Question 1

A company produces two types of gadgets, A and B. The profit from each gadget A is $\$40$ and from each gadget B is $\$50$. If the company wants to achieve a total profit of at least $\$2000$, which inequality represents the minimum number of gadgets A and B they need to sell?

Accepted Answer

Correct Option: A. Solution: The inequality $40x + 50y \geq 2000$ represents the condition where the total profit from selling gadgets A and B is at least $\$2000$. Here, $x$ and $y$ are the numbers of gadgets A and B sold, respectively.

Question 2

Which of the following inequalities represents a slack inequality?

Accepted Answer

Correct Option: C. Solution: A slack inequality includes the equal sign, such as $\leq$ or $\geq$, indicating that the boundary value is included in the solution set.

Question 3

A manufacturer has 600 liters of a 12% acid solution. How many liters of a 30% acid solution must be added to ensure the resulting mixture has an acid content between 15% and 18%?

Accepted Answer

Correct Option: A. Solution: Let $x$ be the liters of 30% solution added. The inequalities $30x + 7200 > 15(x + 600)$ and $30x + 7200 < 18(x + 600)$ solve to $120 < x < 300$.

Question 4

For the inequality $x - 2y < 4$, which of the following points is not part of the feasible region?

Accepted Answer

Correct Option: D. Solution: Substituting $(6, 1)$ into $x - 2y < 4$ gives $6 - 2(1) = 4$, which does not satisfy the strict inequality.

Question 5

If the inequality $4x + 3 < 5x + 7$ is solved, which of the following statements is true?

Accepted Answer

Correct Option: C. Solution: Simplifying the inequality $4x + 3 < 5x + 7$ gives $-x < 4$, or $x > -4$. Thus, the solution set includes all real numbers greater than $-2$.

Question 6

Solve the inequality $30x < 200$ for $x$ when $x$ is a natural number.

Accepted Answer

Correct Option: A. Solution: Dividing both sides by 30 gives $x < \frac{200}{30} = \frac{20}{3} \approx 6.67$. Since $x$ is a natural number, $x$ can be 1, 2, 3, 4, 5, or 6.

Question 7

Solve the compound inequality $$-8 \leq 5x - 3 < 7$$ and express the solution in interval notation.

Accepted Answer

Correct Option: B. Solution: First, solve $$-8 \leq 5x - 3$$ to get $$x \geq -1$$. Then, solve $$5x - 3 < 7$$ to get $$x < 2$$. Therefore, the solution in interval notation is $$[-1, 2)$.

Question 8

If $$5x - 3 < 3x + 1$$, which of the following is the correct solution for $x$?

Accepted Answer

Correct Option: A. Solution: Rearranging the inequality $$5x - 3 < 3x + 1$$ gives $$2x < 4$$, which simplifies to $$x < 2$$.

Question 9

In a laboratory experiment, a chemical reaction requires a temperature range between $50^\circ C$ and $70^\circ C$. What is the equivalent temperature range in Fahrenheit if the conversion formula is given by $C = \frac{5}{9}(F - 32)$?

Accepted Answer

Correct Option: A. Solution: To convert the temperature range from Celsius to Fahrenheit, we use the formula $C = \frac{5}{9}(F - 32)$. Solving for $F$, we get $F = \frac{9}{5}C + 32$. Substituting $C = 50$ and $C = 70$, we find the range $122^\circ F \leq F \leq 158^\circ F$.

Question 10

Solve the inequality $5x - 3 < 3x + 1$ for $x$ when $x$ is a real number.

Accepted Answer

Correct Option: A. Solution: Rearranging the inequality $5x - 3 < 3x + 1$ gives $2x < 4$, so $x < 2$.

Question 11

If $x$ and $y$ are non-negative integers satisfying $2x + 3y \geq 6$, what is the minimum value of $x + y$?

Accepted Answer

Correct Option: B. Solution: To minimize $x + y$, try $x = 0$: $3y \geq 6 \Rightarrow y \geq 2$. So, $x + y = 2$. However, if $x = 1$, $2(1) + 3y \geq 6 \Rightarrow 3y \geq 4$, giving $y \geq 2$, so $x + y = 3$. This is the minimum.

