wmw9-Graded_Assignment_Sep_2025_Mathematics_I_Qualifier

Graded Assignment - (Sep 2025 - Mathematics I - Qualifier)

The due date for submitting this assignment has passed. Due on 2025-11-26, 23:59 IST. You may submit any number of times before the due date. The final submission will be considered for grading.

Last Submitted: You have last submitted on: 2025-11-26, 20:34 IST

Note: Note: This assignment will be evaluated after the deadline passes. You will get your score 48 hrs after the deadline. Until then the score will be shown as Zero.

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Question 1

Match the functions in Column A with the corresponding (signed) area between its graph and the interval $[-1,1]$ on the X-axis in column B and the images of their graphs and the highlighted region corresponding to the area computed in Column C, given in Table M2W3G1.

• i) $\to$ b) $\to$ 1), iii) $\to$ a) $\to$ 2).
• i) $\to$ b) $\to$ 3), ii) $\to$ c) $\to$ 1).
• ii) $\to$ c) $\to$ 1), iii) $\to$ a) $\to$ 2).
• i) $\to$ b) $\to$ 1), ii) $\to$ c) $\to$ 3), iii) $\to$ a) $\to$ 2).

Accepted Answers:

• i) $\to$ b) $\to$ 3), ii) $\to$ c) $\to$ 1).
• ii) $\to$ c) $\to$ 1), iii) $\to$ a) $\to$ 2).

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Question 2

A cylinder of radius $x$ and height $2h$ is to be inscribed in a sphere of radius $R$ centered at O as shown in Figure M2W3G1

                                      

The volume of such a cylinder is given by $V=2\pi x^{2}h$ and the surface area of the outer curved surface is given by $S=4\pi xh$. Choose the set of correct options.

• The cylinder has maximum volume amongst all cylinders which can be inscribed when $h=R$.
• The cylinder has maximum volume amongst all cylinders which can be inscribed when $h=\sqrt{3}R$.
• The cylinder has maximum volume amongst all cylinders which can be inscribed when $h=\frac{R}{\sqrt{3}}$.
• The cylinder has maximum surface area of its curved surface, amongst all cylinders which can be inscribed, when $h=2R$.
• The cylinder has maximum surface area of its curved surface, amongst all cylinders which can be inscribed, when $h=\frac{R}{\sqrt{2}}$.
• The cylinder has maximum surface area of its curved surface, amongst all cylinders which can be inscribed, when $h=\sqrt{2}$.

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

• The cylinder has maximum volume amongst all cylinders which can be inscribed when $h=\frac{R}{\sqrt{3}}$.
• The cylinder has maximum surface area of its curved surface, amongst all cylinders which can be inscribed, when $h=\frac{R}{\sqrt{2}}$.

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Question 3

Which of the curves in the following figures enclose a negative area on the $X$ axis in the interval $[0,1]$?

• Curve 1
• Curve 2
• Curve 3
• Curve 4

Accepted Answers:

• Curve 2
• Curve 4

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Question 4

What will the absolute difference between the minimum values of $f_2$ and $g_2$ in the interval $[0,1]$ be? Your Answer: 1

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Numeric) 1

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Question 5

Choose the correct options from the following.

• The error in prediction for company A is $\frac{5}{12}$.
• The error in prediction for company A is $\frac{11}{12}$.
• The error in prediction for company A is more than that for company B.
• The error in prediction for company B is more than that for company A.
• The error in prediction for Company A and Company B, cannot be compared using the given information.

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

• The error in prediction for company A is $\frac{5}{12}$.
• The error in prediction for company B is more than that for company A.

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Question 6

Let $f(x)=x^3-3x+25$. What is the local minimum value of $f$ attained at a critical point? Your Answer: 23

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Numeric) 23

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Question 7

Let $f(x)=10x^2+\frac{40}{6}$, $0\le x\le 6$. The estimated area obtained by dividing the interval into 3 sub-intervals of equal length and the left end points of the sub-intervals for height of the rectangles is (in square units) Your Answer: 440

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Numeric) 440

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Question 8

Let
$f(x)=\{\begin{array}{ll}-5x+1& 0\le x\le 10\\ x^2& 10<x\le 20\end{array}$

What is the global minimum of $f$ on $[0,20]$ Your Answer: -49

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Numeric) -49

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Question 9

If $x-y=34$, find the least value of $2xy$. Your Answer: -578

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Numeric) -578

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