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Maths Assertion (A) & Reason (B) MCQ

Number systems · Jharkhand Board (JAC) STD 9 (Jharkhand - English Medium). 74 questions.

Questions

Assertion (A) & Reason (B) MCQ

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74 questions · auto-graded multiple-choice test.

MCQ 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: $ \text{x}^4=\frac{\text{X}^5}{\text{x}^1}.$
Reason: $ \frac{\text{a}^{\text{b}}}{\text{a}^{\text{c}}}=\text{a}^{\text{b - c}}.$
  • ✓
    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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MCQ 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: $\sqrt2,\sqrt3,$ are examples of irrational numbers.
Reason: An irrational number can be expressed in the form $\frac{\text{p}}{\text{q}}.$
  • 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.
  • ✓
    Assertion is correct statement but Reason is wrong statement.
  • D
    Assertion is wrong statement but Reason is correct statement.
Answer
Correct option: C.
Assertion is correct statement but Reason is wrong statement.
Assertion is correct statement but Reason is wrong statement.
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MCQ 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: $2, 3, 5, 7$ are the prime numbers.
Reason: A number, other than $1,$ which is not a prime number is called a composite number.
  • A
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • ✓
    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: B.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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MCQ 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: The product of two consecutive positive integers is divisible by $2$
Reason: The decimal expansion of $\frac{15}{169999}=0.0065789$
  • 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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MCQ 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: $32^{\frac{2}{5}}=4$
Reason: $(32)^{\frac{2}{5}}=(2^5)^{\frac{2}{5}}=22=4$
  • ✓
    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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MCQ 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: All whole numbers are rational number except $0.$
Reason: $a^m a^n=a^{m+n}$​​​​​​​
  • A
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • ✓
    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: B.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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MCQ 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: $\frac{1}{6}$ is the reciprocal of $6$
Reason: Improper fraction is the fraction in which numerator is less than denominator.
  • A
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • ✓
    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: B.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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MCQ 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: $(18, 25)$ is a pair of coprime numbers.
Reason: pair of coprime number has common factor $2.$
  • 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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MCQ 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: 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.
  • ✓
    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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MCQ 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: $7\sqrt5, \sqrt2+21$ are the irrational number.
Reason: Every integer is an rational number
  • A
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • ✓
    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: B.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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MCQ 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: The smallest perfect number is $6,$ which is the sum of $1, 2,$ and $3.$
Reason: The numbers which are the positive integers and which can be expressed as the sum of their proper divisors are called as perfect number.
  • ✓
    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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MCQ 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: $5-\sqrt2=5-1.414=3.586$ is an irrational number.
Reason: The difference of a rational number and an irrational number is an irrational number.
  • ✓
    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.
  • D
    Assertion is wrong statement but Reason is correct statement.
Answer
Correct option: A.
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
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MCQ 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: $0.468$ is a terminating decimal.
Reason: A decimal in which a digit or a set of digits is repeated periodically, is called a repeating, or a recurring decimal.
  • A
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  • ✓
    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: B.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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MCQ 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: The terminating decimal has a number of finite terms after the decimal point.
Reason: The decimal expansion of π is terminating.
  • 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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MCQ 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: $\frac{10}{3}$ is non terminating Decimal expansion .
Reason: The remainder of non terminating Decimal expansion is never be zero.
  • ✓
    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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MCQ 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: In $56.49$ the whole part is $56.00$
 Reason: In the number $3456$ the place value of $4$ is $400$
  • A
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  • ✓
    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: B.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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MCQ 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: 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.
  • ✓
    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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MCQ 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: If $\sqrt2=1.414.,$ $\sqrt3=1.732,$ then $\sqrt5=\sqrt2+\sqrt3.$
Reason: Square root of a positive real number always exists.
  • 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.