Question 12

If the inequality $3x - 7 < 5x + 1$ is solved, what is the solution set for $x$?

Accepted Answer

Correct Option: A. Solution: Solving the inequality $3x - 7 < 5x + 1$ gives $x < 4$. Subtract $3x$ from both sides to get $-7 < 2x + 1$, then subtract 1 from both sides to get $-8 < 2x$, and finally divide by 2 to find $x < 4$.

Question 13

Consider the inequality $3x + 4y \leq 12$. Which of the following points lies on the boundary line of the feasible region?

Accepted Answer

Correct Option: A. Solution: The boundary line is $3x + 4y = 12$. Substituting $(4, 0)$ gives $3(4) + 4(0) = 12$, which satisfies the equation.

Question 14

Given the inequality $40x + 20y \leq 120$, which of the following points lies within the feasible region?

Accepted Answer

Correct Option: A. Solution: Substituting $(1, 2)$ into the inequality: $40(1) + 20(2) = 40 + 40 = 80 \leq 120$, which is true.

Question 15

Which of the following inequalities correctly represents the statement: 'The sum of two consecutive odd integers is less than 40'?

Accepted Answer

Correct Option: B. Solution: If $x$ is the smaller odd integer, the next consecutive odd integer is $x + 2$. The inequality is $x + (x + 2) < 40$.

Question 16

Solve the inequality $$-8 \leq 5x - 3 < 7$$ and express the solution in interval notation.

Accepted Answer

Correct Option: A. Solution: To solve the inequality, split it into two inequalities: $$-8 \leq 5x - 3$$ and $$5x - 3 < 7$$. Solving the first gives $$x \geq -1$$, and solving the second gives $$x < 2$$. Thus, the solution in interval notation is $$[-1, 2)$.

Question 17

Reshma has ₹120 and wants to buy registers and pens. If the cost of one register is ₹40 and one pen is ₹20, which inequality represents the maximum number of registers and pens she can buy?

Accepted Answer

Correct Option: A. Solution: The inequality $40x + 20y \leq 120$ represents the condition that the total cost of registers and pens should not exceed ₹120.

Question 18

If $5x - 3 < 3x + 1$, what is the solution for $x$ when $x$ is an integer?

Accepted Answer

Correct Option: A. Solution: Simplifying the inequality $5x - 3 < 3x + 1$ gives $2x < 4$, so $x < 2$. For integers, $x$ can be any integer less than 2.

Question 19

A company produces two types of products, A and B. The profit on each unit of product A is ₹40 and on product B is ₹30. The company can produce up to 100 units of both products combined due to resource constraints. What is the maximum profit the company can achieve if it must produce at least 10 units of each product?

Accepted Answer

Correct Option: C. Solution: Let $x$ be the number of units of product A and $y$ be the number of units of product B. The constraints are $x + y \leq 100$, $x \geq 10$, and $y \geq 10$. The profit function to maximize is $40x + 30y$. Testing the boundary condition $x + y = 100$, we find $40x + 30(100-x) = 4000 - 10x$. Maximizing this function subject to $x \geq 10$ gives $x = 70$, $y = 30$, yielding a profit of $40(70) + 30(30) = 4000$.

Question 20

A man wants to cut three lengths from a board of 91 cm. The second length is 3 cm longer than the shortest, and the third is twice as long as the shortest. If the third piece is at least 5 cm longer than the second, what is the possible range for the shortest length?

Accepted Answer

Correct Option: C. Solution: Let the shortest length be $x$. The second is $x + 3$ and the third is $2x$. Given $2x \geq (x + 3) + 5$, solving gives $x \geq 8$. Also, $x + (x + 3) + 2x \leq 91$ gives $4x + 3 \leq 91$, solving gives $x \leq 22$. Thus, $8 < x < 22$.

Question 21

Consider the inequality $3x - 7 < 5x + 1$. Which of the following is the correct graphical representation of its solution on a number line?

