IITM BS Week 3 Mathematics 1 Questions

01

Consider the two quadratic functions

y_1 = x^2 - 4x + 1

and

y_2 = x^2 - 6x - 3

. A quadratic function

f(x) = ax^2 + bx + c

has its vertex at the intersection point of the graphs of

y_1

and

y_2

, its

y

-intercept is

2

, and its axis of symmetry is parallel to the

y

-axis. What is the equation of

f(x)

?

Single correct

MEDIUM

4 marks

10 May 2026

02

Which of the following statements is/are true about the function

f(x) = x^2 + 2x - 8

?

Multiple correct

EASY

3 marks

21 December 2025

03

Consider a quadratic function

q(x) = ax^2 + bx + c

, where

a, b, c \in \mathbb{R}

and

a \neq 0

with the following information: - The minimum value attained by

q(x)

is at

x = -1

. - Discriminant value of

q(x)

is

8

. - Slope of the function at

x = 1

is

8

. Find the value

q(1)

.

Numerical

MEDIUM

4 marks

21 December 2025

04

If

l

is the minimum value of the function

f

, then find the value of

8l

.

Comprehension

MEDIUM

2 marks

13 April 2025

05

How much time (in seconds) will the arrow take to reach the ground?

Comprehension

EASY

3 marks

13 April 2025

06

Which of the following statements is/are true about the function

f(x) = |x^2 + 2x - 8|

?

Multiple correct

MEDIUM

3 marks

01 September 2024

07

If

\alpha

and

\beta

are the

t

-coordinates of the points of intersection of the curves

v(t)

and

s(t)

, then what is the value of

10(\alpha + \beta)

?

Comprehension

MEDIUM

2 marks

01 September 2024

08

An LED manufacturer determines that in order to sell

x

number of LEDs, the price per LED (in thousands) must be

f(x) = 1000 - x

, if

x \le 800

, and the manufacturer also determines that the total cost (in thousands) of producing

x

number of LEDs is

g(x) = \begin{cases} 30000 + 300x, & \text{if } x \le 400 \\ 100x + 110000, & \text{if } 400 < x \le 800 \end{cases}

Although in the above context,

x

can take only integer values, assume that

x

is a continuous variable in the interval

[0, 800]

and that the functions

f(x)

and

g(x)

are defined as above on this entire interval. Let

P(x)

denote the function representing the profit of the company. Choose the set of correct statements.

Multiple correct

HARD

4 marks

24 December 2023

09

Assume that a ball was thrown from the point

(0, 3)

on the

xy

-plane as shown in Figure 1. The ball reaches a maximum height of

5\text{ meters}

and it returns to a height of

3\text{ m}

after

2\text{ seconds}

. Let

h(t) = a t^2 + b t + c

be the quadratic function which represents the height (in meters) of the ball after

t

seconds, where

a, b, c \in \mathbb{Z} \setminus \{0\}

. Find the value of

a + b + c

.

Single correct

EASY

3 marks

11 December 2022

10

Rohit and his friend are playing a number-guessing game. The game consists of one player choosing a number and performing the following operations on it: - Add 4 to the number. - Square the resulting number. - Multiply the result by 3. - Divide the result by 2. and then announcing the finally obtained number. The other player wins if they correctly guess the original number. Rohit's friend chooses a number and announces the result of the above operations as 600. Determine the original number and help Rohit win the game.

Numerical

EASY

2 marks

07 August 2022

All PYQs

All PYQs