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MATHS Assertion (A) & Reason (B) MCQ

Number systems · Rajasthan Board (RBSE) STD 9 (Rajasthan - English Medium). 74 questions.

Questions · Page 1 of 2

Assertion (A) & Reason (B) MCQ

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50 questions · timed · auto-graded

Question 11 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: $\frac{1}{6}$ is the reciprocal of 6
Reason: Improper fraction is the fraction in which numerator is less than denominator.
  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 21 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: Natural numbers are a subset of integers.
Reason: Natural numbers without zero are called positive integers, and when written with a negative sign are called as 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. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 31 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 terminating decimal has a number of finite terms after the decimal point.
Reason: The decimal expansion of π is terminating.
  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 41 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: $5-\sqrt2=5-1.414=3.586$ is an irrational number.
Reason: The difference of a rational number and an irrational number is an irrational number.
  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 51 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: All the rational and irrational number makes up the collection of real number.
Reason: if r is rational and s is irrational then r + s and r - s are irraational 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 61 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: $\frac{10}{3}$ is non terminating Decimal expansion.
Reason: The remainder of non terminating Decimal expansion is never be 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 71 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 real number is either rational or irrational.
Reason: $ \sqrt7$ is a 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. Assertion is true but the reason is false.
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Question 81 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: $ 8\sqrt15\div2\sqrt3=4\sqrt5$
Reason: Quotient of non zero rational number with an irrational number 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 the correct explanation for Assertion.
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Question 91 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: 5° = 1
Reason: a° = 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. Assertion is true but the reason is false.
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Question 101 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: $\frac{1}{2}=\frac{3}{6}=\frac{4}{8}$ are the equivalent rational numbers.
Reason: Every rational number is 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. Assertion is true but the reason is false.
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Question 111 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 is the multiplicative identity of set of natural number.
Reason: $\sqrt{\text{ab}}=\sqrt{\text{a}}\sqrt{\text{b}}$
  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 121 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: $ 6\sqrt2+7\sqrt2$ is a rational number.
Reason: The sum of every rational and irrational number 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 the correct explanation for Assertion.
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Question 131 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: 0.271 is a terminating decimal and we can express this number as $\frac{271}{1000}$ which is of the form $\frac{\text{p}}{\text{q}}$, where p and q are integers and $q \neq0.$
Reason: A terminating or non - terminating decimal expansion can be expressed as rational number.
  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 correct statement but Reason is wrong statement.
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Question 141 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 151 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 161 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 171 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 181 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 191 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 201 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 211 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 221 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 231 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 241 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 251 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 261 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 271 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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MCQ 281 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: $(16)^4= 2^6$
  • A
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • B
    Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  • ✓
    Assertion is true but the reason is false.
  • D
    Both assertion and reason are false.
Answer
Correct option: C.
Assertion is true but the reason is false.
Assertion is true but the reason is false.
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Question 291 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 301 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 311 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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MCQ 321 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: $17^2 \times 17^5 = 17^3$
Reason: If$ a > 0$ be a real number and $p$ and $q$ be rational numbers. Then $a^p \times a^q = a^{p+q}.$
  • A
    Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  • B
    Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  • C
    Assertion is correct statement but Reason is wrong statement.
  • ✓
    Assertion is wrong statement but Reason is correct statement.
Answer
Correct option: D.
Assertion is wrong statement but Reason is correct statement.
$17^2 \times 17^5 = 17^{2+5} = 17^7$
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Question 331 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 341 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 351 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 361 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 371 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)
e is an irrational number.$\pi$ 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:
    e and $\pi$ both are irratinoal numbers
    So, both Assertion (A) and Reason (R) are true
    But the Reason (R) is not a correct explanation of Assertion (A), so (b) holds.
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Question 381 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: Decimal expansion of every rational number is only terminating.
Reason: Decimal expansion of every irrational number is terminating recurring.
  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 391 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 conjugate of $ 4+\sqrt6$ is $ 4-\sqrt6$
Reason: $\sqrt{27}$ is not a 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 not the correct explanation for Assertion.
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MCQ 401 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: $19^9\div 19^8= 19$
Reason: If $a > 0$ be a real number and $p$ and $q$ be rational number then $a^p\div a^q= a^{p - q}$
  • ✓
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • B
    Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  • C
    Assertion is true but the reason is false.
  • D
    Both assertion and reason are false.
Answer
Correct option: A.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
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Question 411 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: $2+\sqrt6$ is an irrational number.
Reason: Sum of a rational number and an irrational number is always an irrational number.
  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 421 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 431 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 a and b are two positive integers then HCF × LCM = a × b.
Reason: A number N Is divided by 15 gives the remainder 2 then the remainder is same when is divided by 5.
  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 441 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: $\sqrt5$ is an irrational number.
Reason: A number is called irrational, if it cannot be written in the form $\frac{\text{p}}{\text{q}},$ where p and q are integers and $\text{q}\neq 0.$
  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 451 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: $\sqrt2$ is an irrational number.
Reason: A number is called irrational, if it cannot be written in the form $\frac{\text{q}}{\text{p}},$ where p and q are integers and $\text{q}\neq0.$
  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 correct statement but Reason is wrong statement.
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Question 461 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: A rational number between $\frac{1}{3}$ and $\frac{1}{2}$ is $\frac{5}{12}.$
Reason: Rational number between two numbers a and b is $\sqrt{\text{ab}}.$
  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 correct statement but Reason is wrong statement.
    Solution:
    $\frac{1}{2}\Big(\frac{1}{3}+\frac{1}{2}\Big)=\frac{5}{12}$
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Question 471 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: Rational number lying between two rational numbers a and b is $\frac{\text{a}+\text{b}}{2}.$
Reason: There is one rational number lying between any two rational numbers.
  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 correct statement but Reason is wrong statement.
    Solution:
    There are infinitely many rational numbers between any two given rational numbers.
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Question 481 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: $\frac{7}{8}+\frac{9}{8}=\frac{16}{8}$
Reason: $\frac{\text{p}}{\text{q}}+\frac{\text{r}}{\text{q}}=\text{p}+\frac{\text{r}}{\text{q}}$
  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 491 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, 2, 3, 4 are the natural numbers.
Reason: $\frac{1}{4},\frac{2}{7}, \frac{9}{5}$ are the rational numbers.
  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 501 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  $\sqrt2=1.414.,$ $\sqrt3=1.732,$ then $\sqrt5=\sqrt2+\sqrt3.$
Reason: Square root of a positive real number always exists.
  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:
    $=\sqrt2+\sqrt3\neq5$
    $\sqrt3+\sqrt2=1.732+1.414=3.146\neq\sqrt5$ as $\sqrt5=2.236$
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Assertion (A) & Reason (B) MCQ - MATHS STD 9 Questions - Vidyadip