10 Question MCQ (including Assertion)

Question 1 of 10

Solve the double inequality \( -8 \le 5x - 3 < 7 \).

A \( -1 < x \le 2 \) B \( -5 \le x < 10 \) C \( -1 \le x < 2 \) D \( 1 \le x < 4 \)

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Question 2 of 10

Assertion (A): The solution set for the system of inequalities \( x > 5 \) and \( x < -2 \) is an empty set (\( \emptyset \)).
Reason (R): There is no real number that is simultaneously greater than 5 and less than -2.

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. D A is false but R is true.

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Question 3 of 10

Solve \(x+\dfrac{x}{2}+\dfrac{x}{3}<11\) for real \(x\).

A \(x>6\) B \(x\le6\) C \(x\ge6\) D \(x<6\)

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Question 4 of 10

Assertion (A): The solution set of \( 5x - 3 < 7 \) when \( x \) is an integer is \( \{..., -2, -1, 0, 1\} \).
Reason (R): Solving \( 5x - 3 < 7 \) yields \( x < 2 \), and the integers strictly less than 2 are 1, 0, -1, etc.

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. D A is false but R is true.

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Question 5 of 10

Assertion:For real \(x\), the inequality \(30x<200\) has the graph shown.
Reason:For natural-number \(x\), the solution set is \(\{1,2,3,4,5,6\}\).

A Both Assertion and Reason are true, and Reason is the correct explanation of Assertion. B Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion. C Assertion is true, but Reason is false. D Assertion is false, but Reason is true.

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Question 6 of 10

Identify the inequality shown by the following graph:

A \( x > -2 \) B \( x \le -2 \) C \( x < -2 \) D \( x \ge -2 \)

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Question 7 of 10

Assertion:Sunita must score at least \(82\) in her fifth examination to obtain an average of at least \(90\), given marks \(87,92,94,95\) in the first four.
Reason:Her average in the first four examinations is \(92\).

A Both Assertion and Reason are true, and Reason is the correct explanation of Assertion. B Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion. C Assertion is true, but Reason is false. D Assertion is false, but Reason is true.

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Question 8 of 10

Assertion (A): If a student obtains 70 and 75 marks in the first two tests, the minimum marks needed in the third test to average at least 60 is 35.
Reason (R): The inequality formulation is \( \frac{70 + 75 + x}{3} \ge 60 \).

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. D A is false but R is true.

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Question 9 of 10

Assertion (A): If \( -3x < 12 \), then the solution for real \( x \) is \( x > -4 \).
Reason (R): Both sides of an inequality can be multiplied or divided by a negative number, provided the sign of inequality is reversed.

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. D A is false but R is true.

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Question 10 of 10

Select the interval represented by the graph.

A \([-3,2)\) B \([-3,2]\) C \((-3,2)\) D \((-3,2]\)

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10 Question MCQ (including Assertion)