Assertion (A) & Reason (B) MCQ - Maths STD 8 Questions - Vidyadip

Questions

Assertion (A) & Reason (B) MCQ

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60 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 (A): The factorisation of $x^2yz + xy^2z + xyz^2$ is $xyz^2(x + y + z).$
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
✓
$A$ is false but $R$ is true.

Answer

Correct option: D.

$A$ is false but $R$ is true.

$A$ is false but $R$ is true.

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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 (A): The factorisation of $a^3+a^2 b+a b^2$ is a $\left(a^2+a b+b^2\right)$
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer

Correct option: A.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.

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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 (A): The common factor of $7^2 x^3 y^4 z^4, 120 z^2 d^4 x^4$ and $96 y^3 z^4 d^4$ is $72 z^3$
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
✓
$A$ is false but $R$ is true.

Answer

Correct option: D.

$A$ is false but $R$ is true.

$A$ is false but $R$ is true.

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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 (A): The factorisation of $6x + 12y$ is $6 (x + 2y)$
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer

Correct option: A.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.

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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 (A): The common factor of $x^3y^2$ and $x^4y$ is $x^3y$.
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer

Correct option: A.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.

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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 (A): The common factor of $10ab, 30bc, 50ca$ is $10$ Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer

Correct option: A.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.

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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 (A): The common factor of $a^2 m^4$ and $a^4 m^2$ is $a^2 m^4$
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
✓
$A$ is false but $R$ is true.

Answer

Correct option: D.

$A$ is false but $R$ is true.

$A$ is false but $R$ is true.

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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 (A): The factorisation of $10 x^2-18 x^3+14 x^4$ is $2\left(7 x^2-9 x+5\right)$
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
✓
$A$ is false but $R$ is true.

Answer

Correct option: D.

$A$ is false but $R$ is true.

$A$ is false but $R$ is true.

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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 (A): The common factor of $14a^2b$ and $35a^4b^2$ is $14a^2b$
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
C
$A$ is true but $R$ is false.
✓
$A$ is false but $R$ is true.

Answer

Correct option: D.

$A$ is false but $R$ is true.

$A$ is false but $R$ is true.

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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 (A): The factorisation of $a (x + y + z) + b (x + y + z) + c (x + y + z)$ is $(xy + yz + zx) (a + b + c)$
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
C
$A$ is true but $R$ is false.
✓
$A$ is false but $R$ is true.

Answer

Correct option: D.

$A$ is false but $R$ is true.

$A$ is false but $R$ is true.

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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 (A): The factorisation of $6xy - 4y + 6 - 9x$ is $(3x - 2) (2y - 3)$
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer

Correct option: A.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$

Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$

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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 (A): The common factor of $x^2 y^2$ and $x^3 y^3$ is $x^2 y^2$
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
B
Both $A$ and $R $ are true but $R$ is not the correct explanation of $A.$
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer

Correct option: A.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$

Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$

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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 (A): The common factor of $36 p^2 q^3 x^4, 48 p q^3 x^2$ and $54 p^3 q^3 x^4$ is $6 p q^3 x^2$
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer

Correct option: A.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$

Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$

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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 (A): The factorisation of $x^2+ xy + 2x + 2y$ is $(x + 2) (x - y)$
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
✓
$A$ is false but $R$ is true.

Answer

Correct option: D.

$A$ is false but $R$ is true.

$A$ is false but $R$ is true.

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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 (A): The common factor $12y$ and $30$ is $12$
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
C
$A$ is true but $R$ is false.
✓
$A$ is false but $R$ is true.

Answer

Correct option: D.

$A$ is false but $R$ is true.

$A$ is false but $R$ is true.

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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 (A): The factorisation of $28 a^3 b^5-42 a^5 b^3$ is $14 a^3 b^3\left(2 b^2-3 a^2\right)$
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer

Correct option: A.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$

Both $A $ and $R$ are true and $R$ is the correct explanation of $A.$

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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 (A): The common factor of $6 a^3 b^4 c^2, 21 a^2 b$ and $15 a^3$ is $3 a^2$
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer

Correct option: A.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$

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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 (A): The common factor of $p^3 q^4$ and $p^4 q^3$ is $p^3 q^3$
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer

Correct option: A.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$

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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 (A): The common factor of $24 x^3 y^4, 36 x^4 z^4$ and $48 x^3 y^2 z$ is $12 x^3$
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer

Correct option: A.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$

Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$

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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 (A): The common factor of $2 a^2 b^4 c^2, 8 a^4 b^3 c^4$ and $6 a^3 b^4 c^2$ is $2 a^2 b^3 c^2$
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer

Correct option: A.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$

Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$

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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 (A): The factorisation of $ax + bx - ay - by$ is $(x - y) (a + b)$
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer

Correct option: A.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$

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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 (A): The factorisation of $ax^2y + bxy^2+ cxyz$ is $axy (ax + by + cz)$
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
C
$A$ is true but $R$ is false.
✓
$A$ is false but $R$ is true.

