## Mathematics Relations Quiz-20

As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background.
Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced
.

Q1.

•  Ï•(x)=x,x∈[0,∞)
•  Ï•(x)=x,x∈R
•  Ï•(x)=-x,x∈(-∞,0]
•  Ï•(x)=x+|x|,x∈R
Solution
(a)

Q2.

•
•
•
•
Solution
(c)

Q3.

•  1
•  -1
•
•  0
Solution
(b)

Q4. If f:R→R and g:R→R are defined by f(x)=x-[x] and g(x)=[x] for x∈R, where [x] is the greatest integer not exceeding x, then for every x∈R,f(g(x)) is equal to
•  x
•  0
•  f(x)
•  g(x)
Solution
(b)

Q5.If f:R→R and is defined by f(x)=1/(2-cos⁡3x ) for each x∈R, then the range of f is
•  (1/3, 1)
•  [1/3, 1]
•  (1, 2)
•  [1, 2]
Solution
(b)

Q6. If f(x)=ax+b and g(x)=cx+d, then f{g(x)}=g{f(x)} is equivalent to
•  f(a)=f(c)
•  f(b)=g(b)
• f(d)=g(b)
•  f(c)=g(a)
Solution
(c)

Q7.

•  [5,∞)
•  (5,∞)
•  (-∞,+5)
•  None of these
Solution
(b)

Q8.If R denotes the set of all real numbers, then the function f:R→R defined by f(x)=|x| is
•  One-one only
•  Onto only
•  Both one-one and onto
•  Neither one-one nor onto
Solution
(d)

Q9.

•  Bijection
•  Injection but not a surjection
•  Surjection but not an injection
•  Neither an injection nor a surjection
Solution
(a)

Q10. If f∶R→R is defined by f(x)=2x-2[x] for all x∈R, where [x] denotes the greatest integer less than or equal to x, then range of f, is
•  [0,1]
•  {0,1}
•  (0,∞)
• (-∞,0]
Solution
(b)

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