Mathematics - Online Test
Q1. Two events A and B have probabilities 0.25 and 0.50 respectively. The probability that both A and B occur simultaneously is 0.14. Then the probability that neither A nor B occurs is
Answer : Option A
Explaination / Solution:
No Explaination.
Q2. If E denotes expectation, the variance of a random variable X is given by
Answer : Option A
Explaination / Solution:
The variance of a random variable x is given by
E X − E X
Q3. The function f (x) = x + cos x
Answer : Option A
Explaination / Solution:
so,
SO given function is defined for all reals
Q4. India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0, 1 and 2 are 0.45, 0.5 and 0.5 respectively. Assuming that the outcomes are independent, the probability of India getting atleast 7 points is
Answer : Option C
Explaination / Solution:
No Explaination.
Q5. The following plot shows a function which varies linearly with x . The value of
the integral 
is
is
Answer : Option B
Explaination / Solution:
The given plot is straight line whose equation is
Q6. If f then is equal to
Answer : Option B
Explaination / Solution:
this function is defined only if
which is not possible because
so,
Q7. An unbiased dice is rolled four times. The probability that the minimum number on any toss is not less than 3 is
Answer : Option B
Explaination / Solution:
No Explaination.
Q8. For |x| << 1, coth (x) can be approximated as
Answer : Option C
Explaination / Solution:
Q9.
If f (x) = tan x, and g (x) = then domain of the function gof is
Answer : Option C
Explaination / Solution:
which is defined only if
so domain of gof is
Q10. The probability that a man will live for 10 more years is and that his wife will live 10 more years is. The probability that neither will be alive in 10 years is
Answer : Option A
Explaination / Solution:
No Explaination.
