## MATHEMATICS FUNCTION QUIZ-10

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. Let f(x)=x and g(x)=|x| for all x∈R. Then, the function Ï•(x) satisfying {Ï•(x)-f(x) }2+{Ï•(x)-g(x) }2=0, is
•  Ï•(x)=x,x∈[0,∞)
•  Ï•(x)=x,x∈R
•  Ï•(x)=-x,x∈(-∞,0]
•  Ï•(x)=x+|x|,x∈R
Solution

Q2.

•

•

•

•

Solution

Q3.

•  1
•  -1
•  √3
•  0
Solution

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

Q5.

•  (1/3, 1)
•  [1/3, 1]
•  (1, 2)
•  [1, 2]
Solution

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

Q7.The function f(x)=log2x-5⁡(x2-3x-10) is defined for all x belonging to
• [5,∞)
•  (5,∞)
•  (-∞,+5)
•  None of these
Solution

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

Q9.The unction f:[-1/2,1/2]→[-Ï€/2,Ï€/2] defined by f(x)=sin-1(3x-4x3) is
•  Bijection
•  Injection but not a surjection
•  Surjection but not an injection
•  Neither an injection nor a surjection

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

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