Accepted Answer

Correct Option: A. Solution: The inequality simplifies to $2x > 6$, which gives $x < 3$. The solution is represented by a line extending to the left from an open circle at $x = 3$.

Question 22

Consider the system of inequalities: $$3x - 5y < 15$$ and $$2x + 3y > 6$$. Which of the following points is within the solution set of this system?

Accepted Answer

Correct Option: A. Solution: Substitute each point into both inequalities. For option (4, 1): $$3(4) - 5(1) = 12 - 5 = 7 < 15$$ and $$2(4) + 3(1) = 8 + 3 = 11 > 6$$, both conditions are satisfied.

Question 23

Consider the inequality $-12x > 30$. Which of the following is the solution for $x$ when $x$ is an integer?

Accepted Answer

Correct Option: D. Solution: Dividing both sides by $-12$ and reversing the inequality sign gives $x < -2.5$. As $x$ is an integer, $x \leq -3$.

Question 24

A student needs to score an average of at least 80% in five subjects to get a scholarship. If she has scored 78%, 82%, 85%, and 79% in four subjects, what is the minimum score she needs in the fifth subject?

Accepted Answer

Correct Option: C. Solution: Let the score in the fifth subject be $x$. The total score needed for an average of 80% over five subjects is $80 	imes 5 = 400$. The sum of the scores in the first four subjects is $78 + 82 + 85 + 79 = 324$. Therefore, $324 + x \geq 400$, which gives $x \geq 76$. Thus, the student needs a minimum score of 84% in the fifth subject.

Question 25

In the inequality $-5x \leq -10$, what happens to the inequality sign when both sides are divided by -5?

Accepted Answer

Correct Option: B. Solution: When both sides of an inequality are divided by a negative number, the inequality sign is reversed. Thus, $-5x \leq -10$ becomes $x \geq 2$.

Question 26

A student needs to score at least 60 marks on average in three exams. If the scores in the first two exams are 62 and 48, what is the minimum score required in the third exam?

Accepted Answer

Correct Option: A. Solution: Let $x$ be the score in the third exam. The inequality is $\frac{62 + 48 + x}{3} \geq 60$. Solving gives $x \geq 70$.

Question 27

Solve the inequality $3x - 7 > 5x - 1$ and select the correct representation of the solution on a number line.

Accepted Answer

Correct Option: A. Solution: Subtracting $5x$ from both sides gives $-2x > 6$. Dividing by $-2$ and reversing the inequality gives $x < 3$. Thus, the solution is represented by a line extending to the left from $x = 3$.

Question 28

A company wants to produce a new product using two raw materials, A and B. The cost per unit of material A is $50 and the cost per unit of material B is $30. The company wants to spend no more than $6000 on these materials. If $x$ and $y$ represent the number of units of materials A and B used respectively, which of the following inequalities correctly represents the constraint on the budget?

Accepted Answer

Correct Option: A. Solution: The inequality $50x + 30y \leq 6000$ correctly represents the constraint as it indicates that the total cost of materials A and B should not exceed $6000.

Question 29

If Ravi wants to buy packets of rice with a total cost less than ₹200, and each packet costs ₹30, what is the maximum number of packets he can buy?

Accepted Answer

Correct Option: A. Solution: The inequality is $30x < 200$. Solving for $x$, we get $x < \frac{200}{30} = 6.66$. Since $x$ must be an integer, the maximum number of packets is 6.

Question 30

What happens to the inequality sign when both sides of an inequality are multiplied by a negative number?

Accepted Answer

Correct Option: B. Solution: When both sides of an inequality are multiplied by a negative number, the inequality sign is reversed.

Question 31

A student needs to score at least 75 in an exam to pass. If the student has already scored 70 in the first part, what is the minimum score needed in the second part to pass?

Accepted Answer

Correct Option: A. Solution: Let $x$ be the score needed in the second part. Then, $70 + x \geq 75$. Solving gives $x \geq 5$.

Question 32

Consider the inequality $5x - 3 < 3x + 1$. If $x$ is a real number, which of the following is the correct solution set?

Accepted Answer

Correct Option: A. Solution: Rearranging the inequality $5x - 3 < 3x + 1$, we get $5x - 3x < 1 + 3$, which simplifies to $2x < 4$. Thus, $x < 2$.

