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MATHS Assertion (A) & Reason (B) MCQ

Cubes and Cube Roots · Gujarat Board (GSEB) STD 8 (GSEB - English Medium). 5 questions.

Questions

Assertion (A) & Reason (B) MCQ

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5 questions · timed · auto-graded

MCQ 11 Mark
Assertion (A): If $x$ and $y$ are integers such that $x^2>y^2$ then $x^3>y^3$.
Reason (R): Squares of negative integers are positive while their cubes are negative.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • ✓
    Assertion (A) is false but Reason (R) is true.
Answer
Correct option: D.
Assertion (A) is false but Reason (R) is true.
(D) Assertion (A) is false but Reason (R) is true.
Let $x=-2$ and $y=-1$.
Then, $x^2=(-2)^2=4$ and $y^2=(-1)^2=1$. So, $x^2>y^2$.
But, $x^3=(-2)^3=-8$ and $y^3=(-1)^3=-1$. So, $x^3<y^3$.
So, A is false. But, R is true.
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MCQ 21 Mark
Assertion (A): $\left[(-1)^3 \times 2^3 \times(-3)^3 \times 4^3\right]$ is a positive number.
Reason (R): The cube of a negative number is negative while that of a positive number is positive.
  • ✓
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • D
    Assertion (A) is false but Reason (R) is true.
Answer
Correct option: A.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
$(-1)^3 \times 2^3 \times(-3)^3 \times 4^3=(-v e) \times(+v e) \times(-v e) \times(+v e)=(+v e).$
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MCQ 31 Mark
Assertion (A): Each one of $(11)^3,(17)^3$ and $(19)^3$ has only 3 factors in all.
Reason (R): The cube of a prime number always has 3 factors in all namely, 1 , the prime number and the number itself.
  • ✓
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • D
    Assertion (A) is false but Reason (R) is true.
Answer
Correct option: A.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
A
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MCQ 41 Mark
Assertion (A): $3^3>3,(10)^3>10,\left(\frac{6}{5}\right)^3>\frac{6}{5}$
Reason (R): The cube of a rational number is always greater than the number.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • ✓
    Assertion (A) is true but Reason (R) is false.
  • D
    Assertion (A) is false but Reason (R) is true.
Answer
Correct option: C.
Assertion (A) is true but Reason (R) is false.
(C) Assertion (A) is true but Reason (R) is false.
$3^3=27>3 ; 10^3=1000>10 ;\left(\frac{6}{5}\right)^3=\frac{216}{125}>\frac{6}{5}$.
So, A is true.
The cube of a rational number greater than 1 is greater than the number while the cube of a rational number less than 1 is smaller than the number. So, R is false.
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MCQ 51 Mark
Assertion (A): $\left(1 \frac{1}{5}\right)^3=1 \frac{1}{125}$
Reason (R): To find the cube of a mixed fraction, we need to convert it into an improper fraction before finding its cube.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • ✓
    Assertion (A) is false but Reason (R) is true.
Answer
Correct option: D.
Assertion (A) is false but Reason (R) is true.
(D) Assertion (A) is false but Reason (R) is true.
$
\left(1 \frac{1}{5}\right)^3=\left(\frac{6}{5}\right)^3=\frac{216}{125}=1 \frac{91}{125}
$
So, A is false but R is true.
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Assertion (A) & Reason (B) MCQ - MATHS STD 8 Questions - Vidyadip