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Week 3 - Graded Assignment 3

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10 min read
Course: Jan 2026 - Mathematics I
Topic: Real Roots and Intersection (Discriminant) | Marks: 3

Question 1

Find out the points where the curve y=4x2+xy = 4x^2+x and the straight line y=2x−3y = 2x-3 intersect with each other.
  • (32,0)(\frac{3}{2},0) and (32,212)(\frac{3}{2},\frac{21}{2}).
  • Only at the origin.
  • The curve and the straight line do not intersect.
  • (1,−1)(1, -1) and (1,5)(1, 5).
MCQ
3 Unit Assessment
Topic: Consecutive Number Theory (Quadratic Modeling) | Marks: 3

Question 2

Let aa and bb two consecutive positive odd natural numbers such that a2+b2=394a^2+b^2=394. Then find the value of a+ba+b.
MCQ
3 Unit Assessment
Topic: Axis of Symmetry and Vertex Form | Marks: 3

Question 3

The maximum value of a quadratic function ff is −3-3, its axis of symmetry is x=2x=2 and the value of the quadratic function at x=0x=0 is −9-9. What will be the coefficient of x2x^2 in the expression of ff?
  • −1-1
  • 1
  • −1.5-1.5
  • −0.5-0.5
MCQ
3 Unit Assessment
Topic: Parabolic Motion (Vertex and Symmetry) | Marks: 4

Question 4

A ball is thrown from 33 m off the ground and reaches a maximum height of 55 m. Assume that the ball was released from the point (0,3)(0,3) in the xyxy-plane as shown in the Figure M1W3GA-3. The ball returns to a height of 33 m after 22 seconds. Let h(t)=at2+bt+ch(t)=at^2+bt+c be the quadratic function which represents the height of the ball after tt seconds. What is the value of aa ?
Markdown Image
MCQ
3 Unit Assessment
Topic: Economic Modeling (Minimization and Slope) | Marks: 4

Question 5

The daily production cost (in lakh ₹) of manufacturing an electric device is p(x)=7400−60x+15x2p(x) = 7400-60x+15x^2, where xx is the number of electric devices produced per day and the daily transportation cost (in lakh ₹) of xx number of electric devices is given by the slope of the function p(x)p(x) at point xx. If the transportation cost of the electric devices on a particular day is 30 (in lakh ₹), then find the number of transported electric devices.
MCQ
3 Unit Assessment
Topic: Arch Modeling (Parabola with Axis Symmetry) | Marks: 4

Question 6

An Architect is designing an arch which is in the shape of figure M1W3-PARABOLA,
 The details of the design are as follows:
 Height of arch is 20m, width of arch at height of 8m is 4m.
 Consider the axis of symmetry as x=0x=0, find the equation of the arch.
   
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                                                   fig:M1W3-PARABOLA
  • y=−3x2+20y = -3x^2 +20
  • y=−34x2+20y = \frac{-3}{4} x^2 +20
  • y=−x2+x+20y = -x^2+x+20
  • y=−2x2−2x+20y = -2x^2-2x+20
MCQ
3 Unit Assessment
Topic: Quadratic Maximization (Fountain Path) | Marks: 3

Question 7

A water fountain is designed to shoot a stream of water in the shape of a parabolic arc. The equation of the parabola is given by h(t)=−0.5t2+4t+1h(t) = -0.5t^2 + 4t + 1, where h(t)h(t) represents the height of the water stream in meters and t  represents the time in seconds since the water was shot.
Determine the maximum height reached (in meters).
MCQ
3 Unit Assessment
Topic: Quadratic Properties and Definitions | Marks: 2

Question 8

Which of the following is/are correct
  • xx intercepts of the quadratic function f(x)f(x) are known as the real roots of the quadratic equation f(x)=0f(x)=0.
  • If discriminant for two quadratic equations are same then they must be the same quadratic equations.
  • The slope at the vertex of the quadratic function is zero.
  • Every Quadratic function has axis of symmetry.
  • Suppose P(x)P(x) is a Quadratic function and L be any straight line, then L must intersect the graph of P(x)P(x).
MCQ
3 Unit Assessment
Topic: Variation in Speed and Time (PIE/Quadratic) | Marks: 5

