MCQ
Mathematics and Pedagogy MCQ - Practice Questions with Answers
Solve 141 Mathematics and Pedagogy questions for RAS/RPSC preparation.
Practice questions
Q1If z = tan^-1 y/x then the value of ∂²z/∂x² + ∂²z/∂y² is equal to –
The function z = tan⁻¹(y/x) is the polar angle function, and it is harmonic away from the origin. Direct differentiation gives zxx = 2xy/(x² + y²)² and zyy = -2xy/(x² + y²)². Their sum is 0, so option D is correct.
Q2Which of the following is a null set?
Option A is empty because no natural number has absolute value less than 1 when natural numbers start from 1. In contrast, option B contains 5, option C has the real solution -1, and option D contains the integers 1 and -1. Hence A is the null set.
Q3A triangle with vertices (4, 0), (- 1, - 1) and (3, 5) is :
Using the distance formula, the squared side lengths are 26, 26 and 52. Two sides are equal, and 26 + 26 = 52, so the triangle also satisfies Pythagoras' theorem. Therefore it is an isosceles right-angled triangle, making option A correct.
Q4If Matrix A = [ x - 1 2 2 3 x - 1 2 3 3 x - 1 ], then the number of real values of x satisfying the equation d/dx |A| = 0, is
Put a = x - 1. The determinant of the matrix is a^3 - 18a + 30. Since da/dx = 1, d|A|/dx = 3a^2 - 18, and setting it equal to zero gives a = ±√6. Thus there are two real values of x, so option C is correct.
Q5If all the elements of a 3 × 3 matrix P are 1, then P² - 3P is
Let P be the 3 x 3 matrix whose every entry is 1. In P^2, each entry is the sum of three ones, so every entry is 3; hence P^2 = 3P. Therefore P^2 - 3P is the null matrix, so option A is correct.
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More questions
6Let G = {a, a², a³, a⁴ = e}, where ‘e’ is the identity element, be a cyclic group generated by a. H = {a², a⁴ = e} and G itself are its two subgroups, then order of element (a², a) of H×G is -
7The mean and the variance of a binomial distribution are 4 and 2 respectively, then the probability of 2 successes is -
8One of the asymptote of curve x³ + 3x²y − 4y³ − x + y + 3 = 0 is
9Which of the following point/element cannot be the reason to decide the giftedness of a child in Mathematics?
10The number of ordered pairs of integers (x, y) satisfying the equation x^2 + 6x + y^2 = 4 is
11Out of the following which maxims of Teaching is comparatively less appropriate while using Audio – Visual Aids in Teaching of Mathematics –
12When teachers of Science, Economics, Philosophy, Geography etc. uses concepts of Mathematics in their respective teaching at that time correlation of each subject with Mathematics is known as
13The general solution of the differential equation d²y/dx² + (3i - 1) dy/dx - 3iy = 0 is
14Number of distinct chords of the circle x^2 + y^2 - √2x - 1/2 y = 0, passes through the point (√2, 1/2) and bisected by x-axis, is
15Match list – I with list – II and select the correct answer – List – I A. A square matrix such that A² = A B. A square matrix such that Aᵐ = 0 C. A square matrix such that A² = I D. A square matrix such that Aᵀ = A List – II 1. Nilpotent matrix 2. Involutory matrix 3. Symmetric matrix 4. Idempotent matrix