Mathematics and Pedagogy MCQ

Question 1

If r⃗ = (cos nt) a⃗ + (sin nt) b⃗, then
dr⃗/dt × r⃗ =

Accepted Answer

Differentiate r⃗ to get dr⃗/dt = -n sin nt a⃗ + n cos nt b⃗. Then (dr⃗/dt) × r⃗ = -n sin²nt(a⃗ × b⃗) + n cos²nt(b⃗ × a⃗). Since b⃗ × a⃗ = -(a⃗ × b⃗), this simplifies to n(b⃗ × a⃗), so option A is correct.

Question 2

Which one of the following is the first step of Morrison’s Unit Approach?

Accepted Answer

Morrison's Unit Approach begins with exploration, where the teacher surveys learners' previous knowledge and introduces the unit problem or field of study. Presentation, assimilation and organisation come after this initial exploratory step. Hence option D is the first step.

Question 3

If v⃗ = 3xz î + 2xy ĵ – yz^2 k̂ then div v⃗ is –

Accepted Answer

For v⃗ = 3xz î + 2xy ĵ - yz² k̂, divergence is ∂(3xz)/∂x + ∂(2xy)/∂y + ∂(-yz²)/∂z. This gives 3z + 2x - 2yz. Hence option D is correct.

Question 4

If tanα = m/(m + 1) ; (m ≠ -1) and tanβ = 1/(2m + 1) ; (m ≠ -1/2) then α + β is equal to:

Accepted Answer

Option A is correct. Using tan(α + β) = (tanα + tanβ)/(1 - tanα tanβ), the numerator and denominator both simplify to the same factor after substituting the given values. Hence tan(α + β) = 1, so α + β = π/4 in the usual principal value.

Question 5

If A and B are square matrices of order 3 such that
| A | = –1, | B | = 3 then | 3AB | is equal to –

Accepted Answer

For a square matrix of order 3, multiplying the whole matrix by 3 multiplies its determinant by 3³. Also, |AB| = |A||B|. Therefore |3AB| = 3³|A||B| = 27×(-1)×3 = -81, so option B is correct.

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