CBSE Questions for Class 11 Engineering Maths Mathematical Reasoning Quiz 9 - MCQExams.com

Check the validity of the following statement:
$$p:60$$ is a multiple of $$3$$ and $$5$$
  • True
  • False
Check whether the following statements are true or not :
$$p:$$ If $$x,y$$ are integers such that $$xy$$ is even, then at least one of $$x$$ and $$y$$ is an even integer.
  • True
  • False
Check whether the following statements are true or not :
$$p:$$ If $$x$$ and $$y$$ are odd integers, then $$x+y$$ is an integer.
  • True
  • False
Check the validity of the following statement:
$$p:100$$ is a multiple of $$4$$ and $$5$$
  • True
  • False
Determine whether the argument used to check the validity of the following statement is correct.
$$p:$$ If $$x^{2}$$ is irrational, then $$x$$ is rational'
The statement is true because the number $$x^{2}=\pi^{2}$$ is irrational, therefore $$x=\pi$$ irrational.
  • True
  • False
Which of the following is NOT equivalent to $$p\rightarrow q$$?
  • p only if q
  • q is necessary for p
  • q only if p
  • p is sufficient for q
Negation of the statement:
$$\sqrt{5}$$ is an integer or $$5$$ is irrational is?
  • $$\sqrt{5}$$ is not an integer or $$5$$ is not irrational
  • $$\sqrt{5}$$ is not an integer and $$5$$ is not irrational
  • $$\sqrt{5}$$ is irrational or $$5$$ is an integer
  • $$\sqrt{5}$$ is an integer and $$5$$ is irrational
The equivalent form of the statement $$\sim(p\rightarrow \sim q)$$ is ________.
  • $$p\wedge q$$
  • $$p\wedge \sim q$$
  • $$p\vee \sim q$$
  • $$\sim p\vee q$$
The statement pattern $$(p\wedge q)\wedge [\sim r\vee (p\wedge q)]\vee (\sim p\wedge q)$$ is equivalent to _________.
  • r
  • q
  • $$p\wedge q$$
  • p
Tell if the following statement is true or false. In case give a valid reason for saying so
$$p:$$ If $$x$$ and $$y$$ are integers such that $$x>y$$. then $$-x<-y$$.
  • True
  • False
Tell if the following statement is true or false. In case give a valid reason for saying so
$$p:$$ Each radius of a circle is a chord of the circle.
  • True
  • False
 The negation of the compound proposition $$p \vee (p \vee q)$$ is
  • $$(p\wedge ∼q)\wedge ∼p$$
  • $$(p\wedge ∼q)\vee  ∼p$$
  • $$(p\wedge ∼q)\vee ∼p$$
  • none of these
Given, "If I have a Siberian Husky, then I have a dog." Identify the converse
  • If I do not have a Siberian Husky, then I do not have a dog.
  • If I have a dog, then I have a Siberian Husky.
  • If I do not have a dog, then I do not have a Siberian Husky.
  • If I do not have a Siberian Husky, then I have a dog.
The component statements are:

p: You are wet when it rains.

q: You are wet when you are in river.

The compound statement of these component statements using appropriate connective is:
  • You are not wet when you are in river or it rains.
  • You are wet when you are in river and it rains.
  • You are wet when it rains and you are in a river
  • You are wet when it rains or you are in a river.
$$( p \wedge q ) \vee ( \sim p \wedge q ) \vee ( \sim q \wedge r ) =? $$
  • $$q \vee r$$
  • $$q \wedge r$$
  • $$q \rightarrow r$$
  • none of these
$$∼(p⇒q)⟺∼p\vee ∼q  \, is$$
  • a tautology
  • a contradiction
  • neither a tautology nor a contradiction
  • cannot come to any conclusion
Disjunction of two statements p and q is denoted by
  • $$p \leftrightarrow q$$
  • $$p \rightarrow q$$
  • $$p \leftarrow q$$
  • $$p \vee q$$
If p and q are mathematical statements, then in order to show that the statement p and q is true, we need to show that:
  • The statement p is true and the statement q is not true
  • The statement p is false and the statement q is true.
  • The statement p is true and the statement q is false
  • The statement p is true and the statement q is true
An implication or conditional "if p then q "is denoted by
  • $$p \vee q$$
  • $$p \rightarrow q$$
  • $$p \leftarrow q$$
  • None of these
$$[(p)\wedge q]$$ is logically equivalent to
  • $$(p\vee q)$$
  • $$[p\wedge(q)]$$
  • $$p\wedge(q)$$
  • $$p\vee(q)$$
Name the technique used in the first step of the solution to the problem below :
Verify that 5 is irrational
Solution : Let us assume that 5 is rational
  • Counter example
  • Direct method
  • By Contradiction
  • Contrapositive method
Name the technique used in the solution of the problems below :

Question: Show that the following statement is false: If n is an odd integer, then n is prime.

Solution: The given statement is in the form “if p then q” we have to show that this is false, If p then ~q.

If n= 99 is odd integer which is not a prime number. Thus, we conclude that the given statement is false.
  • Counter example
  • Contrapositive method
  • Direct method
  • By Contradiction
Check whether the following statement is true or false? In each case give a valid reason for your answer.
$$p: \sqrt {11}$$ is an irrational number.
  • True
  • False
Check whether the following statement is true or false. Also give a valid reason for your answer.
$$r:$$ Each radius of a circle is a chord of the circle.
  • True
  • False
Check whether the following statement is true or false? Also give a valid reason for your answer.
$$u:$$ The quadratic equation $$x^2+x+1=0$$ has no real roots.
  • True
  • False
Check whether the following statement is true or false? Also give a valid reason for your answer.
$$s:$$ The centre of a circle bisects each chord of the circle.
  • True
  • False
Which of the following  statements are true and which are false? In each case give a valid reason for your answer.
$$q:$$ Circles is a particular case of an ellipse.
  • True
  • False
Check whether the following statement is true or false? Also give a valid reason for your answer.
$$t:$$ If $$a$$ and $$b$$ are integers such that $$a < b$$, then $$-a > -b$$
  • True
  • False
Let $$A=\left\{ 2, 3, 5, 7\right\}$$. Examine whether the statements given below are true or false.
$$\exists \ x\in A$$ such that $$x$$ is even.
  • True
  • False
Let $$A=\left\{ 2, 3, 5, 7\right\}$$. Examine whether the statements given below are true or false.
$$\exists \ x\in A$$ such that $$x+2=6$$.
  • True
  • False
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 11 Engineering Maths Quiz Questions and Answers