$=\sqrt2+\sqrt3\neq5$
$\sqrt3+\sqrt2=1.732+1.414=3.146\neq\sqrt5$ as $\sqrt5=2.236$

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MCQ 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: $1, 2, 3, 4$ are the natural numbers.
Reason: $\frac{1}{4},\frac{2}{7}, \frac{9}{5}$ are the rational numbers.
  • 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.
  • C
    Assertion is true but the reason is false.
  • ✓
    Both assertion and reason are false.
Answer
Correct option: D.
Both assertion and reason are false.
Both assertion and reason are false.
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MCQ 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: $ 8\sqrt15\div2\sqrt3=4\sqrt5$
Reason: Quotient of non zero rational number with an irrational number is irrational.
  • ✓
    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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MCQ 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: The real number is either rational or irrational.
Reason: $ \sqrt7$ is a rational number.
  • 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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MCQ 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: Every whole number is not a natural number.
Reason: Zero is whole number but not natural number.
  • ✓
    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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MCQ 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: Every rational number is written in the form if $\frac{\text{p}}{\text{q}}$ where $p$ and $q$ are integers, $q = 0$
Reason: $7\sqrt3$ is a rational number.
  • 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.
  • C
    Assertion is true but the reason is false.
  • ✓
    Both assertion and reason are false.
Answer
Correct option: D.
Both assertion and reason are false.
Both assertion and reason are false.
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MCQ 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: $\frac{1}{2}=\frac{3}{6}=\frac{4}{8}$ are the equivalent rational numbers.
Reason: Every rational number is an integer.
  • 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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MCQ 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: $\sqrt2$ is a irrational number.
Reason: It can not be written inthe form of $\frac{\text{p}}{\text{q}}.$
  • ✓
    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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MCQ 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: $5^\circ = 1$
Reason: $a^\circ = 1​​​​​​​$​​​​​​​
  • 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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MCQ 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: The Decimal fraction of $\frac{12}{125}$ is $0.096$
Reason: The Decimal fraction of $\frac{1}{9}$ is $0.111.$
  • A
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • ✓
    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: B.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not 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: $ 6\sqrt2+7\sqrt2$ is a rational number.
Reason: The sum of every rational and irrational number is irrational
  • ✓
    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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MCQ 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: $1$ is the multiplicative identity of set of natural number.
Reason: $\sqrt{\text{ab}}=\sqrt{\text{a}}\sqrt{\text{b}}$
  • A
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • ✓
    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: B.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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MCQ 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: $\sqrt{(7\times8)}=\sqrt7\times\sqrt8$
Reason: $\sqrt{\text{ab}}=\sqrt{\text{a}}\times\sqrt{\text{b}}$
  • ✓
    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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MCQ 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: Every integer is a rational number.
Reason: Every integer ‘m’ can be expressed in the form $\frac{\text{m}}{1}.$
  • ✓
    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.
  • D
    Assertion is wrong statement but Reason is correct statement.
Answer
Correct option: A.
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
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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: $0.271$ 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.
  • 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.
  • ✓
    Assertion is correct statement but Reason is wrong statement.
  • D
    Assertion is wrong statement but Reason is correct statement.
Answer
Correct option: C.
Assertion is correct statement but Reason is wrong statement.
Assertion is correct statement but Reason is wrong statement.
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MCQ 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: $15$ is the composite number.
Reason: $15$ is odd number.
  • A
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  • ✓
    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: B.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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MCQ 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: $\frac{7}{8}+\frac{9}{8}=\frac{16}{8}$
Reason: $\frac{\text{p}}{\text{q}}+\frac{\text{r}}{\text{q}}=\text{p}+\frac{\text{r}}{\text{q}}$
  • ✓
    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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MCQ 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: 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.
  • 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.
  • ✓
    Assertion is correct statement but Reason is wrong statement.
  • D
    Assertion is wrong statement but Reason is correct statement.
Answer
Correct option: C.
Assertion is correct statement but Reason is wrong statement.

There are infinitely many rational numbers between any two given rational numbers.

