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Maths Assertion (A) & Reason (B) MCQ

Number System [NEW] · Gujarat Board (GSEB) STD 9 (GSEB - English Medium). 12 questions.

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Assertion (A) & Reason (B) MCQ

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12 questions · timed · auto-graded

MCQ 11 Mark
Statement-1 (A): The sum of any two irrational numbers is an irrational number.
Statement-2 (R): There are two irrational numbers whose sum is a rational number.
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • ✓
    Statement-1 is true, Statement-2 is false.
Answer
Correct option: D.
Statement-1 is true, Statement-2 is false.
d
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MCQ 21 Mark
Statement-1 (A): There are two rational numbers whose sum and product both are rationals.
Statement-2 (R): There are numbers which cannot be written in the form $\frac{p}{q}, q \neq 0, p, q$ both are integers.
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement-1 is true, Statement-2 is false.
Answer
Correct option: B.
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
b
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MCQ 31 Mark
Statement-1 (A): There are infinitely many rational numbers between any two integers.
Statement-2 (R):The square of an irrational number is always a rational number.
  • A
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-5
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • ✓
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: C.
Statement-1 is True, Statement-2 is False.
(c)
Between any two integers a and b, there is a rational number $\frac{a+b}{2}$.Between a and $\frac{a+b}{2}$, there is a rational number $\frac{a+\frac{a+b}{2}}{2}$.Continuing in this manner, we can find infinitely many rational numbers between a and b. So, statement-1 is true.
Let $x=\sqrt{\sqrt{3}}$, be an irrational number, then $x^2=\sqrt{3}$ is an irrational number. So, square of an irrational number is not necessarily a. rational number. Thus, statement-2 is not true.
Hence, option (c) is correct.
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MCQ 41 Mark
Statement-1 (A): The product of any two irrational numbers is an irrational number.
Statement-2 (R): There are two irrational numbers whose product is not an irrational number.
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • ✓
    Statement-1 is true, Statement-2 is false.
Answer
Correct option: D.
Statement-1 is true, Statement-2 is false.
d
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MCQ 51 Mark
Statement-1 (A): The decimal representation of $\frac{3}{8}$ is terminating.
Statement-2 (R): If the denominator of a rational number is of the form $2^m \times 5^n$, where m, n are non-negative integers, then its decimal representation is terminating.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement-1 is true, Statement-2 is false.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
a
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MCQ 61 Mark
Statement-1 (A): $\sqrt{3}$ is an irrational number.
Statement-2 (R): The square root of a positive integer which is not a perfect square is an irrational number.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement-1 is true, Statement-2 is false.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
a
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MCQ 71 Mark
Statement-1 (A): $\sqrt{2}$ is an irrational number.
Statement-2 (R): The sum of a rational number and an irrational number is an irrational number.
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement-1 is true, Statement-2 is false.
Answer
Correct option: B.
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
b
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MCQ 81 Mark
Statement-1 (A): $\sqrt{2}$ is an irrational number.
Statement-2 (R): The decimal expansion of $\sqrt{2}$ is non-terminating non-recurring.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement-1 is true, Statement-2 is false.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
a
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MCQ 91 Mark
Statement-1 (A): $\pi$ is an irrational number.
Statement-2 (R): Euler's constant e is an irrational number.
  • A
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-2
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: B.
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
(b)
$\pi$ and $e$ both are irrational numbers. It is not correct to say that is irrational because e is irrational. Thus, both the statements are true and statement-2 is not a correct explanation for statement-1. So, options (b) is correct.
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MCQ 101 Mark
Statement-1 (A): If x and y are rational and irrational numbers respectively, then x + y is an irrational number.
Statement-2 (R): If x and y are two irrational numbers, then x + y is an irrational number
  • A
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-4
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • ✓
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: C.
Statement-1 is True, Statement-2 is False.
(c)
If possible let x + y be a rational number equal to z, when x is rational and y is irrational.
Then,
$z=x+y \Rightarrow z-x=y \Rightarrow y$ is rational $[\because z-x$ rational $]$
This is a contradiction to fact that y is irrational. Hence, x + y is irrational. So, statement-2 is true.$x=\sqrt{2}$ and $y=3-\sqrt{2}$ are irrational numbers but x + y = 3 is a rational number. So, statement-2 need not be true. Thus, statement-1 is true and statement-2 is not true. Hence, option (c) is correct.
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MCQ 111 Mark
Statement-1 (A): $\frac{13}{20}$ $\frac{14}{20}$ and $\frac{15}{20}$ are three rational numbers between $\frac{1}{2}$ and $\frac{4}{5}$
Statement-2 (R): A rational number between two rational numbers $p$ and $q$ is $\frac{1}{2}(p+q)$.
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-3
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: A.
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-3
(a)
Statement-2 is true. Using statement-2, a rational number between $\frac{1}{2}$and $\frac{4}{5}$ is $\frac{1}{2}\left(\frac{1}{2}+\frac{4}{5}\right)=\frac{13}{20}$. But, $\frac{4}{5}=\frac{16}{20}$, So, rational numbers between $\frac{13}{20}$ and $\frac{16}{20}$ are $\frac{14}{20}$ and $\frac{15}{20}$
Hence, $\frac{13}{20}$, $\frac{14}{20}$ and $\frac{15}{20}$ are rational numbers between $\frac{1}{2}$ and $\frac{4}{5}$.Hence, statement-1 is true and statement-2 is correct explanation for statement-1. So, option (a) is correct.
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MCQ 121 Mark
Statement-1 (A): 0.7 and 0.00323232... are rational numbers.
Statement-2 (R): If the decimal expansion of a real number is either terminating or non-terminating recurring it is a rational number.
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: A.
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1
(a)
Statement-2, being the definition of a rational number, is true. Statement-1 is also true and statement-2 is a correct explanation for statement-1. Hence, option (a) is correct
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Assertion (A) & Reason (B) MCQ - Maths STD 9 Questions - Vidyadip