Test: Mathematical Reasoning- 1 - JEE MCQ

# Test: Mathematical Reasoning- 1 - JEE MCQ

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## 25 Questions MCQ Test Chapter-wise Tests for JEE Main & Advanced - Test: Mathematical Reasoning- 1

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Test: Mathematical Reasoning- 1 - Question 1

### Which of the following is a proposition?

Detailed Solution for Test: Mathematical Reasoning- 1 - Question 1

key Concept: Proposition is a sentence which is either true or false but not both.
Option 1: I am an advocate can be both True or False.
Option 2: Delhi is on the Jupiter is False.
Option 3: A half open door is half closed can be bith True or False.

Test: Mathematical Reasoning- 1 - Question 2

### Let p and q be two propositions given by P : The sky is blue, q : Milk is white, Then , p^q is

Detailed Solution for Test: Mathematical Reasoning- 1 - Question 2

p∧q means statement p and q

=> The sky is blue and  milk is white.

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Test: Mathematical Reasoning- 1 - Question 3

### Let p and q be two prepositions given by p : I play cricket during the holidays, q : I just sleep throughout the day then , the compound statement p ∧ q is

Detailed Solution for Test: Mathematical Reasoning- 1 - Question 3

∧ is replaced by and in verbal form

Test: Mathematical Reasoning- 1 - Question 4

Let p and q be two prepositions given by p : It is hot, q : He wants water Then , the verbal meaning of p → q is

Test: Mathematical Reasoning- 1 - Question 5

Let p and q be two prepositions given by p : I take medicine, q : I can sleep then ,the compound statement ∼p→∼q means

Test: Mathematical Reasoning- 1 - Question 6

Which of the following is true for the propositions p and q ?

Test: Mathematical Reasoning- 1 - Question 7

Which of the following is a compound statement

Detailed Solution for Test: Mathematical Reasoning- 1 - Question 7

Compound statement is connected with And , or , etc.
So, the statement 7 is both odd and prime number is a compound statement.

Test: Mathematical Reasoning- 1 - Question 8

Which of the following is always true ?

Detailed Solution for Test: Mathematical Reasoning- 1 - Question 8

We know that
p→q≡∼p∧q
∼(p→q)≡∼(∼p∧q)
∼(p→q)≡p∨∼q  (De morgan's law)

Test: Mathematical Reasoning- 1 - Question 9

Negation of the statement p→(q ∨ r) is

Detailed Solution for Test: Mathematical Reasoning- 1 - Question 9

The correct option is D p ∧ (∼q ∧∼r)
We know that, ∼(p → q)≡ p ∧ (∼q)
Also, negation of (q ∨ r) is (∼q∧∼r)
So, ∼(p→(q ∨ r))≡ p ∧(∼q∧∼r)

Test: Mathematical Reasoning- 1 - Question 10

For any three propositions p, q, and r, the proposition (p∧q)∧(q∧r) is true, when

Test: Mathematical Reasoning- 1 - Question 11

The negation of the proposition “if a quadrilateral is a square, then it is a rhombus “ is

Test: Mathematical Reasoning- 1 - Question 12

The contrapositive of the statement “ if 22 = 5, then I get first class” is

Test: Mathematical Reasoning- 1 - Question 13

If x = 5 and y = - 2, then x – 2y = 9. The contrapositive of this proposition is

Detailed Solution for Test: Mathematical Reasoning- 1 - Question 13

Let p,q and r be three propositions given by
p:x=5; q:y=−2 and r:x−2y=9
Then, the given statement is (p∧q)→r
Its contrapositive is

Test: Mathematical Reasoning- 1 - Question 14

Let p and q be two propositions. Then, the contrapositive of the implication p→q is

Test: Mathematical Reasoning- 1 - Question 15

Which of the following statement is a tautology ?

Test: Mathematical Reasoning- 1 - Question 16

The statement p→(q→p) is equivalent to

Test: Mathematical Reasoning- 1 - Question 17

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

Detailed Solution for Test: Mathematical Reasoning- 1 - Question 17

Test: Mathematical Reasoning- 1 - Question 18

Logical equivalent proposition to the proposition ∼(p∨q) is

Test: Mathematical Reasoning- 1 - Question 19

Let p and q be two propositions. Then the implication p↔∼q is true ,when

Detailed Solution for Test: Mathematical Reasoning- 1 - Question 19

Notation: Negation is denoted by the symbol ~

Bi-conditional:

Let, p and q are two simple propositions. If p and q both the propositions are either True or False then Bi-conditional gives the output as True otherwise if anyone is False then the output is False.

Notation: Bi-conditional is denoted by the symbol ⇔

Step-2: Truth Table:

The truth table is used to perform logical operations on given propositions. It is used to check whether the given propositional statement is either True or False. Using some of the logical operations like AND, OR, NOR, Conditional, and Bi-conditional.

Given p and q are both simple propositions

The truth table for p⇔~q is given below

pq~qp⇔~q
TT F  F
TFT   T
FTF   T
FFT   F

Where T is True and F is False.

From the above table, we can conclude p⇔~q is True if p is False and q is True.

Hence option 'C' is the correct answer.

Test: Mathematical Reasoning- 1 - Question 20

Which of the following is a proposition ?

Test: Mathematical Reasoning- 1 - Question 21

The contrapositive of 2x + 3 = 9 ⇒ x ≠ 4 is

Test: Mathematical Reasoning- 1 - Question 22

Consider the proposition: “If we control population growth, we prosper “. Negative of this proposition is

Test: Mathematical Reasoning- 1 - Question 23

Consider the proposition: “If the pressure increases, the volume decreases “. Negative of this proposition is

Test: Mathematical Reasoning- 1 - Question 24

Which of the following connectives satisfy commutative law ?

Test: Mathematical Reasoning- 1 - Question 25

Which of the following pairs is logically equivalent ?

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