CBSE Questions for Class 11 Engineering Maths Mathematical Reasoning Quiz 4 - MCQExams.com

State the following statement is True or False
If $$p, q, r$$ are statements with truth values T, F, T respectively, then the truth value of $$(\sim p\vee q)\wedge \sim r \rightarrow p$$, is T
  • True
  • False
The contrapositive of $$(p \vee q)\Rightarrow r$$ is
  • $$r \Rightarrow (p \vee q)$$
  • $$\sim r \Rightarrow (p \vee q)$$
  • $$\sim r \Rightarrow \sim p \wedge \sim q$$
  • $$R \Rightarrow (q \vee r)$$
Which of the following is/are a statement?
  • Give me a glass of water.
  • Asia is continent.
  • The earth revolves round sun.
  • The number $$6$$ has two prime factor $$2,3$$.
State the following statement is True or False
If $$p, q, r$$ are statements, with truth values T, F, T respectively, then the truth value of $$(\sim p \vee q) \wedge \sim r \Rightarrow p$$ is T
  • True
  • False
If $$p\rightarrow  (q \vee r)$$ is false, then the truth values of $$p,q,r$$ are respectively
  • T, F, F
  • F, F, F
  • F, T, T
  • T, T, F
If $$x = 5$$ and $$y = -2$$, then $$x-2y = 9$$. The contrapositive of this statement is/are
  • If $$x-2y$$ $$\neq 9$$, then $$x \neq$$ $$5$$ or $$y \neq 2$$.
  • If $$x-2y$$ $$\neq 9$$, then $$x \neq 5$$ and $$y \neq -2$$.
  • If $$x-2y = 9$$, then $$x = 5$$ and $$y = -2$$.
  • none of these.
The negation of the statement: "If I become a teacher, then I will open a school" is
  • I will become a teacher and I will not open a school.
  • Either I will not become a teacher or I will not open a school.
  • Neither I will become a teacher nor I will open a school.
  • I will not become a teacher or I will open a school.
If $$x = 5$$ and $$ y = 2$$ then $$x - 2y = 9$$. The contrapositive of this statement is
  • If $$x -2y \neq 9$$ then  $$x \neq 5$$  or  $$y \neq 2$$
  • If $$x -2y \neq 9 $$ then  $$x \neq 5$$ and $$y \neq - 2$$
  • If $$x - 2y = 9$$  then  $$x = 5$$ and $$y = -2$$
  • none of these.
Choose the conclusion of given statements:

All scientists working in America are talented. Some Indian scientists are working in America. Therefore, "Some Indian scientists are talented."
  • True
  • May be true
  • False
  • May be false
Consider the statements 
(i)Two plus three is five.
(ii) Every square is a rectangle.
(iii) Sun rises in the east.
(iv) The earth is not a star. 
Which of the above statements have truth value (T) ?
  • (i) and (ii)
  • (ii) and (iii)
  • (iii) and (iv)
  • All of these
The contrapositive of $$p\rightarrow (\sim q\rightarrow \sim r)$$ is equivalent to
  • $$(\sim q\wedge r)\rightarrow \sim p$$
  • $$(q\wedge \sim r)\rightarrow \sim p$$
  • $$p\rightarrow (\sim r\vee q)$$
  • $$p\wedge (q\vee r)$$
Which one of the following statements is not a false statement?
  • $$p:$$ Each radius of a circle is a chord of the circle.
  • $$q:$$ Circle is a particular case of an ellipse.
  • $$r:\>\displaystyle \sqrt{13}$$ is a rational number.
  • $$s:$$ The centre of a circle bisects each chord of the cirlce.
Consider the. following compound statement
(i) Mumbai is the capital of Rajasthan or Maharashtra,
(ii) $$\displaystyle \sqrt{3}$$ is a rational number or an irrational number,
(iii) $$125$$ is a multiple of $$7$$ or $$8$$
(iv) A rectangle is a quadrilateral or a regular hexagon.
Which of the above statements is not true?
  • (i)
  • (ii)
  • (iii)
  • (Iv)
The contrapositive of $$(\sim p\wedge q)\rightarrow \sim r$$ is equivalent to
  • $$(p\wedge q)\rightarrow r$$
  • $$(p\wedge q)\vee r$$
  • $$r\rightarrow (p\vee \sim q)$$
  • none of these
The contrapositive of the statement "If you believe in yourself and are honest then you will get sucess" is
  • If you do not believe yourself and are dishonest then you will not get success.
  • If you do not believe yourself and are dishonest then you will get success.
  • If you get success then you are honest and you also believe in yourself.