Question 33

In an experiment, a solution of hydrochloric acid is to be kept between 30° and 35° Celsius. What is the range of temperature in Fahrenheit?

Accepted Answer

Correct Option: A. Solution: Using the conversion formula $C = \frac{5}{9}(F - 32)$, substituting $30 < C < 35$ gives $86 < F < 95$. Therefore, the range in Fahrenheit is 86°F to 95°F.

Question 34

Which of the following statements about inequalities is true?

Accepted Answer

Correct Option: B. Solution: Adding or subtracting the same number to both sides of an inequality does not affect the inequality sign.

Question 35

Given the inequality $5x - 3 < 3x + 1$, what is the solution set when $x$ is an integer?

Accepted Answer

Correct Option: A. Solution: By solving the inequality $5x - 3 < 3x + 1$, we get $x < 2$. For integer values, the solution set is {-4, -3, -2, -1, 0, 1}.

Question 36

Which of the following inequalities represents the condition where the sum of two consecutive odd natural numbers is less than 40, and both numbers are greater than 10?

Accepted Answer

Correct Option: A. Solution: Let $x$ be the smaller odd number, then the next consecutive odd number is $x + 2$. The sum is $x + (x + 2) < 40$. Both numbers being greater than 10 implies $x > 10$.

Question 37

How is a strict inequality represented on a number line?

Accepted Answer

Correct Option: A. Solution: Strict inequalities are represented with an open circle on a number line to indicate that the endpoint is not included.

Question 38

What is the range of $x$ for the inequality $3x - 7 < 5 + x$?

Accepted Answer

Correct Option: A. Solution: Rearranging the inequality $3x - 7 < 5 + x$ gives $2x < 12$, hence $x < 6$.

Question 39

Which of the following is a correct representation of the inequality $x \geq 1$ on a number line?

Accepted Answer

Correct Option: A. Solution: The inequality $x \geq 1$ is represented by a closed dot at 1 and an arrow extending to the right, indicating all numbers greater than or equal to 1.

Question 40

Which of the following is a correct representation of the inequality $3x - 7 < 5x + 1$ on a number line?

Accepted Answer

Correct Option: A. Solution: Solving the inequality $3x - 7 < 5x + 1$ gives $x > -4$. The correct representation is a line extending from $x = -\infty$ to $x = 4$ with an open circle at $x = 4$.

Question 41

In a class of students, the average score in mathematics needs to be at least 75 for the class to qualify for a competition. If the current average score is 70 and there are 30 students, what is the minimum average score the next 5 students must achieve to ensure the class qualifies?

Accepted Answer

Correct Option: D. Solution: Let the total score of the 30 students be $70 	imes 30 = 2100$. Let the average score of the next 5 students be $x$. The total score for all 35 students must be at least $75 	imes 35 = 2625$. Therefore, $2100 + 5x \geq 2625$. Solving gives $5x \geq 525 \Rightarrow x \geq 105$. Thus, the minimum average score the next 5 students must achieve is 90.

Question 42

Solve the inequality $$2(x - 4) \leq 3(x + 2)$$ and identify the correct solution set.

Accepted Answer

Correct Option: A. Solution: Expanding both sides gives $2x - 8 \leq 3x + 6$. Rearranging terms gives $-x \leq 14$, hence $x \geq -14$. The inequality should be $x \leq 10$ after correcting the calculation.

Question 43

Which of the following inequalities represents a feasible region that includes the origin?

Accepted Answer

Correct Option: B. Solution: The inequality $2x - y \leq 0$ includes the origin $(0,0)$ as $2(0) - 0 \leq 0$ is true.

Question 44

A student needs to maintain an average of at least 60 marks over three tests. If he scored 70 and 75 in the first two tests, what is the minimum score he must achieve in the third test?

Accepted Answer

Correct Option: B. Solution: Let $x$ be the score in the third test. The average is given by $\frac{70 + 75 + x}{3} \geq 60$. Solving for $x$, we get $x \geq 70$. Therefore, the minimum score required is 70.

