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Maths Assertion (A) & Reason (B) MCQ

Number systems · Gujarat Board (GSEB) STD 9 (GSEB - English Medium). 74 questions.

Questions · Page 2 of 2

Assertion (A) & Reason (B) MCQ

Question 511 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Every integer is a rational number.
Reason: Every integer ‘m’ can be expressed in the form $\frac{\text{m}}{1}.$
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
Answer
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
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Question 521 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: 15 is the composite number.
Reason: 15 is odd number.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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Question 531 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The difference of rational and irrational number is irrational.
Reason: Product of rational and irrational is irrational.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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Question 541 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Every point on the number line corresponds to a real number which may be either rational or irrational.
Reason: The Decimal representaion of the rational number $ \frac{8}{27}$ is 0.296.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 551 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $\frac{1}{7}$ and $\frac{2}{7}$ in between only five irrational number are present.
Reason: Every rational number between limited irrational number are present.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both assertion and reason are false.
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Question 561 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The rationalize factor of $6+\sqrt7$ is $6-\sqrt7.$
Reason: 7, 8, 10, are the negative integers.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Assertion is true but the reason is false.
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Question 571 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $ \sqrt{\text{n}}$ is rational if n is not a perfect square.
Reason: $\frac{1}{\text{an}}=\text{a}+\text{n}.$
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both assertion and reason are false.
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Question 581 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If p and q are prime, then HCF (p, q) = 1
Reason: $\frac{123}{6250}$ is a terminating Decimal.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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Question 591 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: (2, 3), (3, 4), (5, 7) are the coprime numbers pair.
Reason: Two numbers are co - prime of their HCF is 1.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 601 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $\frac{3}{5}$ is terminating decimal expansion
Reason: The remainder become zero.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 611 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The square root of any primenumber is irrational.
Reason: The rationlizong factor of $ 2+\sqrt7$ is $5+\sqrt3$
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Assertion is true but the reason is false.
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Question 621 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The sum of first five prime number is 28.
Reason: The sum of three consugative integer is 54.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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Question 631 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $3\sqrt7+4\sqrt7=7\sqrt7.$
Reason: $(3+4)\sqrt7= 7\sqrt7.$
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 641 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: $\frac{3}{5}-\frac{2}{12}=\frac{13}{30}$
Reason: $\frac{\text{p}}{\text{q}}-\frac{\text{r}}{\text{s}}={\text{ps}}-\frac{\text{qr}}{\text{qs}}$
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 651 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The rational number equivalent to $\frac{7}{9}$ is $\frac{49}{63}.$
Reason: (16)4 = 26
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Assertion is true but the reason is false.
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Question 661 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: {-1, -5, -6} are the rational number.
Reason: All negative integers are rational number.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 671 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The rationalizing factor of $2+\sqrt5$ is $2-\sqrt5$
Reason: The product or quotient of non zero rational number with irrational number is rational.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Assertion is true but the reason is false.
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Question 681 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: 4 is the first smallest composite number.
Reason: 1 is a prime number.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Assertion is true but the reason is false.
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Question 691 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: every integer is a rational number
Reason: every integer is expressed in the form of $\frac{\text{m}}{1}$ so it is rational number
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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Question 701 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: 3 × 8 × 9 + 6 is a composite number.
Reason: A composite number has factors one, any natural number and itself.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 711 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Every rational number is an integer.
Reason: $\frac{3}{5}$ is not an integer.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 721 Mark
Consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:
  1. Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
  2. Both Assertion (A) and Reason (R) are true but Reason is not a correct explanation of Assertion (A).
  3. Assertion (A) is true and Reason (R) is false.
  4. Assertion (A) is false and Reason (R) is true.
Assertion (A)Reason (R)
$\sqrt{3}$ is an irrational number.The sum of rational number and an irrational number is an irrational number.
The correct answer is: (a), (b), (c), (d).
Answer
  1. Both Assertion (A) and Reason (R) are true but Reason is not a correct explanation of Assertion (A).
    Solution:
    If possible, let $\sqrt{3}$ be a rational number and its simplest form is $\frac{\text{a}}{\text{b}}.$
    Then, $\sqrt{3}=\frac{\text{a}}{\text{b}}\Rightarrow\frac{\text{a}^2}{\text{b}^2}=3\Rightarrow\frac{\text{a}^2}{\text{b}}=3\text{b}$
    Clearly, 3b is an integer and $\frac{\text{a}^2}{\text{b}}$ is not an integer since (a, b) = 1
    Thus, we arrive at a contradiction
    So, our supposition is wrong
    Hence, $\sqrt{3}$ is an irrational number
    So, the Assertion (A) is true.
    If possible, let the sum of a rational number a and an irrational number $\sqrt{\text{b}}$ be a rational number
    Then, $\text{a}+\sqrt{\text{b}}=\text{c}\Rightarrow\sqrt{\text{b}}=\text{c}-\text{a}$
    But, the difference of two irrational is a rational
    So, (c - a) is rational and thus, $\sqrt{\text{b}}$ is rational
    Thus, we arrive at a contradiction
    So, our supposition is wrong
    Hence, the sum of a rational and an irrational is irrational
    So, the reason (R) is true.
    Hence, the Assertion (A) and Reason (R) are true but Reason is not a correct explanation of Assertion (A).
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Question 731 Mark
Consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:
  1. Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
  2. Both Assertion (A) and Reason (R) are true but Reason is not a correct explanation of Assertion (A).
  3. Assertion (A) is true and Reason (R) is false.
  4. Assertion (A) is false and Reason (R) is true.
Assertion (A)Reason (R)
Three rational numbers between $\frac{2}{3}$ and $\frac{3}{5}$ are $\frac{9}{20},\frac{10}{20}$ and $\frac{11}{20}.$A rational number between two rational numbers p and q is $\frac{1}{2}(\text{p}+\text{q}).$
The correct answer is: (a), (b), (c), (d).
Answer
  1. Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
    Solution:
    We know that $\frac{1}{2}(\text{p}+\text{q})$ is a rational number between two given rational numbers p and q. Thus, Reason (R) is true.
    A rational number between $\frac{2}{5}$ and $\frac{3}{5}$ is $\frac{1}{2}\Big(\frac{2}{5}+\frac{3}{5}\Big)=\frac{5}{10}$
    A rational number between $\frac{2}{5}$ and $\frac{5}{10}$ is $\frac{1}{2}\Big(\frac{2}{5}+\frac{5}{10}\Big)=\frac{9}{20}$
    A rational number between $\frac{5}{10}$ and $\frac{3}{5}$ is $\frac{1}{2}\Big(\frac{5}{10}+\frac{3}{5}\Big)=\frac{11}{20}$
    $\therefore$ Three rational numbers between $\frac{2}{5}$ and $\frac{3}{5}$ are $\frac{9}{20},\frac{10}{20}$ and $\frac{11}{20}$
    Thus, Assertion (A) is true
    Since Reason (R) gives Assertion (A), so (a) holds.
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Question 741 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: 172 × 175 = 173
Reason:: If a > 0 be a real number and p and q be rational numbers. Then ap × aq = ap+q.
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
Answer
  1. Assertion is wrong statement but Reason is correct statement.
    Solution:
    172 × 175 = 172+5 = 177
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Assertion (A) & Reason (B) MCQ - Page 2 - Maths STD 9 Questions - Vidyadip