MATHEMATICS RELATIONS QUIZ-8

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. The range of the function sin⁡(sin-1x+cos-1⁡x ),|x|≤1 is
•  [-1, 1]
•  [1, -1]
•  {0}
•  {1}
Solution

Q2. On the set N of all natural numbers define the relation R by aRb if and only if the GCD of a and b is 2, then R is
•  Reflexive, but not symmetric
•  Symmetric only
•  Reflexive, and transitive
•  Reflexive, symmetric and transitive
Solution
(i) aRa, then GCD of a and a is a.
∴Ris not reflexive.
(ii) aRb⇒bRa
If GCD of a and b is 2, then GCD of b and a is 2.
∴Ris symmetric.
(iii) aRa,bRc⇏cRa
If GCD of a and b is 2 and GCD of b and c is 2, then it is need not to be GCD of c and a is 2.
∴Ris not transitive.

Q3.  Which of the following functions is (are) not an injective map(s)?
•  f(x)=|x+1|,x∈[-1,∞)
•  g(x)=x+1/x,x∈(0,∞)
•  h(x)=x2+4 x-5,x∈(0,∞)
•  k(x)=e-x,x∈[0,∞)
Solution

Q4.

•  1≤x≤5
•  1<x<4
•  1≤x<4
•  1≤x≤4
Solution

Q5.If n is an integer, the domain of the function √(sin⁡2x ) is
•

•

•

•

Solution

Q6.

•

•

•

•  None of these
Solution

Q7.The function f(x)=max⁡{(1-x),(1+x),2}, x∈(-∞,∞) is equivalent to

•

•

•  None of these
Solution

Q8.If f:[2,3]→R is defined by f(x)=x3+3x-2, then the range f(x) is contained in the interval
•  [1, 12]
•  [12, 34]
•  [35, 50]
•  [-12, 12]
Solution

Q9.Let f(x)=|x-2|+|x-3|+|x-4| and g(x)=x+1. Then,
•  g(x) is an even function
•  g(x) is an odd function
•  g(x) is neither even nor odd
•  g(x) is periodic
Solution

Q10. Let f(x)=x+1 and Ï•(x)=x-2. Then the values of x satisfying |f(x)+Ï•(x) |=|f(x)|+|Ï•(x) | are :
•  (-∞,1]
•  [2,∞)
•  (-∞,-2]
•  [1,∞)
Solution
We observe that
|f(x)+Ï•(x) |=|f(x) |+|Ï•(x)| is true, if
f(x)≥0 and Ï•(x)≥0
OR
f(x)<0 and Ï•(x)<0
⇒(x>-1 and x>2) or (x<-1 and x<2)
⇒x∈(2,∞)∪(-∞,-1)

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