Mathematics HSC Important Questions

Practice questions from 33-40, the final set of questions in this series is provided below. Go through these samples and practice them well. Post your answers (working solution) to help others learn..

33) Which of the following is not a binary operation on R:

a) $ a*b = ab $

b) $ a*b = a-b $

c) $ a*b = \sqrt{ab} $

d) $ a*b = \sqrt{a^2+b^2} $



34) The order of [7] in $ (Z_{9}, \; +9) $ is:

a) 9

b) 6

c) 3

d) 1



35) If p is true and q is unknown, then

a) $ p\vee q $ is true

b) $ p\vee (~p) $ is false

c) $ p \wedge (~p) $ is true

d) ~p is true



36) In the set of integers under the operation * defined by a*b = a+b-1, the identity element is:

a) 0

b) 1

c) a

d) b



37) A continuous random variable x and the p.d.f defined by $ f(x)=\left \{ ce^{-ax} 0<x<\infty , 0 \;elsewhere \right. $ then the value of c is:

a) 1

b) a

c) $ \frac{1}{a} $

d) –a



38) If the mean and s.d. of a binomial distribution are 12 and 2 respectively, then the value of its parameter p is:

a) $ \frac{1}{2} $

b) $ \frac{1}{3} $

c) $ \frac{2}{3} $

d) $ \frac{1}{4} $



39) Given $ \mu_{2}=20 $, $ \mu^1_{2}=276 $ for a discrete random variable x. then the mean of the random variable x is:

a) 16

b) 5

c) 2

d) 1



40) If in a Poisson distribution P(x=0) = K, then the variance is:

a) $ log\frac{1}{K} $

b) $ log K $

c) $ e^\lambda $^

d) $ \frac{1}{K} $

For previous set of questions refer to the related post section below.