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MCQ 361 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 $0.296.$
  • ✓
    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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MCQ 371 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.
  • A
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • ✓
    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: B.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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MCQ 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: $7$ is rational number
Reason: Square root of all rational number is irrational.
  • 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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MCQ 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: Coprime number are the number which are the having $GCF$ as$1.$
Reason: Any two prime numbers does not form the pairs of coprime numbers.
  • 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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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: $ \sqrt{\text{n}}$ is rational if n is not a perfect square.
Reason: $\frac{1}{\text{an}}=\text{a}+\text{n}.$
  • 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.
  • C
    Assertion is true but the reason is false.
  • ✓
    Both assertion and reason are false.
Answer
Correct option: D.
Both assertion and reason are false.
Both assertion and reason are false.
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MCQ 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: The rationalize factor of $6+\sqrt7$ is $6-\sqrt7.$
Reason: $7, 8, 10,$ are the negative integers.
  • 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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MCQ 421 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.
  • 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.
  • C
    Assertion is true but the reason is false.
  • ✓
    Both assertion and reason are false.
Answer
Correct option: D.
Both assertion and reason are false.
Both assertion and reason are false.
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MCQ 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: $\frac{3}{5}$ is terminating decimal expansion
Reason: The remainder become zero.
  • ✓
    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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MCQ 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: $(2, 3), (3, 4), (5, 7)$ are the coprime numbers pair.
Reason: Two numbers are co $-$ prime of their $\text{HCF}$ is $1.$
  • ✓
    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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MCQ 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: The sum of first five prime number is $28.$
Reason: The sum of three consugative integer is $54.$
  • A
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • ✓
    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: B.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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MCQ 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: $31$ is rational number.
Reason: Square root of all rational number is always rational.
  • 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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MCQ 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: If p and q are prime, then $HCF (p, q) = 1$
Reason: $\frac{123}{6250}$ is a terminating Decimal.
  • A
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • ✓
    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: B.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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MCQ 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: $\sqrt2$ 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 $\text{q}\neq0.$
  • 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.
  • ✓
    Assertion is correct statement but Reason is wrong statement.
  • D
    Assertion is wrong statement but Reason is correct statement.
Answer
Correct option: C.
Assertion is correct statement but Reason is wrong statement.
Assertion is correct statement but Reason is wrong statement.
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MCQ 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: $3\sqrt7+4\sqrt7=7\sqrt7.$
Reason: $(3+4)\sqrt7= 7\sqrt7.$
  • ✓
    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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MCQ 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: The square root of any primenumber is irrational.
Reason: The rationlizong factor of $ 2+\sqrt7$ is $5+\sqrt3$
  • 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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MCQ 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: $\sqrt5$ 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 $\text{q}\neq 0.$
  • ✓
    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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MCQ 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: 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 $5.$
  • A
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • ✓
    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: B.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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MCQ 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 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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MCQ 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: $\frac{3}{5}-\frac{2}{12}=\frac{13}{30}$
Reason: $\frac{\text{p}}{\text{q}}-\frac{\text{r}}{\text{s}}={\text{ps}}-\frac{\text{qr}}{\text{qs}}$
  • ✓
    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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MCQ 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: $2+\sqrt6$ is an irrational number.
Reason: Sum of a rational number and an irrational number is always an irrational number.
  • ✓
    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.
  • D
    Assertion is wrong statement but Reason is correct statement.
Answer
Correct option: A.
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
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MCQ 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: $\{-1, -5, -6\}$ are the rational number.
Reason: All negative integers are rational number.
  • ✓
    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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MCQ 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: $19^9 \div 19^8=19$
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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MCQ 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: The conjugate of $ 4+\sqrt6$ is $ 4-\sqrt6$
Reason: $\sqrt{27}$ is not a rational number.
  • A
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • ✓
    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: B.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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MCQ 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: The rationalizing factor of $2+\sqrt5$ is $2-\sqrt5$
