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 R and S be two equivalence relations on a set A. Then,

Solution

No solution available

No solution available

**Q3.**In a certain town 25% families own a cell phone, 15% families own a scooter and 65%

families own neither a cell phone nor a scooter. If 1500 families own both a cell phone and

a scooter, then the total number of families in the town is

**Q5.**If A={Ï•,{Ï•} }, then the power set of A is

Solution

No solution available

No solution available

**Q6.**For any two sets A and B, if A∩X=B∩X=Ï• and A∪X=B∪X for some set X, then

Solution

Given, A∩X=B∩X=Ï• ⇒A and X,B and X are disjoint sets. Also, A∪X=B∪X⇒A=B

Given, A∩X=B∩X=Ï• ⇒A and X,B and X are disjoint sets. Also, A∪X=B∪X⇒A=B

**Q7.**Let L be the set of all straight lines in the Euclidean plane. Two lines l

_{1}and l

_{1}is parallel to l

_{2}. Then, the relation R is not

Solution

No solution available

No solution available

**Q9.**Let R be a relation on the set N of natural numbers defined by nRm⇔n is a factor of m(i.e. n | m). Then, R is

Solution

Since n|n for all n∈N. Therefore, R is reflexive. Since 2|6 but 6∤2, therefore R is not symmetric Let n R m and m R p ⇒n R m and m R p ⇒n|m and m|p⇒n|p⇒n R p So, R is transitive

Since n|n for all n∈N. Therefore, R is reflexive. Since 2|6 but 6∤2, therefore R is not symmetric Let n R m and m R p ⇒n R m and m R p ⇒n|m and m|p⇒n|p⇒n R p So, R is transitive

**Q10.**If A and B are two sets such that n(A)=7,n(B)=6 and (A∩B)≠Ï•. The least possible value of n(A Î” B), is

Solution

We have, A ∆ B=(A∪B)-(A∪B) ⇒n(A ∆ B)=n(A)+n(B)-2 n(A∩B) So, n(A ∆ B) is greatest when n(A∩B) is least It is given that A∩B≠Ï•. So, least number of elements in A ∩B can be one ∴ Greatest possible value of n(A ∆ B) is 7+6-2×1=11

We have, A ∆ B=(A∪B)-(A∪B) ⇒n(A ∆ B)=n(A)+n(B)-2 n(A∩B) So, n(A ∆ B) is greatest when n(A∩B) is least It is given that A∩B≠Ï•. So, least number of elements in A ∩B can be one ∴ Greatest possible value of n(A ∆ B) is 7+6-2×1=11