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****MATHEMATICS REASONING QUIZ-3**

**MATHEMATICS REASONING QUIZ-3**

**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.

**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.

**Q1.**The false statement in the following is

p⇒q is logically equivalent to ∼q⇒∼p ∴ (p⇒q)⇔(∼q⇒∼p) Is a tautology but not a contradiction

**Q2.**The switching function for switching network is :

∵ Switches x and y

^{'}are connected parallel which is denoted by (x∧y)

^{'}) Similarly, y and z

^{'}and z and x

^{'}are also connected parallel Which are denoted by (y∧z

^{'}) and (z∧x

^{'}) respectively Now, x∧y

^{'},y∧z

^{'}and z∧x

^{'}are connected in series. So, switching function of given network is (x∧y

^{'})∨(y∧z

^{'})∨(z∧x

^{'})

**Q4.**A compound sentence formed by two simple statements p and q using connective 'and' is called

**Q5.**Simplify (p∨q)∧(p∨~q)

(p∨q)∧(p∨∼q) =p∨(q∧∼q) (distributive law) =p∨0 (complement law) =p (0 is identify for v)

**Q7.**~(~p)↔p is

We have, ∼(∼p)=p ∴∼(∼p)↔p≅p↔p Hence, ∼(∼p)↔p is a tautology

**Q8.**If p and q are two simple propositions, then p↔~q is true when

From the truth table of p↔q it is evident that p↔q is true when p and q both are true or both are false ∴p↔~q is true when p is false and ~q is false i.e.p is false and q is true

**Q9.**If p=∆ ABC is equilateral and q=each angle is 60°. Then, symbolic form of statement

The symbolic form of given statement is p⇔q

**Q10.**If p,q,r have truth values T,F,T respectively, which of the following is true?

Since p is true and q is false ∴p→q has truth value F Statement r has truth value T ∴(p→q)∧r has truth value F. Also, (p→q)∧∼r has truth value F p∧q has truth value F and p∨r has truth value T ∴(p∧q)∧(p∨r) has truth value F As p∧r has truth value T. Therefore, q→(p∧r) has truth value T