Answer

Correct option: D.

$A$ is false but $R$ is true.

$A$ is false but $R$ is true.

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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 (A): The factorisation of $6x - 42$ is $6 (x + 7)$
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
✓
$A$ is false but $R$ is true.

Answer

Correct option: D.

$A$ is false but $R$ is true.

$A$ is false but $R$ is true.

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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 (A): The common factor of $3 a^2 b^4 c^2, 12 b^2 c^4$ and $15 a^3 b^4 c^4$ is $15 b^2 c^4$
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
✓
$A$ is false but $R$ is true.

Answer

Correct option: D.

$A$ is false but $R$ is true.

$A$ is false but $R$ is true.

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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 (A): The common factor of $8 a^2 b^4 c^2, 12 a^4 b c^4$ and $20 a^3 b^4$ is $4 a^2 b$
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
✓
$A$ is false but $R$ is true.

Answer

Correct option: D.

$A$ is false but $R$ is true.

$A$ is false but $R$ is true.

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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 (A): The common factor of $2x, 3 × 3, 4$ is $1$
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer

Correct option: A.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$

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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 (A): The factorisation of $ab - a - b + 1$ is $(a - 1) (b - 1)$
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer

Correct option: A.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.

Both $A$ and $R$ are true and $R$ is the correct explanation of $ A.$

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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 (A): The factorisation of $x^2+ x + xy + y + zx + z$ is $(x + y + z) (x + y)$
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
✓
$A$ is false but $R$ is true.

Answer

Correct option: D.

$A$ is false but $R$ is true.

$A$ is false but $R$ is true.

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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 (A): The factorisation of $12a^2b + 15ab^2$ is $3ab (4a + 5b)$
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
C
$A$ is true but $R$ is false.
D
$A$ is false but $R$ is true.

Answer

Correct option: A.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.

Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$

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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 (A): The factorisation of $x^2 y^2+x y+x y^2 z+y z+x^2 y z+x z$ is $(x y+y z+z x)(z x+1)$
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
C
$A$ is true but $R$ is false.
✓
$A$ is false but $R$ is true.

Answer

Correct option: D.

$A$ is false but $R$ is true.

$A$ is false but $R$ is true.

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MCQ 311 Mark

Assertion (A): The factorisation of 6xy - 4y + 6 - 9x is (3x - 2) (2y - 3)
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.

Answer

Correct option: A.

Both A and R are true and R is the correct explanation of A.

A

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MCQ 321 Mark

Assertion (A): The factorisation of 6x + 12y is 6 (x + 2y)
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.

Answer

Correct option: A.

Both A and R are true and R is the correct explanation of A.

A

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MCQ 331 Mark

Assertion (A): The factorisation of 12a²b + 15ab² is 3ab (4a + 5b)
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.

Answer

Correct option: A.

Both A and R are true and R is the correct explanation of A.

A

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MCQ 341 Mark

Assertion (A): The common factor of 7²x³y⁴z⁴, 120z²d⁴x⁴ and 96y³z⁴d⁴ is 72z³
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
✓
A is false but R is true.

Answer

Correct option: D.

A is false but R is true.

D

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MCQ 351 Mark

Assertion (A): The common factor of 2x, 3 × 3, 4 is 1
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

✓
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.

Answer

Correct option: A.

Both A and R are true and R is the correct explanation of A.

A

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MCQ 361 Mark

Assertion (A): The common factor of 2a²b⁴c², 8a⁴b³c⁴ and 6a³b⁴c² is 2a²b³c²
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

✓
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.

Answer

Correct option: A.

Both A and R are true and R is the correct explanation of A.

A

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MCQ 371 Mark

Assertion (A): The common factor of 10ab, 30bc, 50ca is 10
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

✓
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.

Answer

Correct option: A.

Both A and R are true and R is the correct explanation of A.

A

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MCQ 381 Mark

Assertion (A): The common factor 12y and 30 is 12
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
✓
A is false but R is true.

Answer

Correct option: D.

A is false but R is true.

D

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MCQ 391 Mark

Assertion (A): The factorisation of x²y² + xy + xy²z + yz + x²yz + xz is (xy + yz + zx) (zx + 1)
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
✓
A is false but R is true.

Answer

Correct option: D.

A is false but R is true.

D

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MCQ 401 Mark

Assertion (A): The factorisation of x²yz + xy²z + xyz² is xyz²(x + y + z).
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
✓
A is false but R is true.

Answer

Correct option: D.

A is false but R is true.

D

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MCQ 411 Mark

Assertion (A): The factorisation of x² + xy + 2x + 2y is (x + 2) (x - y)
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
✓
A is false but R is true.