Question 45

If a triangle's longest side is 3 times the shortest side, and the third side is 2 cm shorter than the longest side, what is the minimum length of the shortest side if the perimeter is at least 61 cm?

Accepted Answer

Correct Option: B. Solution: Let the shortest side be $x$. Then, the longest side is $3x$ and the third side is $3x - 2$. The perimeter is $x + 3x + (3x - 2) \geq 61$, which simplifies to $7x - 2 \geq 61$. Solving gives $x \geq 11$.

Question 46

Given the inequality $-12x > 30$, what is the solution for $x$ when $x$ is an integer?

Accepted Answer

Correct Option: A. Solution: Dividing both sides by -12 and reversing the inequality sign, we get $x < -\frac{30}{12} = -2.5$. Thus, $x$ must be less than -2.5.

Question 47

Which of the following is a correct representation of the inequality $$3 \leq x < 5$$ in interval notation?

Accepted Answer

Correct Option: A. Solution: The inequality $$3 \leq x < 5$$ includes 3 but not 5, so it is represented as $$[3, 5)$ in interval notation.

Question 48

Which of the following inequalities represents a feasible region that includes the boundary line?

Accepted Answer

Correct Option: C. Solution: The inequalities $ax + by \leq c$ and $ax + by \geq c$ include the boundary line as part of the feasible region.

Question 49

Given the inequality $4x + 3 < 5x + 7$, which of the following is the solution for $x$?

Accepted Answer

Correct Option: A. Solution: Subtracting $4x$ from both sides gives $3 < x + 7$. Subtracting 7 from both sides results in $x > -4$.

Question 50

If the inequality $$4x + 3 < 5x + 7$$ is solved for $x$, which of the following represents the correct solution set?

Accepted Answer

Correct Option: A. Solution: Subtract $4x$ from both sides to get $3 < x + 7$. Subtract 7 from both sides to get $x > -4$. Thus, the solution set is $x > -4$.

Question 51

Ravi wants to buy pencils and erasers. Each pencil costs ₹5 and each eraser costs ₹3. If he has ₹50, what is the maximum number of pencils he can buy if he also wants to buy at least one eraser?

Accepted Answer

Correct Option: C. Solution: Let the number of pencils be $x$ and the number of erasers be $y$. The inequality is $5x + 3y \leq 50$. If $y = 1$, then $5x + 3 \leq 50 \Rightarrow 5x \leq 47 \Rightarrow x \leq 9.4$. Hence, the maximum integer value of $x$ is 9. However, buying 9 pencils would leave no money for an eraser, so the maximum number of pencils Ravi can buy is 7, allowing for the purchase of one eraser.

Question 52

Which of the following represents a linear inequality in two variables?

Accepted Answer

Correct Option: B. Solution: A linear inequality in two variables is represented by expressions like $ax + by < c$, where $a$ and $b$ are not both zero.

Question 53

What is the solution set for the inequality $30x < 200$ when $x$ is a natural number?

Accepted Answer

Correct Option: B. Solution: The inequality $30x < 200$ simplifies to $x < \frac{200}{30} = \frac{20}{3}$. For natural numbers, $x$ can be 1, 2, 3, 4, 5, or 6.

Question 54

A farmer has a rectangular field with a perimeter of 200 meters. He wants to maximize the area of the field. What should be the dimensions of the field?

Accepted Answer

Correct Option: A. Solution: Let the length be $l$ and the width be $w$. The perimeter constraint is $2(l + w) = 200$, so $l + w = 100$. To maximize the area $A = lw$, substitute $w = 100 - l$ into the area function: $A = l(100 - l) = 100l - l^2$. This is a quadratic equation opening downwards, so its maximum is at the vertex $l = \frac{100}{2} = 50$. Thus, $w = 50$. The dimensions that maximize the area are 50m by 50m.

Question 55

Find the range of mental age for a group of 12-year-old children if their IQ is between 80 and 140.

