Mathematics I 2023 - Objective

i) Number of proper subsets of the set A = {a, b, c, d, e} is

a) 32    b) 31    c) 30    d) 35

ii) Let z be a complex number then \( \frac{z^{2x}}{z} \) is equal to

a) Re(z)    b) Im(z)    c) 2z    d) 2z

iii) Let the function \( f: \mathbb{R} \to \mathbb{R} \) be defined by \( f(x) = 3x + 5 \) then its inverse is

a) x    b) \( \frac{1}{3} \)    c) \( \frac{-5}{3} \)    d) \( \frac{x-5}{3} \)

iv) Sum of the series \( 6, \frac{6}{2}, \frac{6}{4}, ... \) up to infinity is equal to

a) 1    b) 4    c) 6    d) 8

v) The fifth term and eighth term of a G.P. are 20 and 32, then the common ratio is

a) 2    b) 1    c) 1/2    d) 3/2

vi) Length of the vector \( \vec{a} = 3\hat{i} + 4\hat{j} - 5\hat{k} \) is

a) 5    b) 2    c) 5√2    d) 2√5

vii) If A is a matrix of order m × n and matrix B is of order n × p then the order of the product matrix (AB) is

a) m × n    b) n × n    c) n × p    d) m × p

viii) How many different sums of money can be made from 4 coins of different denominations?

a) 20    b) 14    c) 15    d) 16

ix) In how many ways letters of the word COMPUTER is permuted?

a) 40320    b) 40300    c) 43675    d) 45 775

x) Resultant vector of the product of two vectors is

a) along ā    b) along b̄    c) between ā and b̄    d) perpendicular to the plane of ā and b̄