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MATHS Assertion (A) & Reason (B) MCQ

Polynomials · Rajasthan Board (RBSE) STD 9 (Rajasthan - English Medium). 65 questions.

Questions · Page 2 of 2

Assertion (A) & Reason (B) MCQ

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: $If (x - 1)$ is the factor of $4x^3+ 3x^2- 4x + k$ then $k = -3.$
Reason: $(x + y)^2 = x^2+ y^2+ 2xy.$
  • 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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Question 521 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: In a homogeneous expression, all the terms will have same degree.
Reason: The degree of the equation, given (x + 2) (x - 1) = (x + 1) (x + 3), is 1.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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Question 531 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If one zero of polynomial p(x) = (k2 + 4) x2 + 13x + 4k is reciprocal of the other, then k = 2.
Reason: If (x - a) is a factor of p(x), then p(a) = 0 i.e., a is a zero of p(x).
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
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MCQ 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: $x^3+ 0x^2+ 0x - 64$ by $x - 4$ quotient is $x^2+ 4x + 16.$
Reason: Dividend $=$ divisor $\times$ quotient $+$ remainder
  • ✓
    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: If $a^3- 3a^2b + 3ab^2$ is divided by $a - b$ then the remainder is $0$
Reason: A linear polynomial is always represented by straigth line.
  • 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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Question 561 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The degree of the sum of two polynomials each of degree 5 is always 5.
Reason: 3x - 2 is a quadratic polynomial.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
Answer
  1. Both assertion and reason are false.
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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: $4x^2+ 7x + 8$ cofficent of the polynomial are $4, 7, 8.$
Reason: $8$ is the constant term in above polynomial.
  • 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 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 factor of $x^4+ 4$ are $(x^2+ 2x + 2) (x^2- 2x + 2).$
Reason: The sum of zeroes of $ax^2+ bx + c$ is $\frac{\text{-b}}{\text{a}}.$
  • 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 $\text{LCM}$ of $(x^2+ x - 6)$ and $4 (4 - x)^2$ is $4 (x + 3) (x + 2) (x - 2)$
Reason: $x^{100}+ 2x^{99}+ k$ is divisible by $(x + 1)$ then the value of $k$ is $2.$
  • 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 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 quadratic polynomial can have at most two zero.
Reason: $x^2+ 7x + 9$ has two zero.
  • 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 611 Mark
Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The value of polynomial $x^8- x^5+ x^2- x + 1$ is positive for all real numbers.
Reason: $f (x)$ is positive f$ (x) > 0, f(x)$ is positive for all real value $x.$
  • ✓
    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 621 Mark
$\text{LCM}$ 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 zeroes of the quadratic polynomial $x^2+ 99x + 127$ are more than $4.$
Reason: The number of polynomials having zeroes as $-2$ and $5$ is $1.$
  • 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 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: Degree of $\text{p}(\text{x})= \frac{-2}{7}$ is $0.$
Reason: Degree of $p(x) = x^3y^2z^5$ is $10.$
  • 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 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: If one zero of poly $-$ nominal $p(x) = (k^2+ 4) x^2 + 13x + 4k$ is reciprocal of other, then $k = 2.$
Reason: $If (x - a)$ is a factor of $p(x),$ then $p(a) = 0$ i.e. a is a zero of $p(x)$
  • 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 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: $(3x + 4y)^3= 27x^3+ 64y^3+ 36xy (3x + 4y).$
Reason: $(x + y)^3= x^3+ y^3+ 3xy (x + y).$
  • ✓
    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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