2.5 marks
25 February 2024
16
Calculate the value of
B
B
B
Comprehension
EASY
2.5 marks
25 February 2024
17
Ram and Shyam want to solve a quadratic equation. Ram made a mistake in writing down the constant term and ended up in getting roots as
3
3
3
and
4
4
4
. Shyam made a mistake in writing down the coefficient of
x
x
x
and got the roots as
2
2
2
and
3
3
3
. Consider the leading coefficient to be
1
1
1
in all cases. The correct roots of the quadratic equation are:
Single correct
MEDIUM
4 marks
25 February 2024
18
Consider a quadratic function
q
(
x
)
=
a
x
2
+
b
x
+
c
q(x)=ax^2+bx+c
q
(
x
)
=
a
x
2
+
b
x
+
c
, where
a
,
b
,
c
∈
R
a,b,c\in\mathbb{R}
a
,
b
,
c
∈
R
and
a
≠
0
a\neq0
a
=
0
with the following information: • The maximum value attained by
q
(
x
)
q(x)
q
(
x
)
is at
x
=
−
1
x=-1
x
=
−
1
. • Discriminant value of
q
(
x
)
q(x)
q
(
x
)
is
8
8
8
. • Slope of the function at
x
=
1
x=1
x
=
1
is
8
8
8
. Find the value
q
(
2
)
q(2)
q
(
2
)
.
Numerical
HARD
3 marks
16 July 2023
19
Find the quantity of the raw material such that the company has the maximum profit.
Comprehension
EASY
2 marks
16 July 2023
20
Find the quantity of the raw material
(
x
>
1
)
(x>1)
(
x
>
1
)
such that the company has no profit.
Comprehension
EASY
2 marks
16 July 2023
21
Enter the value of
a
+
b
+
c
a+b+c
a
+
b
+
c
. NOTE: Enter your answer to the nearest integer.
Comprehension
MEDIUM
2 marks
16 October 2022
22
Enter the value of
d
d
d
. NOTE: Enter your answer to the nearest integer.
Comprehension
MEDIUM
2 marks
16 October 2022
23
Choose the set of correct option(s).
Comprehension
MEDIUM
3 marks
16 October 2022
24
Enter the
x
x
x
-coordinate of the vertex of
q
(
x
)
q(x)
q
(
x
)
. NOTE: Enter your answer to the nearest integer.
Comprehension
EASY
1 marks
05 June 2022
25
Enter the
y
y
y
-coordinate of the vertex of
q
(
x
)
q(x)
q
(
x
)
. NOTE: Enter your answer to the nearest integer.
Comprehension
EASY
1 marks
05 June 2022
26
Sonia and Henna want to solve a quadratic equation. Sonia made a mistake in writing down the constant term and ended up in roots
3
3
3
and
4
4
4
. Henna made a mistake in writing down the coefficient of
x
x
x
and got the roots
2
2
2
and
3
3
3
. Consider the leading coefficient to be
1
1
1
in all cases. The correct roots of the equation are:
Multiple correct
MEDIUM
4 marks
05 June 2022
27
NOTE: Enter your answer to the nearest integer. Consider two quadratic functions,
p
(
x
)
p(x)
p
(
x
)
and
q
(
x
)
q(x)
q
(
x
)
, whose roots are shown in Figure 1. The leading coefficients of
p
(
x
)
p(x)
p
(
x
)
and
q
(
x
)
q(x)
q
(
x
)
are
+
1
+1
+
1
and
−
1
-1
−
1
, respectively. The
y
y
y
-coordinate of the vertex of
p
(
x
)
p(x)
p
(
x
)
is
c
c
c
and the
y
y
y
-coordinate of the vertex of
q
(
x
)
q(x)
q
(
x
)
is
−
c
-c
−
c
. Find the value of
d
d
d
(See Figure 1). Pic required
Numerical
MEDIUM
4 marks
05 June 2022
28
The value of a quadratic function
f
(
x
)
f(x)
f
(
x
)
increases over the interval
(
−
∞
,
−
5
)
(-\infty,-5)
(
−
∞
,
−
5
)
and decreases over the interval
(
−
5
,
∞
)
(-5,\infty)
(
−
5
,
∞
)
. Also,
f
(
0
)
=
f
(
−
10
)
=
20
f(0)=f(-10)=20
f
(
0
)
=
f
(
−
10
)
=
20
. Which of the following statements about
f
(
x
)
f(x)
f
(
x
)
can be true?
