JEE Main 2019 (Online) 10th January Evening Slot | Mathematical Reasoning Question 100 | Mathematics

Consider the following three statements :

P : 5 is a prime number

Q : 7 is a factor of 192

R : L.C.M. of 5 and 7 is 35

Then the truth value of which one of the following statements is true ?

(P $$ \wedge $$ Q) $$ \vee $$ ($$ \sim $$ R)

P $$ \vee $$ ($$ \sim $$ Q $$ \wedge $$ R)

(~ P) $$ \wedge $$ ($$ \sim $$ Q $$ \wedge $$ R)

($$ \sim $$ P) $$ \vee $$ (Q $$ \wedge $$ R)

JEE Main 2019 (Online) 10th January Morning Slot

MCQ (Single Correct Answer)

-1

Out of Syllabus

Consider the statement : "P(n) : n² – n + 41 is prime". Then which one of the following is true ?

P(5) is false but P(3) is true

Both P(3) and P(5) are true

P(3) is false but P(5) is true

Both P(3) and P(5) are false

JEE Main 2019 (Online) 9th January Evening Slot

MCQ (Single Correct Answer)

-1

Out of Syllabus

The logical statement

[ $$ \sim $$ ( $$ \sim $$ p $$ \vee $$ q) $$ \vee $$ (p $$ \wedge $$ r)] $$ \wedge $$ ($$ \sim $$ q $$ \wedge $$ r) is equivalent to :

( $$ \sim $$ p $$ \wedge $$ $$ \sim $$ q) $$ \wedge $$ r

$$ \sim $$ p $$ \vee $$ r

(p $$ \wedge $$ r) $$ \wedge $$ $$ \sim $$ q

(p $$ \wedge $$ $$ \sim $$ q) $$ \vee $$ r

JEE Main 2019 (Online) 9th January Morning Slot

MCQ (Single Correct Answer)

-1

Out of Syllabus

If the Boolean expression
(p $$ \oplus $$ q) $$\wedge$$ (~ p $$ \odot $$ q) is equivalent
to p $$\wedge$$ q, where $$ \oplus , \odot \in \left\{ { \wedge , \vee } \right\}$$, then the
ordered pair $$\left( { \oplus , \odot } \right)$$ is :

$$\left( { \vee , \wedge } \right)$$

$$\left( { \vee , \vee } \right)$$

$$\left( { \wedge , \vee } \right)$$

$$\left( { \wedge , \wedge } \right)$$

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