Question 9

Consider three Airports A, B, and C. Two friends Ananya and Madhuri want to meet at Airport C. Ananya Boarded Flight 1 from Point A to C which is 1200 km, due to bad weather, Flight 1 slowed down, and the average speed was reduced by 200 km/h and the time increased by 30 minutes. Madhuri boarded Flight 2 from Point B to C which is 1800 km, the average speed of Flight 2 is 720 km/h. What is the waiting time, and who will be waiting at the airport? (Given Ananya and Madhuri boarded at the same time)
  • Waiting Time is 1 hr and Ananya is waiting.
  • Waiting Time is 1 hr and Madhuri is waiting.
  • Waiting Time is 30 min and Ananya is waiting.
  • Waiting Time is 30 min and Madhuri is waiting.
MCQ
3 Unit Assessment
Topic: Slope and Tangency at a Point | Marks: 3

Question 10

Which of the following options is/are true?
  • The point at which the slope of the equation x2+2x−5x^2 +2x-5 equals 10 is (4,17)
  • x=2x=2 is the axis of symmetry of the quadratic function f(x)=x2+4x+5f(x)= x^2+4x+5
  • If two different quadratic equations have the same discriminant then the roots of both equations can be the same.
  • The point at which the slope of the equation x2+2x−5x^2 +2x-5 equals 10 is (4,19)
MCQ
3 Unit Assessment
Topic: Calculating Model Parameters from Slope | Marks: 3

Question 11

If the slope of parabola y=Ax2+Bx+Cy=Ax^2 + Bx+ C, where A,B,C∈RA, B, C \in \mathbb{R} at points (3, 2) and (2, 3) are 16 and 12 respectively.
Calculate the value of AA.
Your Answer: 2
Status: Yes, the answer is correct.
Accepted Answers:
(Type: Numeric) 2
Topic: Root Restoration (Leading Coefficient 1) | Marks: 3

Question 12

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 and 4. Shyam made a mistake in writing down the coefficient of xx and got the roots as 2 and 3. Consider the leading coefficient to be 1 in all cases. The correct roots of the quadratic equation are:
  • 1 and 5
  • 2 and 6
  • 1 and 6
  • 2 and 5
Status: Yes, the answer is correct.
Accepted Answers:
1 and 6

Question 13

Consider a quadratic function q(x)=ax2+20x+15q(x) = ax^2+ 20x+ 15, where a∈R∖{0}a \in \mathbb{R}\setminus\{0\}. If the slope of q(x)q(x) at x=2x=2 is equal to the slope of the line y=40x+5y=40x+5.
Then which of the following options is true?
  • a=5a= 5
  • a=8a= 8
  • q(x)q(x) has a unique root.
  • q(x)q(x) has the minimum value at x=2x=2.
Status: Yes, the answer is correct.
Accepted Answers:
a=5a= 5

Question 14

Find out the maximum height(in meters) attained by the missile.
Your Answer: 72
Status: Yes, the answer is correct.
Accepted Answers:
(Type: Numeric) 72

Question 15

Find out the time (in seconds) when the missile hits the tank.
Your Answer: 5
Status: Yes, the answer is correct.
Accepted Answers:
(Type: Numeric) 5

Question 16

Suppose an air defense system is present at the origin, and it follows the straight line path h(t)=10th(t) = 10t, find the height from the ground at which the air defense missile will destroy the ballistic missile in the air.
  • 40 m
  • 12.5 m
  • 4 m
  • 1.25 m
Status: Yes, the answer is correct.
Accepted Answers:
40 m

Question 17

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)2−9q(x) = − (x − 7)^2 − 9. Calculate the value of aa.
Your Answer: -1
Status: Yes, the answer is correct.
Accepted Answers:
(Type: Numeric) -1

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