Multiple correct
MEDIUM
4 marks
10 July 2022
29
NOTE: Enter your answer to the nearest integer. Consider two quadratic polynomials
p
(
x
)
p(x)
p
(
x
)
and
q
(
x
)
q(x)
q
(
x
)
whose roots are shown in the figure. The leading coefficient of
p
(
x
)
p(x)
p
(
x
)
and
q
(
x
)
q(x)
q
(
x
)
is
+
1
+1
+
1
and the
y
y
y
-coordinate of the vertex point of
p
(
x
)
p(x)
p
(
x
)
is equal to the
y
y
y
-coordinate of the vertex point of
q
(
x
)
q(x)
q
(
x
)
. Find the value of
d
d
d
.
Numerical
MEDIUM
4 marks
10 July 2022
Showing 29 questions.
Mathematics 1 > Week 3
All PYQs
Topic-Wise PYQs
Start Weekly Test
Mock tests
Week mock
Topic mock
Subject mock
Type:
All
Difficulty:
All
Year:
All
29Q
01
If the product of two consecutive positive integers is
182
182
182
, find the smaller integer.
Numerical
EASY
4 marks
15 March 2026
02
Consider the two quadratic functions
f
(
x
)
=
x
2
−
4
x
+
c
,
g
(
x
)
=
−
x
2
+
3
x
+
c
,
f(x)=x^2-4x+c, \qquad g(x)=-x^2+3x+c,
f
(
x
)
=
x
2
−
4
x
+
c
,
g
(
x
)
=
−
x
2
+
3
x
+
c
,
where
c
∈
R
c \in \mathbb{R}
c
∈
R
. Which of the following statements are true?
Multiple correct
MEDIUM
5 marks
15 March 2026
03
Consider the two quadratic functions
y
1
=
x
2
−
4
x
+
1
y_1 = x^2 - 4x + 1
y
1
=
x
2
−
4
x
+
1
and
y
2
=
x
2
−
6
x
−
3
y_2 = x^2 - 6x - 3
y
2
=
x
2
−
6
x
−
3
. A quadratic function
f
(
x
)
=
a
x
2
+
b
x
+
c
f(x) = ax^2 + bx + c
f
(
x
)
=
a
x
2
+
b
x
+
c
has its vertex at the intersection point of
y
1
y_1
y
1
and
y
2
y_2
y
2
, its
y
y
y
-intercept is 2, and its axis of symmetry is parallel to the
y
y
y
-axis. What is the equation of
f
(
x
)
f(x)
f
(
x
)
?
Single correct
MEDIUM
4 marks
26 October 2025
04
Which of the following statements is/are true?
Multiple correct
MEDIUM
4 marks
26 October 2025
05
A quadratic equation of the form
a
x
2
+
b
x
+
c
=
0
ax^2 + bx + c = 0
a
x
2
+
b
x
+
c
=
0
has its vertex at
(
3
,
−
2
)
(3, -2)
(
3
,
−
2
)
and its
y
y
y
-intercept at 4. Due to a recording error, the coefficient
b
b
b
was written as 5 instead of its correct value. Find the absolute difference between the sum of the roots of the incorrectly recorded quadratic equation and that of the correct quadratic equation.
