##
**
****MATHEMATICS RELATIONS QUIZ-2**

**MATHEMATICS RELATIONS QUIZ-2**

Dear Readers,

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.

**Q2.**If f(x)=sin

^{2}(x,g(x)=√x) and h(x)=cos

^{-1}(x,0≤x≤1,) then

Solution

We have,

We have,

hogof (x)=cos

^{-1}(|sinx | ) and,fogoh (x)=sin

^{2}(√(cos^{-1}x )) Clearly, hogof (x)≠fogoh(c)

Thus, option (a) is not correct

Now,
gofoh (x)=|sin(cos

^{-1}x ) |=|sin(sin^{-1}√(1-x^{2}) ) |=√(1-x^{2})**Q3.**If f(x) and g(x) are two real functions such that f(x)+g(x)=e

^{x}and f(x)-g(x)=e

^{-x}, then

Solution

**Q6.**If f(x) is an odd function, then the curve y=f(x) is symmetric

Solution

**Q10.**The number of reflexive relations of a set with four elements is equal to

Solution

Number of reflexive relations of a set of 4 elements=2

Number of reflexive relations of a set of 4 elements=2

^{(42)}-4 =2^{12}