Reason: The product or quotient of non zero rational number with irrational number is rational.
  • ✓
    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
Assertion is true but the reason is false.
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MCQ 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: 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 $\sqrt{\text{ab}}.$
  • 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.
  • ✓
    Assertion is correct statement but Reason is wrong statement.
  • D
    Assertion is wrong statement but Reason is correct statement.
Answer
Correct option: C.
Assertion is correct statement but Reason is wrong statement.
$\frac{1}{2}\Big(\frac{1}{3}+\frac{1}{2}\Big)=\frac{5}{12}$
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MCQ 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: $17^2 \times 17^5=17^3$
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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MCQ 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: $4$ is the first smallest composite number.
Reason: $1$ is a prime number.
  • 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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MCQ 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: $\left(5^7\right)^3=5^{21}$
Reason: $9$ is a irrational number.
  • 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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MCQ 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: Decimal expansion of every rational number is only terminating.
Reason: Decimal expansion of every irrational number is terminating recurring.
  • 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.
  • C
    Assertion is true but the reason is false.
  • ✓
    Both assertion and reason are false.
Answer
Correct option: D.
Both assertion and reason are false.
Both assertion and reason are false.
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MCQ 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: Every rational number is an integer.
Reason: $\frac{3}{5}$ is not an integer.
  • ✓
    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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MCQ 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: Sum of two irrational numbers $5+\sqrt3$ and $7+\sqrt3$ is a irrational number.
Reason: If the product of two irraational numbers is rational the each one is called the rationalizing factor of other.
  • A
    Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  • ✓
    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: B.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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MCQ 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: $3 × 8 × 9 + 6$ is a composite number.
Reason: A composite number has factors one, any natural number and itself.
  • ✓
    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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MCQ 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: $HCF$ of $(23, 53)$ is $1.$
Reason: If $p$ anand are primes, then $HCF (p, q) = 1$
  • ✓
    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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MCQ 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: Sum of two natural numbers is a natural number.
Reason: All whole numbers are natural numbers.
  • 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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MCQ 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: every integer is a rational number
Reason: every integer is expressed in the form of $\frac{\text{m}}{1}$ so it is rational number
  • ✓
    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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MCQ 711 Mark
Consists of two statements, namely, Assertion $(A)$ and Reason $(R).$ For selecting the correct answer, use the following code:
Assertion (A)
Reason (R)
$\sqrt{3}$ is an irrational number.
Square root a positive integer which is not a perfect square is an irrational number.
The correct answer is: $(a), (b), (c), (d).$
  • ✓
    Both Assertion $(A)$ and Reason $(R)$ are true and Reason $(R)$ is a correct explanation of Assertion $(A).$
  • B
    Both Assertion $(A)$ and Reason $(R)$ are true but Reason is not a correct explanation of Assertion $(A).$
  • C
    Assertion $(A)$ is true and Reason $(R)$ is false.
  • D
    Assertion $(A)$ is false and Reason $(R)$ is true.
Answer
Correct option: A.
Both Assertion $(A)$ and Reason $(R)$ are true and Reason $(R)$ is a correct explanation of Assertion $(A).$
We know that if $\sqrt{\text{x}}$ is an irratinal number, it means $x$ is not a perfect square.
Thus, Assertion $(A)$ is true
Since Reason $(R)$ gives Assertion $(A),$ so $(a)$ holds.
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MCQ 721 Mark
Consists of two statements, namely, Assertion $(A)$ and Reason $(R).$ For selecting the correct answer, use the following code:
Assertion (A)
Reason (R)
e is an irrational number.
$\pi$ is an irrational number.
The correct answer is: $(a), (b), (c), (d).$
  • A
    Both Assertion $(A)$ and Reason $(R)$ are true and Reason $(R)$ is a correct explanation of Assertion $(A).$
  • ✓
    Both Assertion $(A)$ and Reason $(R)$ are true but Reason is not a correct explanation of Assertion $(A).$
  • C
    Assertion $(A)$ is true and Reason $(R)$ is false.
  • D
    Assertion (A) is false and Reason (R) is true.
Answer
Correct option: B.
Both Assertion $(A)$ and Reason $(R)$ are true but Reason is not a correct explanation of Assertion $(A).$
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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MCQ 731 Mark
Consists of two statements, namely, Assertion $(A)$ and Reason $(R).$ For selecting the correct answer, use the following code:
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: $(a), (b), (c), (d).$
  • ✓
    Both Assertion $(A)$ and Reason $(R)$ are true and Reason $(R)$ is a correct explanation of Assertion $(A).$
  • B
    Both Assertion $(A)$ and Reason $(R)$ are true but Reason is not a correct explanation of Assertion $(A).$
  • C
    Assertion $(A)$ is true and Reason $(R)$ is false.
  • D
    Assertion $(A)$ is false and Reason $(R)$ is true.
Answer
Correct option: A.
Both Assertion $(A)$ and Reason $(R)$ are true and Reason $(R)$ is a correct explanation of Assertion $(A).$
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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MCQ 741 Mark
Consists of two statements, namely, Assertion $(A)$ and Reason $(R).$ For selecting the correct answer, use the following code:
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: $(a), (b), (c), (d).$
  • A
    Both Assertion $(A)$ and Reason $(R)$ are true and Reason $(R)$ is a correct explanation of Assertion $(A).$
  • ✓
    Both Assertion $(A)$ and Reason $(R)$ are true but Reason is not a correct explanation of Assertion $(A).$
  • C
    Assertion $(A)$ is true and Reason $(R)$ is false.
  • D
    Assertion $(A)$ is false and Reason $(R)$ is true.
Answer
Correct option: B.
Both Assertion $(A)$ and Reason $(R)$ are true but Reason is not a correct explanation of Assertion $(A).$
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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