REASONING-QUIZ-8

MATHEMATICS REASONING QUIZ-8

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 switching function of network is

•  ∼p∨r∧(∼q∧∼r)∧p^'∨q
•  (∼p∧r)∧(∼q∨∼r)∧p^'∨q
•  (∼p∧r)∧(∼q∨∼r)∧p^'∨q
•  None of the above

Q2.Which is not a statement?

•  3 > 4
•  4 > 3
•  Raju is an intelligent boy
•  He lives in Agra

Q3.  Let p: is not greater than and q: Pairs is in France Be two statements. Then, ~(p∨q) is the statement

•  7 is greater than or Pairs is not in France
•  7 is not greater than 4 and Pairs is not in France
•  7 is greater than 4 and Pairs is in France
•  7 is greater than 4 and Pairs is not in France

Solution
∼(p∨q)≡∼p∧∼q ∴ 7 is greater than 4 and Paris is not in France.

Q4. If (p∧~r)→(~p∨q) is false, then the truth values of p,q and rare respectively

•  T, F and F
•  F, F and T
•  F, T and T
•  T, F and T

Solution

Q5.H:Set of holiday, S: Set of Sunday and U:Set of day's Then, the Venn diagram of statement, 'Every Sunday implies holiday' is

•  
• 
  
  
•  
• 
  
  
• 
  
  
•  
• 
  
  

Solution

Q6. If p and q are two simple propositions, then p↔q is false when

•  p and q both are true
•  p is false and q is true
•  p is fale and q is true
•  None of these

Solution

Q7.The negative of the proposition : “If a number is divisible by 15, then it is divisible by 5 or 3”

• If a number is divisible by 15, then it is not divisible by 5 and 3
•  A number is divisible by 15 and it is not divisible by 5 and 3
•  A number is divisible by 15 and it is not divisible by 5 or 3
•  A number is not divisible by 15 or it is not divisible by 5 and 3

Solution
Consider the following statements: p= Number is divisible by 15 q= Number is divisible by 5 or 3 We have, p→q≅∼p∨q ∴∼(p→q)≅∼(∼p∨q)≅p∧∼q Clearly, p∧∼q is equivalent to: A number is divisible by 15 and it is not divisible by 5 and 3

Q8.If p:A man is happy q:A man is rich Then, the statement, ""If a man is not happy, then he is not rich" is written as

•  ∼p→∼q
•  ∼q→p
•  ∼q→∼p
•  q→∼p

Solution
∵p:A man is happy and q:A man is rich 'If a man is not happy, then he is not rich' is written as ∼p→∼q

Q9.Which of the following is a tautology?

•  p∧q
•  p∨q
•  p∨∼p
•  p∧∼p

Q10. ~(p∨q)∨(~p∧q) is logically equivalent to

•  ~p
•  p
•  q
•  ~q

Solution
∼(p∨q)∨(∼p∧q)≡(∼p∧∼q)∨(∼p∧q) ≡∼p∧(∼q∨q)≡∼p∧t≡∼p