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JEE • MATHEMATICS • MATHEMATICAL REASONING

Mathematical reasoning practice · Hard

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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1 Hard

1 of 3

Understanding +4 | -1

The contrapositive statement and the converse statement of "If the points

P, Q

and

\mathrm{R}

are collinear, then

\triangle P Q R

is not possible' are respectively ...... and ...... .

View answer and explanation

Correct option: D

Contrapositive statement : If

\triangle \mathrm{PQR}

is possible, then the points

\mathrm{P}, \mathrm{Q}

and

\mathrm{R}

are not collinear, Converse : If

\triangle \mathrm{PQR}

is not possible, then the points

\mathrm{P}, \mathrm{Q}

and

\mathrm

Option C is correct because it correctly identifies the converse of the given implication.

2 Hard

2 of 3

Application +4 | -1

S\left( {p,\;q,\;r} \right) = \left( { \sim P} \right) \vee \left[ { \sim \left( {q \wedge r} \right)} \right]

is a compound statement, then

S\left( { \sim p, \sim q,\; \sim r} \right)

View answer and explanation

Correct option: D

p \vee \left( {q \vee r} \right)

Option D (

p \vee \left( {q \vee r} \right)

) is correct because by applying De Morgan's laws and simplifying the expression, we arrive at this result.

3 Hard

3 of 3

Analyzing +4 | -1

The number of choices for

\Delta \in \left\{ { \wedge , \vee , \Rightarrow , \Leftrightarrow } \right\},

such that

\left( {p\Delta q} \right) \Rightarrow \left( {\left( {p\Delta \sim q} \right) \vee \left( {\left( { \sim p} \right)\Delta q} \right)} \right)

is a tautology, is

View answer and explanation

Correct option: B

The correct answer is 2 because only two logical connectives,

\vee

and

\Rightarrow

, result in a tautology when substituted for

\Delta

in the given expression.

Revision notes and key takeaways

Review MATHEMATICAL REASONING in your textbook or class notes, then use this set to check your understanding.

Key Takeaways

✓ This set contains 3 single-correct-answer MCQs on MATHEMATICAL REASONING.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

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