Product of two odd functions is
Options:
A.Even function
B.Odd function
C.Neither even nor odd
D.Cannot be determined
Answer: Option A
: A

Let f(x), g(x) be odd
Let F(x) = f(x)g(x)
F(–x) = f(–x)g(–x) = F(x)
therefore F(x) is even

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More Questions on This Topic :

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=73∴Ri=(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 x≠0, 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.