IITM BS Question 5 - Week 9 Practice

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IITM BS Question 5 - Week 9 Practice | Prasnya

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Q5Comprehension7 Marks10 May 2026

Passage

Consider the function

f: \mathbb{R}^3 \to \mathbb{R}

defined as

f(x, y, z) = e^{x^2 + y^2 + z^2}

. Based on the above data, answer the given subquestions.

Consider the following statements about the function f. S1: The range of f contains 0. S2: The domain of the gradient is

\mathbb{R}^3

. S3: The directional derivative of f in the direction of v =

(-1, 3, -1)

(0, 0, 0)

is 2. What is the number of correct statements? Write 0 if none of the statements is correct.

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10 May 2026

Mathematics 2 · Week 9

Q5.Consider the following statements about the function f. S1: The range of f contains 0. S2: The domain of the gradient is

\mathbb{R}^3

. S3: The directional derivative of f in the direction of v =

(-1, 3, -1)

(0, 0, 0)

is 2. What is the number of correct statements? Write 0 if none of the statements is correct.@passage

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