Mathematics - Online Test
Q1. If A is a finite set containing n distinct elements, then the number of relations on A is equal to
Answer : Option D
Explaination / Solution:
The number of elements in A x A is n x n = n2. hence ,the number of relations on A = number of subsets of A x A = 2nxn =.
Q2. The equation of the line which passes through the point ( 1 , - 2 ) and cuts off equal intercepts from the axis is
Answer : Option B
Explaination / Solution:
Let the equation of the line which has equal intercepts be
+ =1
Substituting the values for x and y
1 -2 =a
Therefore a = -1
Hence the equation of the line is x+y+1=0
Q3. The logically equivalent propositions of p↔q is
Answer : Option C
Explaination / Solution:
p↔q≡(p→q)∧(q→p)
Q4. The value of the integral dx lies in
Answer : Option B
Explaination / Solution:
Q5. Vectors A and B are equal
Answer : Option B
Explaination / Solution:
Two vectors having same magnitude as well as same direction are always equal.
Q6.
Let ( be a partition of a sample space and suppose that each of has nonzero probability. Let A be any event associated with S,then
Answer : Option A
Explaination / Solution:
Let {E1, E2, ...,En) be a partition of a sample space and suppose that each of E1, E2, ..., En has nonzero probability. Let A be any event associated with S,then P(A) = P(E1) P (A|E1) + P (E2) P (A|E2) + ... + P (En) P(A|En) .by addition law of probability.
Q7. If is equal to
Answer : Option A
Explaination / Solution:
Q8. is divisible by 64 for all
Answer : Option A
Explaination / Solution:
when n = 1 the value is 64. By induction process the consecutive replacement of n = 2,3,4....will be multiples of 64.
Q9.
is equal to
Answer : Option B
Explaination / Solution:
limx→0tanxlog(1+x)=limx→0tanxxxlog(1+x)=limx→0tanxx.limx→011xlog(1+x)=1.11=1
Q10. The equation represents a circle only if
Answer : Option D
Explaination / Solution:
recalling the general form of a circle as
(i) It is a quadratic equation in both x and y.
(ii) Coefficient of 
= Coefficient of .
(iii) There is no term containing xy i.e., the coefficient of xy is zero.
(iv) radius is
To satisfy (i) and (ii) condition we have
To satisfy (iii) condition we have
To satisfy (iv) and as we cant have neagtive sign in root so
