Linear Inequalities in One or Two Variables MCQ Quiz in বাংলা - Objective Question with Answer for Linear Inequalities in One or Two Variables - বিনামূল্যে ডাউনলোড করুন [PDF]

To find the minimum additional amount of sugar needed, we can set up the inequality: 95 + \( x \) >= 150, where \( x \) is the additional sugar needed. By subtracting 95 from both sides, we get \( x \) >= 55. Therefore, the minimum additional amount of sugar needed is 55 grams. Thus, the correct answer is 55 grams. Option 1 (45 grams) is incorrect because it results in a total of 140 grams, which is less than 150 grams. Option 2 (50 grams) results in 145 grams, also less than the required amount. Option 4 (60 grams) exceeds the minimum requirement but is not the least amount needed.

To determine how many more units are needed, we set up the inequality: 1,320 + x \(\geq\) 1,500, where x is the number of additional units required. Solving gives x \(\geq\) 180, so 180 additional units must be produced. Option 3 (180 units) is correct. Option 1 (150 units) results in only 1,470 units, which is short. Option 2 (170 units) yields 1,490 units, still insufficient. Option 4 (200 units) exceeds the minimum requirement but is not necessary.

We are tasked with finding how much additional water can be added without exceeding 200 liters. The inequality is: 173 + x \(\leq\) 200, where x is the additional water. Subtracting 173 from both sides gives x \(\leq\) 27. So, the maximum additional water that can be added is 27 liters. Option 2 (27 liters) is correct. Option 1 (25 liters) is a possible addition but not the maximum. Option 3 (30 liters) and Option 4 (32 liters) would exceed the tank's capacity.

The problem requires solving the inequality: 357 + x \( \geq \) 400, where x is the number of additional trees needed. By subtracting 357 from both sides, we find x \( \geq \) 43. Therefore, the farmer needs to plant at least 43 more trees. Option 3 (43 trees) is the correct choice. Option 1 (35 trees) leads to only 392 trees, which is insufficient. Option 2 (40 trees) results in 397 trees, still not enough. Option 4 (45 trees) exceeds the minimum requirement but is not the smallest number needed.

To find the minimum speed increase needed, we use the inequality: 38 + x \( \geq \) 45, where x is the increase in speed needed. Subtracting 38 from both sides, we find x \( \geq \) 7. Therefore, the car needs to increase its speed by at least 7 miles per hour to meet the speed limit. The correct answer is 7 miles per hour. Option 1 (5 miles per hour) would only increase the speed to 43 miles per hour, which is below the limit. Option 3 (8 miles per hour) is correct but not the minimal increase, and Option 4 (10 miles per hour) exceeds the minimum increase needed.

The inequality to solve is 620 + x \( \geq \) 850, where x represents additional tickets needed. Subtracting 620 from both sides results in x \( \geq \) 230. Therefore, at least 230 more tickets must be sold to break even. Option 3 (230 tickets) is correct. Option 1 (200 tickets) would only bring the total to 820, which is insufficient. Option 2 (220 tickets) totals 840, still under the requirement. Option 4 (250 tickets) exceeds the break-even point but is not the minimum needed.

The problem states that the maximum value of \(y\) is \(15\) less than \(3\) times a number \(m\). This means that \(y\) can be at most \(3m - 15\). Therefore, \(y\) must be less than or equal to \(3m - 15\), which is represented by the inequality \(y \leq 3m - 15\). Thus, the correct answer is option 1. Option 2 is incorrect because it suggests that \(y\) is greater than or equal to \(3m - 15\), which does not fit the description. Option 3 and Option 4 invert the order of subtraction, suggesting \(y\) is either less than or greater than \(15 - 3m\), which is not the correct interpretation of the relationship.

The problem states that the minimum value of \(w\) is \(10\) less than \(5\) times a number \(q\). Therefore, \(w\) must be at least \(5q - 10\), which translates to the inequality \(w \geq 5q - 10\). Thus, option 2 is correct. Option 1 would imply \(w\) is less than or equal to \(5q - 10\), which contradicts the problem statement. Options 3 and 4 reverse the terms, which changes the meaning of the inequality and are therefore incorrect.

The problem describes the cost \(x\) of cupcakes being no more than \(5\) dollars less than twice the number of cupcakes, \(c\). This means the cost \(x\) can be at most \(2c - 5\). Thus, the correct inequality is \(x \leq 2c - 5\), making option 1 the correct choice. Option 2 suggests \(x\) is greater than or equal to \(2c - 5\), which contradicts the 'no more than' condition. Options 3 and 4 are incorrect as they misrepresent the relationship by inverting the terms of the inequality.

The question states that the train's speed \(s\) is at least \(20\) kilometers per hour less than \(3\) times the speed of a car \(c\). Hence, \(s\) must be greater than or equal to \(3c - 20\), which corresponds to \(s \geq 3c - 20\). Option 2 correctly captures this inequality. Option 1 suggests \(s\) is less than or equal to \(3c - 20\), which is incorrect according to the problem. Options 3 and 4 incorrectly swap the terms, altering the intended inequality.