MCQ
Mathematics and Pedagogy MCQ - Practice Questions with Answers
Solve 142 Mathematics and Pedagogy questions for RAS/RPSC preparation.
Practice questions
Q1In an assignment problem, if all cᵢⱼ ≥ 0, then xᵢⱼ = Xᵢⱼ will be an optimal solution where
In a minimization assignment problem with all cᵢⱼ ≥ 0, the objective value cannot be negative. If a feasible assignment X gives ΣᵢΣⱼ cᵢⱼXᵢⱼ = 0, it has attained the least possible objective value. Therefore xᵢⱼ = Xᵢⱼ is optimal, so option D is correct.
Q2A particle is thrown vertically upward with a velocity of 490 cm/s. It will return to this position after –
For vertical projection, the time to return to the same level is T = 2u/g. With u = 490 cm/s and g = 980 cm/s², T = 2 × 490 / 980 = 1 second. Therefore option A is correct.
Q3The equation of plane parallel to x-axis is
A plane parallel to the x-axis must contain a direction parallel to (1, 0, 0). Therefore its normal vector must be perpendicular to the x-axis, so the coefficient of x in the plane equation must be zero. The equation then has the form by + cz + d = 0, which is option C.
Q4If the primal problem has an unbounded solution, then dual has -
By linear-programming duality, if the primal objective is unbounded, the dual cannot have an ordinary finite optimum. In the standard feasible-primal case, the dual is infeasible; among the given choices, option D is the only one that includes the no-solution outcome. Options A, B, and C assert definite forms that do not follow.
Q5The maximum number of normals which can be drawn common to y² = 4ax and x² = 4by is
For y² = 4ax, the normal with parameter t is y = -tx + a(t³ + 2t). For x² = 4by, using parameter s, the normal is y = -x/s + b(s² + 2). A common normal must have the same slope, so s = 1/t; equating intercepts gives a fifth-degree equation in t. Therefore at most 5 common normals are possible, so option D is correct.
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6Given that : x : 1 2 3 4 5 y : 2 5 10 17 26 then μ⁴y₃ is equal to -
7If Aₙ = [1/n, 1] ∀ n ∈ N is a infinite closed set, then ∪∞ₙ₌₁ Aₙ is -
8Which of following approach of sequencing a frame in a programmed instruction employs inductive reasoning?
9If f⃗ = (ax + 3y + 4z)î + (x − 2y + 3z)ĵ +(3x + 2y − z)k̂ is a solenoidal vector, then value of a is -
10The condition that transformation w = (az+b)/(cz+d), transforms the unit circle in the w-plane into straight line in the z-plane is -
11∫₀¹ ∫ₓ^√x (x² + y²) dy dx =
12If a⃗ + b⃗ + c⃗ = 0⃗ and |a⃗| = 3, |b⃗| = 5 and |c⃗| = 7, then the angle between vectors a⃗ and b⃗ is -
13Which mathematician imagined the concept of ‘infinity’ for division of any number by zero?
14The point of concurrency of medians of a triangle is known as
15The line joining centre O of a sphere of radius 3, to the point A (3, 4, 0) meets the polar plane of A in R, then OR equals -