CBSE Questions for Class 11 Engineering Maths Mathematical Reasoning Quiz 10 - MCQExams.com

Let $$A=\left\{ 2, 3, 5, 7\right\}$$. Examine whether the statements given below are true or false.
$$\forall x \ in A, x$$ is prime.
  • True
  • False
State whether the statements are true (T) or false (F).
There are countless rational numbers between $$\dfrac{5}{6}$$ and $$\dfrac{8}{9}.$$
  • True
  • False
The contrapositive of $$(p \vee q) \Rightarrow r$$ is
  • $$r \Rightarrow (p \vee q)$$
  • $$\sim r \Rightarrow (p \vee q)$$
  • $$\sim r \Rightarrow (\sim p \wedge \sim q)$$
  • $$p \Rightarrow (q \vee r)$$
If p: Every equilateral triangle is an isosceles and q: Every square is a rectangle, then which of following is equivalent to ~
$$\, ( p \Rightarrow  q )$$?
  • The negation of "Every equilateral triangle is not isosceles or every square is a rectangle".
  • "Every equilateral triangle is not isosceles, then every square is not a rectangle".
  • Every equilateral triangle is isosceles, then every square is a rectangle".
  • None of these
An electrical circuit for a set of 4 lights depends on a system of switches A, B, C and D. When these switches work they have the following effect on the lights: They each toggle the state of two lights (i.e. on becomes off and off becomes on). The lights that each switch controls are as follows.
ABCD
1 and 22 and 41 and 33 and 4
In configuration I shown below, switches C-B-D-A are asserted in order, resulting in configurationOne switch did not work and had no effect at all. Which was that switch?
205464_682c47c8cb3c457cb63ced6ffd061c20.png
  • A
  • B
  • C
  • D
Let P(n) denote the statement that $$n^2+n$$ is odd. It is seen that $$P(n)\Rightarrow P(n+1), P(n)$$ is true for all.
  • $$n > 1$$
  • n
  • $$n > 2$$
  • None of these
The converse of $$\sim p \rightarrow q$$ is equivalent to
  • $$p\rightarrow \sim q$$
  • $$p\rightarrow q$$
  • $$\sim q\rightarrow p$$
  • $$q\rightarrow \sim p$$
Of the following metals that cannot be obtained by electrolysis of the aqueous solution of their salts are
  • Ag and Mg
  • Ag and Al
  • Mg and Al
  • Cu and Cr
Consider statement " If I do not work, I will sleep. If I am worried, I will not sleep. Therefore if I am worried, I will work". This statement is
  • valid
  • invalid
  • a fallacy
  • none of these
The inverse of the statement "If a student join in NARAYANA collage then he  get a seat in IIT" is
  • If a student get a seat in IIT then he was the student of NARAYANA college
  • If a student not joined in NARAYANA college then he does not get a seat in IIT
  • If a student does not a get a seat in IIT then he was not the student of NARAYANA college
  • A student get success if he joined in a NARAYANA college
Rohith makes a statements p,q about future.If it is Known that p$$\rightarrow $$q and probability of occurance of p is $$\frac { 3 }{ 5 } $$. what is the probability that q doesn't happen.
  • $$\dfrac { 1 }{ 5 } $$
  • $$\dfrac { 2 }{ 5 } $$
  • $$\dfrac { 3 }{ 5 } $$
  • can't be determined by given information
While simplifying $$\sqrt { \frac { 1-cosx }{ 1+cosx }  } $$, two students got the following two answers A & B.
A)  cosec x - cot x  (B)   $$\frac { 1 }{ cosecx+cotx } $$ What can you say about answers ?
  • Both A & B are wrong
  • Both A & B are right
  • A is right B is wrong
  • B is right A is wrong
- (The teacher will teach iff students are sincere )
  • the teacher will teach , if students are not sincere .
  • the teacher will teach but students are not sincere or the teacher will not teach but students are sincere .
  • the teacher will teach or students are not sincere , and the teacher will not teach or students are sincerer
  • the teacher will not teach iff students are not sincerer
Consider the following statements. The number $$12375$$ is
(1) divisible by $$3$$  
(2) divisible by $$11$$  
(3) divisible by $$9$$
Of these statements:
  • 1, 2 and 3 are correct
  • 1 and 2 are correct
  • 2 and 3 are correct
  • 1 and 3 are correct
Select and write the most appropriate answer from the given alternatives in each of the following questions:
Contrapositive of $$p\rightarrow\left(q\rightarrow r\right)$$ is logically equivalent to 
  • $$p\rightarrow\left(q\rightarrow r\right)$$
  • $$\left(q\rightarrow r\right)\rightarrow\simp$$
  • $$\left(p\vee q\right)\rightarrow r$$
  • $$\left(p \rightarrow q\right)\rightarrow p$$
The converse of the statement "if $$p < q$$, then $$p-x < q-x$$" is :
  • If $$ p < q$$, then $$p-x > q-x$$
  • If $$ p > q$$, then $$p-x > q-x$$
  • If $$p-x > q-x$$, then $$p > q$$
  • If $$p-x < q-x$$, then $$p < q$$
The logically equivalent proportion of $$p \leftrightarrow q$$ is
  • $$(p \wedge q) \vee (p \vee q)$$
  • $$(p \rightarrow q) \wedge (p \rightarrow q)$$
  • $$(p \rightarrow q) \vee (p \rightarrow q)$$
  • $$(p \wedge q) \rightarrow (p \vee q)$$
Which of the following proportional is a tautology? 
  • $$\sim (p \rightarrow q) \vee (p \sim \wedge q)$$
  • $$(p \rightarrow p) \vee (p \sim \wedge q)$$
  • $$(p \rightarrow q) \vee (p \sim \wedge q)$$
  • $$(p \rightarrow q) \wedge (p \wedge \sim q)$$
If  p, q, r are statements with truth values false, true and false respectively.  then truth value of $$(\sim pv \sim q) v r$$  is 
  • True
  • False
  • False, if r is true
  • False, if q is false
The converse of the contra positive of $$
\sim p \rightarrow q
 $$ is ........(1)
  • $$

