Mathematics - Online Test
Q1. A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.
Answer : Option A
Explaination / Solution:
Q2. Consider the system
where p and q are arbitrary real numbers. Which of the following statements about the controllability of the system is true ?
Answer : Option C
Explaination / Solution:
Since S is singular, system is completely uncontrollable for all values of p and q .
Q3.
If f (x) = for 0 < x <, then
Answer : Option C
Explaination / Solution:
No Explaination.
Q4.
Answer : Option D
Explaination / Solution:
Let are events of selection of a hostlier and a day scholar respectively.
Let A = event of getting grade A.
Let A = event of getting grade A.
Q5. Consider two independent random variables X and Y with identical distributions. The variables X and Y take values 0, 1 and 2 with probabilities 1/2,1/4 and 1/4 respectively. What is the conditional probability P(X + Y = 2 X - Y = 0) ?
Answer : Option C
Explaination / Solution:
We have
Q6. Two functions and g : are defined as follows :
then (gof)(e) + (fog)( ) =
Answer : Option D
Explaination / Solution:
No Explaination.
Q7. In answering a question on a multiple choice test, a student either knows the answer or guesses. Let be the probability that he knows the answer and be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability . What is the probability that the student knows the answer given that he answered it correctly?
Answer : Option B
Explaination / Solution:
Let are events that the student knows the answer and the student guesses respectively.
Q8. The Taylor series expansion of 
is given by
is given by
Answer : Option D
Explaination / Solution:
Q9. Let function f : R R be defined by f (x )= 2x + sin x for x R. Then f is
Answer : Option C
Explaination / Solution:
No Explaination.
Q10. A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?
Answer : Option A
Explaination / Solution:
Let
are events that a person has disease and the person has not disease. .
Let A = event that the test result is positive.
are events that a person has disease and the person has not disease. .
Let A = event that the test result is positive.
