Mathematics - Online Test
Q1. A coin tail on both sides is tossed twice. The probability of getting ‘a head’ is
Answer : Option D
Explaination / Solution:
No Explaination.
Q2. A condition for a function y = f (x) to have an inverse is that it should be
Answer : Option B
Explaination / Solution:
No Explaination.
Q3. The chance that an event E ‘occurs’ or does not occur’s
Answer : Option A
Explaination / Solution:
No Explaination.
Q4. Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A to B is
Answer : Option D
Explaination / Solution:
No Explaination.
Q5. Mean number of ‘sixes’ in four throws of a fair dic is
Answer : Option C
Explaination / Solution:
No Explaination.
Q6.
The range of the function is
Answer : Option B
Explaination / Solution:
No Explaination.
Q7. From a deck of 52 cards, the probability of drawing a court card is
Answer : Option B
Explaination / Solution:
No Explaination.
Q8.
On the set Z of all integers define f ; Z Z as follows : f ( x ) = x/2 if x is even , and f ( x ) = 0 if x is odd , then f is
Answer : Option D
Explaination / Solution:
No Explaination.
Q9. Two players toss four coins each. The probability that both obtain the same number of heads is
Answer : Option D
Explaination / Solution:
Let X denote same number of heads Both will get.
So X can take values
X=0 ( both get 0 number of head)
X =1 ( both get 1 head)
X = 2 ( both get 2 heads)
X = 3 ( both get 3 heads)
X = 4 ( both get 4 heads)
So , P(X = 0 ) =Probabilty of getting no heads= 1/16 × 1/16 = 1/256 [by multiplication theorem P(Xi Xj) = P(Xi).P(Xj) ]
P(X=1) = Probabilty of getting 1 head = 4/16 × 4/16 = 16/256
P(X =2) = Probabilty of getting 2 heads = 6/16 × 6/16 = 36/256
P ( X = 3) =Probabilty of getting 3 heads=4/16 × 4/16 = 16/256
P( X= 4) =Probabilty of getting 4 heads = 1/16 × 1/16 = 1/256
Therefore P ( both get same number of head in a throw of 4 coins each )
= P(X=0) + P(X=1) + P(X=2) + P(X =3) + P(X =4)
= 1/256 + 16/256 + 36/256 + 16/256 + 1/256
= 70/256 = 35/128
Q10.
Let f : R R be defined by f (x) = 3x – 4, then (x) is equal to
Answer : Option B
Explaination / Solution:
No Explaination.