Accepted Answer

Correct Option: A. Solution: Using the formula $IQ = \frac{MA}{CA} 	imes 100$, where $CA = 12$, solve the inequalities $80 \leq \frac{MA}{12} 	imes 100 \leq 140$. This gives $9.6 \leq MA \leq 16.8$. Thus, the range of mental age is 9.6 to 16.8 years.

Question 56

When solving inequalities, multiplying or dividing both sides by a negative number does not affect the direction of the inequality.

Accepted Answer

Answer: False. Solution: When solving inequalities, if both sides are multiplied or divided by a negative number, the direction of the inequality must be reversed. For example, if $$a > b$$, then $$-a < -b$$ when both sides are multiplied by -1.

Question 57

When solving a linear inequality, multiplying both sides by a negative number does not change the direction of the inequality.

Accepted Answer

Answer: False. Solution: When both sides of an inequality are multiplied or divided by a negative number, the direction of the inequality sign is reversed.

Question 58

In solving linear inequalities, when both sides are multiplied by a negative number, the inequality sign is reversed.

Accepted Answer

Answer: True. Solution: When both sides of an inequality are multiplied or divided by a negative number, the inequality sign is reversed. This is a fundamental rule in solving inequalities.

Question 59

The inequality $30x < 200$ has a solution set of natural numbers $\{1, 2, 3, 4, 5, 6\}$.

Accepted Answer

Answer: True. Solution: For $x$ as a natural number, the inequality $30x < 200$ holds true for $x = 1, 2, 3, 4, 5, 6$. Therefore, the solution set is $\{1, 2, 3, 4, 5, 6\}$.

Question 60

When solving inequalities, multiplying or dividing both sides by a negative number reverses the inequality sign.

Accepted Answer

Answer: True. Solution: Multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign, as shown by the example where $3 > 2$ becomes $-3 < -2$.

Question 61

The solution to the inequality $-8 \leq 5x - 3 < 7$ can be expressed in interval notation as $[-1, 2)$.

Accepted Answer

Answer: True. Solution: Solving the inequality $-8 \leq 5x - 3 < 7$, we add 3 to all parts: $-5 \leq 5x < 10$. Dividing by 5 gives $-1 \leq x < 2$. Thus, the interval notation is $[-1, 2)$.

Question 62

When solving linear inequalities, if both sides of an inequality are multiplied by a negative number, the direction of the inequality sign remains unchanged.

Accepted Answer

Answer: False. Solution: When both sides of an inequality are multiplied by a negative number, the direction of the inequality sign is reversed. For example, if $a > b$, then $-a < -b$ when multiplied by -1.

Question 63

In solving linear inequalities, the sign of inequality is reversed when both sides are multiplied or divided by a negative number.

Accepted Answer

Answer: True. Solution: When solving inequalities, multiplying or dividing both sides by a negative number requires reversing the inequality sign to maintain the truth of the statement.

Question 64

Solving the compound inequality $$-8 \leq 5x - 3 < 7$$ and expressing the solution in interval notation results in the interval $$[-1, 2)$$.

Accepted Answer

Answer: True. Solution: To solve the inequality $$-8 \leq 5x - 3 < 7$$, split it into two inequalities: $$-8 \leq 5x - 3$$ and $$5x - 3 < 7$$. Solving the first gives $$x \geq -1$$ and the second gives $$x < 2$$. Thus, the solution in interval notation is $$[-1, 2)$$.

Linear Inequalities

Learning Objectives

Learning Objectives

Revision Notes & Summary

Chapter Notes

Linear Inequalities in One Variable

Linear Inequalities in Two Variables

Properties of Inequalities

Graphical Representation of Inequalities

System of Inequalities

Applications of Inequalities

Double Inequalities and Interval Solutions

Feasible Region for Two-Variable Inequalities

Examples

Exam Tips & Common Mistakes

Common Mistakes & Exam Tips

Linear Inequalities in One Variable

Linear Inequalities in Two Variables

Properties of Inequalities

Graphical Representation of Inequalities

System of Inequalities

Applications of Inequalities

Double Inequalities and Interval Solutions

Feasible Region for Two-Variable Inequalities

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Multiple Choice Questions

Correct Answer: A

Q2.Which of the following inequalities represents a slack inequality?

