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Question 1. Range of the function f(x)=x2+x+2x2+x+1;xϵR is
  1.    (1,∞)
  2.    (1,117]
  3.    (1,73]
  4.    (1,75]
Answer: Option C
: C

Wehave,f(x)=x2+x+2x2+x+1=(x2+x+1)x2+x+1=1+1(x+12)2+34Wecanseeherethatasx,f(x)1whichistheminvalueoff(x).Alsof(x)ismaxwhen(x+12)2+34isminwhichissowhenx=12andthen34.fmax=1+134=73Ri=(1,73]

Question 2. If f(x) is a function whose domain is symmetric about the origin, then f(x) + f(–x) is
  1.    One-one
  2.    Even
  3.    Odd
  4.    Both even and odd
Answer: Option B
: B

(a, b)
g(x) = f(x) + f(–x)
g(–x) = f(–x) + f(x) = g(x)
therefore g(x) is even

Question 3. Let f be a function satisfying 2f(x)3f(1x)=x2 for any x0, then the value of f(2) is
  1.    -2
  2.    −74
  3.    −78
  4.    4
Answer: Option B
: B

2f(x)3f(1x)=x2(i)Replacingxby1x2f(1x)3f(x)=1x2(ii)
Solving (i) and (ii) we get
5f(x)=2x2+3x2f(x)=15(2x2+3x2)f(2)=15(8+34)=74

Question 4. Let A = {1, 2, 3}. The total number of distinct relations that can be defined over A  is
  1.    29 
  2.    6
  3.    8
  4.    None of these
Answer: Option A
: A

n ( A× A) = n(A)n(A) = 32 = 9 So, the total number of subsets of A× A is 29 and a subset of A× A is a relation over the set A .

Question 5. With reference to a universal set, the inclusion of a subset in another, is relation, which is
  1.    Symmetric only
  2.    Equivalence relation
  3.    Reflexive only
  4.    None of these
Answer: Option D
: D

Since A A . Relation ' ' is relfexive Since A B , B C A C Relation ' ' is transitive. But A ' ' B , B A . relation is not symmetric.

Question 6. A relation from P to Q is
  1.    A universal set of P × Q
  2.    P × Q
  3.    An equivalent set of P × Q
  4.    A subset of P × Q
Answer: Option D
: D

A relation from P to Q is a subset of P × Q.