Answer

Correct option: D.

A is false but R is true.

D

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MCQ 421 Mark

Assertion (A): The factorisation of x² + x + xy + y + zx + z is (x + y + z) (x + y)
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
✓
A is false but R is true.

Answer

Correct option: D.

A is false but R is true.

D

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MCQ 431 Mark

Assertion (A): The factorisation of a (x + y + z) + b (x + y + z) + c (x + y + z) is (xy + yz + zx) (a + b + c)
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
✓
A is false but R is true.

Answer

Correct option: D.

A is false but R is true.

D

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MCQ 441 Mark

Assertion (A): The factorisation of ax²y + bxy² + cxyz is axy (ax + by + cz)
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
✓
A is false but R is true.

Answer

Correct option: D.

A is false but R is true.

D

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MCQ 451 Mark

Assertion (A): The factorisation of ax + bx - ay - by is (x - y) (a + b)
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.

Answer

Correct option: A.

Both A and R are true and R is the correct explanation of A.

A

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MCQ 461 Mark

Assertion (A): The factorisation of a³ + a²b + ab² is a (a² + ab + b²)
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.

Answer

Correct option: A.

Both A and R are true and R is the correct explanation of A.

A

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MCQ 471 Mark

Assertion (A): The factorisation of ab - a - b + 1 is (a - 1) (b - 1)
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.

Answer

Correct option: A.

Both A and R are true and R is the correct explanation of A.

A

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MCQ 481 Mark

Assertion (A): The factorisation of 6x - 42 is 6 (x + 7)
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
✓
A is false but R is true.

Answer

Correct option: D.

A is false but R is true.

D

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MCQ 491 Mark

Assertion (A): The factorisation of 28a³b⁵ - 42a⁵b³ is 14a³b³(2b² - 3a²)
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.

Answer

Correct option: A.

Both A and R are true and R is the correct explanation of A.

A

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MCQ 501 Mark

Assertion (A): The factorisation of 10x² - 18x³ + 14x⁴ is 2 (7x² - 9x + 5)
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
✓
A is false but R is true.

Answer

Correct option: D.

A is false but R is true.

D

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MCQ 511 Mark

Assertion (A): The common factor of x³y² and x⁴y is x³y.
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.

Answer

Correct option: A.

Both A and R are true and R is the correct explanation of A.

A

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MCQ 521 Mark

Assertion (A): The common factor of x²y² and x³y³ is x²y²
Reasons (R): The factorisation is defined as expressing or decomposing a number or an algebraic expression as a product of its prime factors or irreducible factors.

✓
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.

Answer

Correct option: A.

Both A and R are true and R is the correct explanation of A.

A

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MCQ 531 Mark

Assertion (A): The common factor of p³q⁴ and p⁴q³ is p³q³
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

✓
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.

Answer

Correct option: A.

Both A and R are true and R is the correct explanation of A.

A

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MCQ 541 Mark

Assertion (A): The common factor of a²m⁴ and a⁴m² is a²m⁴
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
✓
A is false but R is true.

Answer

Correct option: D.

A is false but R is true.

D

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MCQ 551 Mark

Assertion (A): The common factor of 8a²b⁴c², 12a⁴bc⁴ and 20a³b⁴ is 4a²b.
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
✓
A is false but R is true.

Answer

Correct option: D.

A is false but R is true.

D

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MCQ 561 Mark

Assertion (A): The common factor of 6a³b⁴c², 21a²b and 15a³ is 3a²
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

✓
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.

Answer

Correct option: A.

Both A and R are true and R is the correct explanation of A.

A

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MCQ 571 Mark

Assertion (A): The common factor of 3a²b⁴c², 12b²c⁴ and 15a³b⁴c⁴ is 15b²c⁴
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
✓
A is false but R is true.

Answer

Correct option: D.

A is false but R is true.

D

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MCQ 581 Mark

Assertion (A): The common factor of 36p²q³x⁴, 48pq³x² and 54p³q³x⁴ is 6pq³x²
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

✓
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.

Answer

Correct option: A.

Both A and R are true and R is the correct explanation of A.

A

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MCQ 591 Mark

Assertion (A): The common factor of 24x³y⁴, 36x⁴z⁴ and 48x³y²z is 12x³
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

✓
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
D
A is false but R is true.

Answer

Correct option: A.

Both A and R are true and R is the correct explanation of A.

A

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MCQ 601 Mark

Assertion (A): The common factor of 14a²b and 35a⁴b² is 14a²b
Reasons (R): A common factor is a number that can be divided into two different numbers, without leaving a remainder.

A
Both A and R are true and R is the correct explanation of A.
B
Both A and R are true but R is not the correct explanation of A.
C
A is true but R is false.
✓
A is false but R is true.

Answer

Correct option: D.

A is false but R is true.

D

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