Correct Answer: C

Q3.A manufacturer has 600 liters of a 12% acid solution. How many liters of a 30% acid solution must be added to ensure the resulting mixture has an acid content between 15% and 18%?

Correct Answer: A

Q4.For the inequality x−2y<4x - 2y < 4x−2y<4, which of the following points is not part of the feasible region?

Correct Answer: D

Q5.If the inequality 4x+3<5x+74x + 3 < 5x + 74x+3<5x+7 is solved, which of the following statements is true?

Correct Answer: C

Q6.Solve the inequality 30x<20030x < 20030x<200 for xxx when xxx is a natural number.

Correct Answer: A

Q7.Solve the compound inequality −8≤5x−3<7-8 \leq 5x - 3 < 7−8≤5x−3<7 and express the solution in interval notation.

Correct Answer: B

Q8.If 5x−3<3x+15x - 3 < 3x + 15x−3<3x+1, which of the following is the correct solution for xxx?

Correct Answer: A

Q9.In a laboratory experiment, a chemical reaction requires a temperature range between 50∘C50^\circ C50∘C and 70∘C70^\circ C70∘C. What is the equivalent temperature range in Fahrenheit if the conversion formula is given by C=59(F−32)C = \frac{5}{9}(F - 32)C=95​(F−32)?

Correct Answer: A

Q10.Solve the inequality 5x−3<3x+15x - 3 < 3x + 15x−3<3x+1 for xxx when xxx is a real number.

Correct Answer: A

Q11.If xxx and yyy are non-negative integers satisfying 2x+3y≥62x + 3y \geq 62x+3y≥6, what is the minimum value of x+yx + yx+y?

Correct Answer: B

Q12.If the inequality 3x−7<5x+13x - 7 < 5x + 13x−7<5x+1 is solved, what is the solution set for xxx?

Correct Answer: A

Q13.Consider the inequality 3x+4y≤123x + 4y \leq 123x+4y≤12. Which of the following points lies on the boundary line of the feasible region?

Correct Answer: A

Q14.Given the inequality 40x+20y≤12040x + 20y \leq 12040x+20y≤120, which of the following points lies within the feasible region?

Correct Answer: A

Q15.Which of the following inequalities correctly represents the statement: 'The sum of two consecutive odd integers is less than 40'?

Correct Answer: B

Q16.Solve the inequality −8≤5x−3<7-8 \leq 5x - 3 < 7−8≤5x−3<7 and express the solution in interval notation.

Correct Answer: A

Q17.Reshma has ₹120 and wants to buy registers and pens. If the cost of one register is ₹40 and one pen is ₹20, which inequality represents the maximum number of registers and pens she can buy?

Correct Answer: A

Q18.If 5x−3<3x+15x - 3 < 3x + 15x−3<3x+1, what is the solution for xxx when xxx is an integer?

Correct Answer: A

Correct Answer: C

Q20.A man wants to cut three lengths from a board of 91 cm. The second length is 3 cm longer than the shortest, and the third is twice as long as the shortest. If the third piece is at least 5 cm longer than the second, what is the possible range for the shortest length?

Correct Answer: C

Q21.Consider the inequality 3x−7<5x+13x - 7 < 5x + 13x−7<5x+1. Which of the following is the correct graphical representation of its solution on a number line?

Correct Answer: A

Q22.Consider the system of inequalities: 3x−5y<153x - 5y < 153x−5y<15 and 2x+3y>62x + 3y > 62x+3y>6. Which of the following points is within the solution set of this system?

Correct Answer: A

Q23.Consider the inequality −12x>30-12x > 30−12x>30. Which of the following is the solution for xxx when xxx is an integer?

Correct Answer: D

Q24.A student needs to score an average of at least 80% in five subjects to get a scholarship. If she has scored 78%, 82%, 85%, and 79% in four subjects, what is the minimum score she needs in the fifth subject?

Correct Answer: C

Q25.In the inequality −5x≤−10-5x \leq -10−5x≤−10, what happens to the inequality sign when both sides are divided by -5?

Correct Answer: B