Numerical
HARD
4 marks
26 October 2025
06
The polynomial
p
(
x
)
=
a
(
x
−
4
)
(
x
−
6
)
(
x
−
8
)
(
x
−
10
)
p(x) = a(x-4)(x-6)(x-8)(x-10)
p
(
x
)
=
a
(
x
−
4
)
(
x
−
6
)
(
x
−
8
)
(
x
−
10
)
passes through the vertex of the quadratic function
q
(
x
)
=
−
(
x
−
7
)
2
−
9
q(x) = -(x-7)^2 - 9
q
(
x
)
=
−
(
x
−
7
)
2
−
9
. Based on this information, calculate the value of
a
a
a
.
Numerical
MEDIUM
5 marks
26 October 2025
07
What is the minimum value of
f
(
x
)
f(x)
f
(
x
)
?
Comprehension
MEDIUM
3 marks
13 July 2025
08
Which of the following graphs can represent
q
(
x
)
q(x)
q
(
x
)
?
Comprehension
EASY
4 marks
13 July 2025
09
If
x
=
2
x = 2
x
=
2
is a root of
q
(
x
)
q(x)
q
(
x
)
, then which of the following options can be the expression for
q
(
x
)
q(x)
q
(
x
)
?
Comprehension
MEDIUM
4 marks
13 July 2025
10
Aman and Prakash want to solve a quadratic equation. Aman made a mistake in writing down the constant term and ended up getting roots as 3 and 4. Prakash made a mistake in writing down the coefficient of
x
x
x
and got the roots as 2 and 3. What are the roots of the correct equation?
Single correct
MEDIUM
4 marks
23 February 2025
11
If
α
\alpha
α
and
β
\beta
β
are the roots of the equation
x
2
+
4
x
+
1
=
0
x^2+4x+1=0
x
2
+
4
x
+
1
=
0
, then the equation whose roots are
α
2
\alpha^2
α
2
and
β
2
\beta^2
β
2
is:
Single correct
MEDIUM
5 marks
24 October 2024
12
Consider the parabola
y
=
x
2
+
4
x
+
12
y=x^2+4x+12
y
=
x
2
+
4
x
+
12
. Which of the following option(s) are true?
Multiple correct
EASY
4 marks
07 July 2024
13
Consider the quadratic equation
a
x
2
+
b
x
+
c
=
0
ax^2+bx+c=0
a
x
2
+
b
x
+
c
=
0
where
a
,
b
,
c
a,b,c
a
,
b
,
c
are integers with
a
≠
0
a\ne 0
a
=
0
. Which of the following option(s) are true?
Single correct
EASY
4 marks
07 July 2024
14
Which of the following options is/are true?
Multiple correct
MEDIUM
4 marks
25 February 2024
15
Calculate the value of
A
A
A
Comprehension
MEDIUM
2.5 marks
25 February 2024
16
Calculate the value of
B
B
B
Comprehension
EASY
2.5 marks
25 February 2024
17
Ram and Shyam want to solve a quadratic equation. Ram made a mistake in writing down the constant term and ended up in getting roots as
3
3
3
and
4
4
4
. Shyam made a mistake in writing down the coefficient of
x
x
x
and got the roots as
2
2
2
and
3
3
3
. Consider the leading coefficient to be
1
1
1
in all cases. The correct roots of the quadratic equation are:
Single correct
MEDIUM
4 marks
25 February 2024
18
Consider a quadratic function
q
(
x
)
=
a
x
2
+
b
x
+
c
q(x)=ax^2+bx+c
q
(
x
)
=
a
x
2
+
b
x
+
c
, where
a
,
b
,
c
∈
R
a,b,c\in\mathbb{R}
a
,
b
,
c
∈
R
and
a
≠
0
a\neq0
a
=
0
with the following information: • The maximum value attained by
q
(
x
)
q(x)
q
(
x
)
is at
x
=
−
1
x=-1
x
=
−
1
. • Discriminant value of
q
(
x
)
q(x)
q
(
x
)
is
8
8
8
. • Slope of the function at
x
=
1
x=1
x
=
1
is
8
8
8
. Find the value
q
(
2
)
q(2)
q
(
2
)
.
