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.
AnswerCorrect 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.
View full question & answer→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.
AnswerCorrect 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.
View full question & answer→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.
AnswerCorrect option: C. Assertion is true but the reason is false.
Assertion is true but the reason is false.
View full question & answer→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.
AnswerCorrect 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.
View full question & answer→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.
AnswerCorrect 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.
View full question & answer→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.
AnswerCorrect 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.
View full question & answer→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.
AnswerCorrect 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.
View full question & answer→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.
AnswerCorrect 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.
View full question & answer→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.
AnswerCorrect option: A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Assertion is true but the reason is false.
View full question & answer→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.
AnswerCorrect option: C. Assertion is correct statement but Reason is wrong statement.
$\frac{1}{2}\Big(\frac{1}{3}+\frac{1}{2}\Big)=\frac{5}{12}$
View full question & answer→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.
AnswerCorrect option: D. Assertion is wrong statement but Reason is correct statement.
$17^2 \times 17^5=17^{2+5}=17^7$
View full question & answer→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.
AnswerCorrect option: C. Assertion is true but the reason is false.
Assertion is true but the reason is false.
View full question & answer→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.
AnswerCorrect option: C. Assertion is true but the reason is false.
Assertion is true but the reason is false.
View full question & answer→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.
AnswerCorrect option: D. Both assertion and reason are false.
Both assertion and reason are false.
View full question & answer→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.
AnswerCorrect 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.
View full question & answer→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.
AnswerCorrect 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.
View full question & answer→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.
AnswerCorrect 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.
View full question & answer→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.
AnswerCorrect 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.
View full question & answer→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.
AnswerCorrect option: C. Assertion is true but the reason is false.
Assertion is true but the reason is false.
View full question & answer→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.
AnswerCorrect 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
View full question & answer→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.
AnswerCorrect 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.
View full question & answer→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.
AnswerCorrect 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.
View full question & answer→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.
AnswerCorrect 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.
View full question & answer→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.
AnswerCorrect 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 $(A).$
View full question & answer→