Mathematics - Online Test
Q1. If P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find P(A ∪ B)
Answer : Option A
Explaination / Solution:
Q2. The principal value of
Answer : Option A
Explaination / Solution:
Q3. In case of strict increasing functions, slope of the tangent and hence derivative is
Answer : Option D
Explaination / Solution:
If f is strictly increasing function , then f ‘ (x) can be 0 also . For example , f(x) = x3 is strictly increasing , but its derivative is 0 at x = 0. As another example , take f(x) = x + cosx ; here f ‘(x) = 1 – sinx , which is either +ve or 0 and the function x + cos x is strictly increasing.
Q4.
The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle is
Answer : Option A
Explaination / Solution:
Since the circle passes through (0,0) the equation reduces to
c= 0 -----(1)
Since it passes through (1,0),
1 + 2g + c = 0
This implies g = -1/2
Since the circle touches the circle x2 + y2 = 9, their radii should be equal
2 = 3
Substituting the values and simplifying we get f =
Hence the centre is (1/2, )
Q5.
Let is a prime number . then :
Answer : Option C
Explaination / Solution:
Since when n = 41 we have , which is not a prime number.
Q6. The value of tan - cot is equal to
Answer : Option A
Explaination / Solution:
Q7. Find the shortest distance between the lines
Answer : Option C
Explaination / Solution:
Q8. The number of distinguishable ways in which the 4 faces of a regular tetrahedron can be painted with 4 different colours is
Answer : Option C
Explaination / Solution:
We have a regular tetrahedron has 4 faces and we have to colour it with 4 different colours in ways.
But in this we will be getting many overcountings .
We have there are 12 ways in which we can orient a regular tetrahedron
Hence the number of distinct ways of colouring a regular tetrahedron with 4 different colours is
Q9. The locus of the equation xy + yz = 0 is
Answer : Option D
Explaination / Solution:
No Explaination.
Q10. f A and B are two matrices such that A + B and AB are both defined, then
Answer : Option D
Explaination / Solution:
If A and B are square matrices of same order , both operations A + B and AB are well defined.
