Reasoning QUIZ-12

 

Mathematical Reasoning Quiz-12

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. Which of the following connectives satisfy commutative law?

•  
  
•  V
•  
  
•  All the above

Solution
(d)

Q2.The statement p∨q is

•  A tautology
•  A contradiction
•  Contingency
•  None of these

Solution
(c)

Q3.  The negation of the proposition "If 2 is prime, then 3 is odd" is

•  If 2 is not prime, then 3 is not odd
•  2 is prime and 3 is not odd
•  2 is not prime and 3 is odd
•  If 2 is not prime, then 3 is odd

Solution
(b) Let p=2 is prime and q=3 is odd Given, p→q Negation of p→q is p→q ⟹ p∧∼q ⟹ 2 is prime and 3 is not odd.

Q4. Let p be the statement 'Ravi races' and let q be the statement 'Ravi wins'. Then, the verbal translation of

•  Ravi does not race and Ravi does not win
•  It is not true that Ravi races and that Ravi does not win
•  Ravi does not race and Ravi wins
•  It is not true that Ravi races or that Ravi does not win

Solution
(c) Given, p:Ravi races, q: Ravi wins ∴The statement of given proposition ∼(p∨(∼q)) Which is equivalent to ∼p∧q. "It is not true that Ravi races or that Ravi does not win."

Q5.Which of the following statements is a tautology?

•  (~q∧p)∧q
•  (~q∧p)∧(p∧~p)
•  (~q∧p)∨(p∨~p)
•  (p∧q)∧(~(p∧q))

Solution
 (c) 

Q6. p∨q is true when

 Both p and q are true

 p is true and q is false

p is false and q is true

 All of these

Solution
(c)

Q7.If p and q are two statements, then p∨∼(p⇒∼q) is equivalent to

•  p∧∼q
•  p
•  q
•  ∼p∧q

Solution
(b)

Q8.Which of the following statement has the truth value 'F'?

•  A quadratic equation has always a real root
•  The number of ways of seating 2 persons in two chairs out of n persons is P(n,2)
•  The cube roots of unity are in GP
•  None of the above

Solution
(a) The root of the quadric equation can be imaginary.

Q9.The inverse of the proposition (p∧∼q)→r is

•  ~r→~p∨q
•  ∼p∨q→~r
•  r→p∧∼q
•  None of these

Solution
(b) The inverse of (𝑝∧∼𝑞)→𝑟 is ∼(𝑝∧∼𝑞)→∼𝑟 ⇒(∼𝑝∨𝑞)→∼𝑟

Q10. Let truth values of p be F and qbe T. Then, truth value of ∼(∼p∨q) is

•  T
•  F
•  Either T or F
• Neither T or F

Solution
(b)