MCQ
Mathematics and Pedagogy MCQ - Practice Questions with Answers
Solve 142 Mathematics and Pedagogy questions for RAS/RPSC preparation.
Practice questions
Q1If r⃗ = (cos nt) a⃗ + (sin nt) b⃗, then dr⃗/dt × r⃗ =
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.
Q2Which one of the following is the first step of Morrison’s Unit Approach?
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.
Q3If v⃗ = 3xz î + 2xy ĵ – yz^2 k̂ then div v⃗ is –
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.
Q4If tanα = m/(m + 1) ; (m ≠ -1) and tanβ = 1/(2m + 1) ; (m ≠ -1/2) then α + β is equal to:
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.
Q5If A and B are square matrices of order 3 such that | A | = –1, | B | = 3 then | 3AB | is equal to –
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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More questions
6If the arcs of the same length in two circles subtend angles of 60° and 75° at their respective centres, then ratio of their radii is
7Out of the following which is not an example of Visual aids –
8Which of the following formula is the Simpson’s 3/8 th rule for numerical integration?
9If \(\frac{a}{x} + \frac{b}{y}\) = m and \(\frac{b}{x} + \frac{a}{y}\) = n, then \(\frac{y}{x}\) is equal to
10If d²y/dx² + sin x = 0, then the solution of this differential equation is -
11Integrating factor of the differential equation (1 - x²) dy/dx - xy = 1 is -
12Two forces P and Q have a resultant R. If P is increased, the new resultant bisects the angle between R and P. Then increase in P is –
13The equation of the plane passing through(2, 3, 4) and parallel to the plane 5x – 6y + 7z = 3 is –
14If u = sec⁻¹(x/y) + cosec⁻¹(y/x), then x ∂u/∂x + y ∂u/∂y is equal to -
15Four forces P, 2P, 3P and 4P are acting along the sides of a square taken in order. The magnitude of their resultant is equal to -