  • If you will not get success then you don't not believe in yourself or are not honest
The converse of $$p \rightarrow (q \rightarrow r)$$ is 
  • $$(q \wedge \sim r) \vee p $$
  • $$ (\sim q \vee r)\vee p$$
  • $$(q \wedge \sim r) \wedge \sim p $$
  • $$(q \wedge \sim r) \wedge p $$
In the following letter sequence, some of the letters are missing. These are given in order as one of the alternatives below. Choose the correct alternative.
$$\alpha \beta$$ _$$\alpha \alpha$$ _$$\beta \beta \beta$$ _$$\alpha \alpha \alpha \alpha$$ _$$\beta \beta \beta ...$$
  • $$\alpha \beta \beta \alpha $$
  • $$\beta \alpha \beta \alpha $$
  • $$\alpha \alpha \alpha \beta $$
  • $$\alpha \beta \alpha \beta $$
The negation of the statement $$q \vee  (p \wedge \sim r)$$ is equivalent to 
  • $$\sim q \wedge(p \rightarrow r)$$
  • $$\sim q \vee \sim(p \rightarrow r)$$
  • $$q \wedge (\sim p \wedge r)$$
  • None of these.
The converse of $$p \rightarrow (q \rightarrow r)$$ is
  • $$(q \wedge \sim r) \vee p$$
  • $$(\sim q \vee r) \vee p$$
  • $$(q \wedge \sim r) \wedge \sim p$$
  • $$(q \wedge \sim r) \wedge p$$
The contrapositive of $$\sim p \rightarrow ( q \rightarrow \sim r)$$ is
  • $$(~q \wedge r) \rightarrow ~p$$
  • $$(q \rightarrow r) \rightarrow~p$$
  • $$(q \vee ~r) \rightarrow ~ p$$
  • None of these
The negative of the statement "If a number is divisible by $$15$$ then it is divisible by $$5$$ or $$3$$"
  • If a number is not divisible by $$15$$, then it is not divisible by $$5$$ and $$3$$
  • A number is divisible by $$15$$ and it is not divisible by $$5$$ or $$3$$
  • A number is not divisible by $$15$$ or it is not divisible by $$5$$ and $$3$$
  • A number is divisible by $$15$$ and it is not divisible by $$5$$ and $$3$$
If statements $$p, q, r$$ have truth values T, F, T respectively then which of the following statement is true 
  • $$(p \rightarrow q) \wedge r $$
  • $$ (p \rightarrow q) \vee \sim r$$
  • $$(p \wedge q)\vee (q \wedge r) $$
  • $$ (p \rightarrow q) \rightarrow r$$
The contrapositive of $$p \rightarrow (\sim q \rightarrow \sim r)$$ is 
  • $$(\sim q\wedge r) \rightarrow \sim p $$
  • $$ (q \rightarrow r) \rightarrow \sim p$$
  • $$( q \vee \sim r) \rightarrow \sim p $$
  • none of these.
Negation of $$\displaystyle q \vee \sim \left ( p\wedge r \right )$$ is
  • $$\displaystyle \sim q\wedge \sim \left ( p\wedge r \right )$$
  • $$\displaystyle \sim q\wedge \left ( p\wedge r \right )$$
  • $$\displaystyle \sim q\vee \left ( p\wedge r \right )$$
  • None of these
Find the truth value of the compound statement, 4 is the first composite number and $$2+5=7$$.
  • T
  • F
  • Neither T nor F
  • cannot be determined
The negation of the statement "$$2 + 3 = 5$$" and "$$8 < 10$$" is
  • $$2 + 3 \neq 5$$ and $$8\nless 10$$
  • $$2 + 3 $$\neq 5 or $$8 > 10$$
  • $$2 + 3 \neq 5$$ or $$8 \ngeqslant 10$$
  • None of these
Find the quantifier which best describes the variable of the open sentence $$x^2+2\ge0$$
  • Universal.
  • Existential.
  • Neither (a) nor (b).
  • Does not exist.
The inverse of the statement $$(p \wedge \sim q)  \rightarrow r$$ is
  • $$\sim (p \vee \sim q) \rightarrow \sim r$$
  • $$(\sim p \wedge \sim q) \rightarrow \sim r$$
  • $$(\sim p \vee q) \rightarrow \sim r$$
  • None of these.
What is the truth value of the statement 'Two is an odd number iff 2 is a root of $$x^2+2=0$$'?
  • T
  • F
  • Neither T nor F
  • Cannot be determined
The negative of the statement "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 or 3
  • a number is divisible by 15 or it is not divisible by 5 and 3
  • a number is divisible by 15 and it is not divisible by 5 and 3
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