## MATHEMATICS RELATIONS QUIZ-9

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. If R is an equivalence relation on a set A, then R-1 is
•  Reflexive only
•  Symmetric but not transitive
•  Equivalence
•  None of the above
Solution
Since, inverse of an equivalent relation is also an equivalent relation.
∴R-1is an equivalent relation.

Q2. The range of the function f(x)=1+sin⁡x+sin3⁡x+sin5x+⋯ when x∈(-Ï€/2,Ï€/2), is
•  (0,1)
•  R
•  (-2,2)
•  None of these
Solution

Q3.

•  (0,Ï€)
•  (-2 Ï€,-Ï€)
•  (3 Ï€,4 Ï€)
•  (4 Ï€,6 Ï€)
Solution

Q4. Let f:A→B and g:B→C be two functions such that gof:A→C is one-one. Then,
•  f is one-one
•  f is one-one
•  f is both are one-one
•  None of these

Q5.If g(x)=1+√x and f(g(x) )=3+2√x+x then, f(x) is equal to
•  1+2x2
•  2+x2
•  1+x
•  2+x
Solution
We have,
g(x)=1+√x and f(g(x) )=3+2√x+x
Now, f(g(x) )=3+2√x+x
⇒f(g (x) )=2+(1+√x)2
⇒f(g (x) )=2+{g(x) }2
⇒f(x)=2+x2

Q6.

•

•

•

•

Solution

Q7.Let a and b be two integers such that 10a+b=5and P(x)=x+ax+b. The integer n such that P(10).P(11)=P(n) is
• 15
•  65
•  115
•  165
Solution

Q8.

•  Injective but not surjective
•  Neither injective nor surjective
•  Surjective but not injective
•  Bijective
Solution

Q9.

•  (0,∞)
•  (-∞,∞)
•  [0,1]
•  [-1/3,1]-{0}
Solution
Here, we have to find the range of the function which is [-1/3,1]

Q10.

•  Surjective but not injective
•  Injective but not surjective
•  Bijective
•  Neither injective nor surjective
Solution

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