Numerical
HARD
3 marks
16 July 2023
19
Find the quantity of the raw material such that the company has the maximum profit.
Comprehension
EASY
2 marks
16 July 2023
20
Find the quantity of the raw material
(
x
>
1
)
(x>1)
(
x
>
1
)
such that the company has no profit.
Comprehension
EASY
2 marks
16 July 2023
21
Enter the value of
a
+
b
+
c
a+b+c
a
+
b
+
c
. NOTE: Enter your answer to the nearest integer.
Comprehension
MEDIUM
2 marks
16 October 2022
22
Enter the value of
d
d
d
. NOTE: Enter your answer to the nearest integer.
Comprehension
MEDIUM
2 marks
16 October 2022
23
Choose the set of correct option(s).
Comprehension
MEDIUM
3 marks
16 October 2022
24
Enter the
x
x
x
-coordinate of the vertex of
q
(
x
)
q(x)
q
(
x
)
. NOTE: Enter your answer to the nearest integer.
Comprehension
EASY
1 marks
05 June 2022
25
Enter the
y
y
y
-coordinate of the vertex of
q
(
x
)
q(x)
q
(
x
)
. NOTE: Enter your answer to the nearest integer.
Comprehension
EASY
1 marks
05 June 2022
26
Sonia and Henna want to solve a quadratic equation. Sonia made a mistake in writing down the constant term and ended up in roots
3
3
3
and
4
4
4
. Henna made a mistake in writing down the coefficient of
x
x
x
and got the roots
2
2
2
and
3
3
3
. Consider the leading coefficient to be
1
1
1
in all cases. The correct roots of the equation are:
Multiple correct
MEDIUM
4 marks
05 June 2022
27
NOTE: Enter your answer to the nearest integer. Consider two quadratic functions,
p
(
x
)
p(x)
p
(
x
)
and
q
(
x
)
q(x)
q
(
x
)
, whose roots are shown in Figure 1. The leading coefficients of
p
(
x
)
p(x)
p
(
x
)
and
q
(
x
)
q(x)
q
(
x
)
are
+
1
+1
+
1
and
−
1
-1
−
1
, respectively. The
y
y
y
-coordinate of the vertex of
p
(
x
)
p(x)
p
(
x
)
is
c
c
c
and the
y
y
y
-coordinate of the vertex of
q
(
x
)
q(x)
q
(
x
)
is
−
c
-c
−
c
. Find the value of
d
d
d
(See Figure 1). Pic required
Numerical
MEDIUM
4 marks
05 June 2022
28
The value of a quadratic function
f
(
x
)
f(x)
f
(
x
)
increases over the interval
(
−
∞
,
−
5
)
(-\infty,-5)
(
−
∞
,
−
5
)
and decreases over the interval
(
−
5
,
∞
)
(-5,\infty)
(
−
5
,
∞
)
. Also,
f
(
0
)
=
f
(
−
10
)
=
20
f(0)=f(-10)=20
f
(
0
)
=
f
(
−
10
)
=
20
. Which of the following statements about
f
(
x
)
f(x)
f
(
x
)
can be true?
Multiple correct
MEDIUM
4 marks
10 July 2022
29
NOTE: Enter your answer to the nearest integer. Consider two quadratic polynomials
p
(
x
)
p(x)
p
(
x
)
and
q
(
x
)
q(x)
q
(
x
)
whose roots are shown in the figure. The leading coefficient of
p
(
x
)
p(x)
p
(
x
)
and
q
(
x
)
q(x)
q
(
x
)
is
+
1
+1
+
1
and the
y
y
y
-coordinate of the vertex point of
p
(
x
)
p(x)
p
(
x
)
is equal to the
y
y
y
-coordinate of the vertex point of
q
(
x
)
q(x)
q
(
x
)
. Find the value of
d
d
d
.
Numerical
MEDIUM
4 marks
10 July 2022
Showing 29 questions.
