Week 3 Mathematics 1 Questions | Prasnya
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Topic wise questions
Q1
If the product of two consecutive positive integers is
182
182
, find the smaller integer.
Integer answer
MARCH 15, 2026
MARCH 15, 2026
Q2
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,
where
c
∈
R
c \in \mathbb{R}
. Which of the following statements are true?
Multiple correct
MARCH 15, 2026
MARCH 15, 2026
Q3
Consider the two quadratic functions
y
1
=
x
2
−
4
x
+
1
y_1 = x^2 - 4x + 1
and
y
2
=
x
2
−
6
x
−
3
y_2 = x^2 - 6x - 3
. A quadratic function
f
(
x
)
=
a
x
2
+
b
x
+
c
f(x) = ax^2 + bx + c
has its vertex at the intersection point of
y
1
y_1
and
y
2
y_2
, its
y
y
-intercept is 2, and its axis of symmetry is parallel to the
y
y
-axis. What is the equation of
f
(
x
)
f(x)
?
Single correct
OCTOBER 26, 2025
OCTOBER 26, 2025
Q4
Which of the following statements is/are true?
Multiple correct
OCTOBER 26, 2025
OCTOBER 26, 2025
Q5
A quadratic equation of the form
a
x
2
+
b
x
+
c
=
0
ax^2 + bx + c = 0
has its vertex at
(
3
,
−
2
)
(3, -2)
and its
y
y
-intercept at 4. Due to a recording error, the coefficient
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.
Integer answer
OCTOBER 26, 2025
OCTOBER 26, 2025
Q6
The polynomial
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
. Based on this information, calculate the value of
a
a
.
Integer answer
OCTOBER 26, 2025
OCTOBER 26, 2025
Q7
What is the minimum value of
f
(
x
)
f(x)
?
Integer answer
JULY 13, 2025
JULY 13, 2025
Q8
Which of the following graphs can represent
q
(
x
)
q(x)
?
Comprehension
JULY 13, 2025
JULY 13, 2025
Q9
If
x
=
2
x = 2
is a root of
q
(
x
)
q(x)
, then which of the following options can be the expression for
q
(
x
)
q(x)
?
Comprehension
JULY 13, 2025
JULY 13, 2025
Q10
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
and got the roots as 2 and 3. What are the roots of the correct equation?
Single correct
FEBRUARY 23, 2025
FEBRUARY 23, 2025
