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MATHS Assertion (A) & Reason (B) MCQ

Linear Inequalities · UP Board (UPMSP) STD 11 Science (UPMSP - English Medium). 4 questions.

Questions

Assertion (A) & Reason (B) MCQ

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4 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: If $11\text{x}-9\leq68,$ then $\text{x}\in(-\infty,7).$
Reason: If an inequality consist of signs $\leq$ or $\geq,$ then the point on the line are also included in the solution region.
  • 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.
we have, $11\text{x}-9\leq68$
$\Rightarrow11\text{x}\leq77$
$\Rightarrow\text{x}\leq7$
$\therefore\text{x}\in(-\infty,7).$
So, Assertion is wrong but Reason is correct.
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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:$|38x - 5| > 9\Rightarrow\text{x}\in\Big(-\infty,\frac{-4}{3}\Big)\cup\Big(\frac{14}{3},\infty\Big).$
Reason: The region containing all the solutions of an inequality is called the solution region.
  • A
    Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  • ✓
    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: B.
Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
We have, $|3x - 5| > 9$
$\Rightarrow 3x - 5 < -9$ or $3x - 5 > 9$
$\Rightarrow 3x < -4$ or $3x > 14$
$\Rightarrow\text{x}<\frac{-4}{3}$ or $\text{x}<\frac{14}{3}$
$\therefore\text{x}\in\Big(-\infty,\frac{-4}{3}\Big)\cup\Big(\frac{14}{3},\infty\Big).$
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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: If f $a < b, c < 0,$ then $\frac{\text{a}}{\text{c}}<\frac{\text{b}}{\text{c}}.$
Reason: If both sides are divided by the same negative quantity, then the inequality is reversed.
  • 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.
Because if $a < b, c < 0$ then $\frac{\text{a}}{\text{c}}<\frac{\text{b}}{\text{c}}.$
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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: If $\text{x}\geq-3,$ then $\text{x}+5\geq2.$
Reason: Same number can be added to both sides of the inequality without changing the sign of inequality.
  • ✓
    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.
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