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MATHS Assertion (A) & Reason (B) MCQ

Linear Inequalities · Rajasthan Board (RBSE) STD 11 Science (Rajasthan - English Medium). 5 questions.

Questions

Assertion (A) & Reason (B) MCQ

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5 questions · self-marked practice — reveal the answer and mark yourself.

Question 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.
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
Answer
  1. Assertion is wrong statement but Reason is correct statement.

Solution:

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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Question 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.

  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
Answer
  1. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.

Solution:

We have, |3x - 5| > 9

⇒ 3x - 5 < -9 or 3x - 5 > 9

⇒ 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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Question 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 $-5\leq2\text{x}+9\leq2,$ then $\text{x}\in[-7,-3.5].$

Reason: The graphical representation of $-5\leq2\text{x}+9\leq2$ is

  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
Answer
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.

Solution:

We have, $-5\leq2\text{x}+9\leq2$

$\Rightarrow-14\leq2\text{x}\leq-7$

$\Rightarrow-7\leq\text{x}\leq\frac{-7}{2}$

$\therefore\text{x}\in\Big[-7,\frac{-7}{2}\Big].$

 

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Question 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 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.
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
Answer
  1. Assertion is wrong statement but Reason is correct statement.

Solution:

Because if a < b, c < 0 then $\frac{\text{a}}{\text{c}}<\frac{\text{b}}{\text{c}}.$

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Question 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: 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.
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
Answer
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
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