    q \rightarrow p

    $$
  • $$

    \sim p \rightarrow p

    $$
  • $$

    p \rightarrow \sim q

    $$
  • $$

    \sim q \rightarrow \sim p

    $$
The contrapositive of $$( p \wedge q ) \Rightarrow r$$ is
  • $$\sim r \Rightarrow ( p \vee q )$$
  • $$r \Rightarrow ( p \vee q )$$
  • $$- r \Rightarrow ( - p \vee - q )$$
  • $$p \Rightarrow ( q \vee r)$$
Consider the statement :$$"P\left( n \right) :{ n }^{ 2 }-n+41$$ is prime." Then which one of the following is true?
  • P(3) is false but P(3) is true.
  • P(3)is false but P(5) is true.
  • Both P(3) and P(5) are true.
  • Both P(3) and P(5) are false.
Two pairs of statement are:
p: If a quadrilateral is a rectangle, then its opposite sides are equal.
q: If opposite sides of a quadrilateral are equal, then the quadrilateral is a rectangle.
The combined statement of these pairs using If and only if is:
  • A quadrilateral is a rectangle if and only if its all sides are equal.
  • A quadrilateral is a rectangle if and only if its opposite sides are equal.
  • A quadrilateral is a square if and only if its opposite sides are equal.
  • A quadrilateral is not a rectangle if and only if its opposite sides are equal.
Let A and B denote the statements
A:$$\cos { \alpha  } +\cos { \beta  } +\cos { \gamma  } =0$$ & B:$$\sin { \alpha  } +\sin { \beta  } +\sin { \gamma  } =0$$
If $$\cos { (\beta -\gamma ) } +\cos { (\gamma -\alpha ) } +\cos { (\alpha -\beta ) } =-\frac { 3 }{ 2 } $$ then
  • A is true and Bis false
  • A is false and B is true
  • Both A and B are true
  • Both A and B are false
If $$x = 5$$ and $$y = - 2$$ then $$x - 2 y = 9 .$$ The contrapositive of this statement is
  • If $$x - 2 y = 9$$ then $$x = 5$$ and $$y = - 2$$
  • If $$x - 2 y \neq 9$$ then $$x \neq 5$$ and $$y \neq - 2$$
  • If $$x - 2 y \neq 9$$ then $$x \neq 5$$ or $$y \neq - 2$$
  • If $$x - 2 y \neq 9$$ then either $$x \neq 5$$ or $$y = - 2$$
Choose the incorrect statements
  • Digit at the units place of $$3^{51}$$ is $$9$$
  • If $$i-f=(9-\sqrt{82})^{11}$$ and $$< f < 1 $$, then $$'i'$$ is an even integers
  • If $$7^{80}$$ is divided by $$13$$, then the remainder is $$9$$
  • If only $$6^{th}$$ term in the expression of $$\left(\dfrac{x}{5}+\dfrac{2}{5}\right)^{n} $$ ahs numerically greatest coefficient, then $$n=7$$
State whether the statements are true (T) or false (F).
There are 200 natural numbers between $$100^2$$ and $$101^2$$.
  • True
  • False
State whether the statements are true (T) or false (F).
For every rational numbers $$x, y$$ and $$z, x + (y \times z) = (x + y) \times (x + z).$$
  • True
  • False
Let $$A=\left\{ 2, 3, 5, 7\right\}$$. Examine whether the statements given below are true or false.
$$\forall x \ in A, x+4\ge 11$$
  • True
  • False
Let $$A=\left\{ 2, 3, 5, 7\right\}$$. Examine whether the statements given below are true or false.
$$\exists \ x\in A$$ such that $$x+3>9$$.
  • True
  • False
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