Mathematics - Online Test
Q1. Let f (x) = and g (x) = then
Answer : Option B
Explaination / Solution:
No Explaination.
Q2. If A and B are two events such that P(A) = ¼ , P(B) = ½ and , Find P(not A and not B ) .
Answer : Option A
Explaination / Solution:
Since A and B are independent events .
not A and not B are also independent events .
not A and not B are also independent events .
Q3. Given 
then the value of k is
then the value of k is
Answer : Option D
Explaination / Solution:
By final value theorem
Q4.
Suppose that g (x) = 1 + and f ( g (x)) = 3 + 2 + x, then f (x) is
Answer : Option C
Explaination / Solution:
No Explaination.
Q5. If A and B are two events such that A ⊂ B and P(B) ≠ 0, then which of the following is correct?
Answer : Option A
Explaination / Solution:
since A⊂B A⋂B=AP(A/B)=P(A⋂B)P(B)=P(A)P(B)
Q6. A fair coin is tossed 10 times. What is the probability that only the first two tosses will yield heads?
Answer : Option C
Explaination / Solution:
Number of elements in sample space is 210 Only one element "H,H,T,T,T,T,T,T,T,T, is event. Thus probability is 1/210
Q7. If f : [1, [2, ) is given by equals]
Answer : Option C
Explaination / Solution:
No Explaination.
Q8. The probability of obtaining an even prime number on each die , when a pair of dice is rolled, is given by :
Answer : Option A
Explaination / Solution:
Clearly , n(s) =36. Favourable cases are { 2, 2 } Therefore required probability = 1/36 .
Q9. 
Answer : Option C
Explaination / Solution:
We have
Q10. The minimum value of (x -α) (x – β) is
Answer : Option D
Explaination / Solution:
No Explaination.
