Class 11 Maths MCQ – Mathematical Reasoning

Here, you will find multiple-choice questions (MCQs) for Class 11 Maths Chapter 14, Mathematical Reasoning, along with their correct answers and explanations. These questions have been created following the latest exam pattern and align with the CBSE syllabus. Practicing these MCQs will enhance your reasoning skills, which can be applied to various mathematical concepts.

Students can solve the objective-type questions for Chapter 14, Mathematical Reasoning, and cross-check their answers with the provided solutions. Detailed explanations are also included to help students understand the reasoning techniques used to select the correct answers, making it easier to perform well in their board exams for 2024-2025.

MCQs for Class 11 Maths Chapter 14 Mathematical Reasoning with Solutions

• A sentence that is either true or false but not both is called a:
  a) Sentence
  b) Statement
  c) Proposition
  d) Argument
  Answer: b) Statement
• Which of the following is not a statement?
  a) 2 + 3 = 5
  b) “Close the door”
  c) 7 – 4 = 3
  d) “The sun rises in the east”
  Answer: b) “Close the door”
• The negation of “All apples are red” is:
  a) No apples are red
  b) Some apples are red
  c) Some apples are not red
  d) All apples are not red
  Answer: c) Some apples are not red
• If a statement is true, its negation is:
  a) True
  b) False
  c) Undefined
  d) Sometimes true, sometimes false
  Answer: b) False
• The logical connective “AND” is true when:
  a) Both statements are true
  b) Both statements are false
  c) At least one statement is true
  d) None of these
  Answer: a) Both statements are true
• The logical connective “OR” is false when:
  a) Both statements are true
  b) Both statements are false
  c) At least one statement is true
  d) None of these
  Answer: b) Both statements are false

• The statement “If p, then q” is called:
  a) Conjunction
  b) Disjunction
  c) Conditional
  d) Biconditional
  Answer: c) Conditional
• The converse of “If p, then q” is:
  a) If q, then p
  b) If not p, then not q
  c) If not q, then not p
  d) None of these
  Answer: a) If q, then p
• The biconditional statement “If and only if” is true when:
  a) Both statements are true or both are false
  b) Both statements are true
  c) Both statements are false
  d) None of these
  Answer: a) Both statements are true or both are false
• What is the contrapositive of “If it rains, then the ground will be wet”?
  a) If it does not rain, then the ground will not be wet
  b) If the ground is wet, then it rains
  c) If the ground is not wet, then it does not rain
  d) If it rains, then the ground is not wet
  Answer: c) If the ground is not wet, then it does not rain

• A statement that is always true is called a:
  a) Contradiction
  b) Tautology
  c) Proposition
  d) None of these
  Answer: b) Tautology
• A statement that is always false is called a:
  a) Contradiction
  b) Tautology
  c) Proposition
  d) None of these
  Answer: a) Contradiction
• The statement “p ∧ ¬p” is a:
  a) Tautology
  b) Contradiction
  c) Conditional
  d) None of these
  Answer: b) Contradiction
• The statement “p ∨ ¬p” is a:
  a) Tautology
  b) Contradiction
  c) Conditional
  d) None of these
  Answer: a) Tautology

• The statements “p → q” and “¬p ∨ q” are:
  a) Not equivalent
  b) Equivalent
  c) Tautology
  d) Contradiction
  Answer: b) Equivalent
• De Morgan’s law states:
  a) ¬(p ∧ q) = ¬p ∨ ¬q
  b) ¬(p ∨ q) = ¬p ∧ ¬q
  c) Both a and b
  d) None of these
  Answer: c) Both a and b

• Which of the following is a statement?
  a) Is 5 a prime number?
  b) 5 is a prime number
  c) Close the door
  d) None of these
  Answer: b) 5 is a prime number
• The negation of “No student failed the exam” is:
  a) All students failed the exam
  b) Some students failed the exam
  c) No student passed the exam
  d) None of these
  Answer: b) Some students failed the exam