CUET UG Applied Mathematics Booster Test 1 - Components, Assumptions, and Mathematical Formulation -

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CUET UG Applied Mathematics Booster Test 1 - Components, Assumptions, and Mathematical Formulation

⏱️ 30 Minutes

❓ 19 Questions

📌 Answers are locked once submitted — results and explanations appear at the end.

CUET UG Applied Mathematics Booster Test 1 - Components, Assumptions, and Mathematical Formulation

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QUESTION 1 OF 19

Match the Following:

List I (Practical Scenario)	List II (LPP Representation)
1. Number of items	a. Objective coefficient
2. Profit margin	b. Constraint limit
3. Maximum space	c. Decision variable
4. Restrictions	d. x ≥ 0, y ≥ 0

Answer Review

1 Match the Following:

List I (Practical Scenario)	List II (LPP Representation)
1. Number of items	a. Objective coefficient
2. Profit margin	b. Constraint limit
3. Maximum space	c. Decision variable
4. Restrictions	d. x ≥ 0, y ≥ 0

A 1–a, 2–b, 3–c, 4–d

B 1–b, 2–a, 3–d, 4–c

C 1–c, 2–a, 3–b, 4–d

D 1–c, 2–d, 3–b, 4–a

💡 Short Explanation

Number of items represents decision variables. Profit margin becomes the objective function coefficient. Maximum space acts as a constraint limit.

✅ Correct Answer Explanation

Each practical situation corresponds to a standard component of a Linear Programming Problem. Number of items → Decision variable because it represents the unknown quantity to be determined. Profit margin → Objective coefficient because it represents the profit earned per unit. Maximum space → Constraint limit because it restricts production or storage. Restrictions → Non-negative conditions such as x ≥ 0, y ≥ 0. Thus, the correct matching is: 1 → c 2 → a 3 → b 4 → d Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A) 1–a, 2–b, 3–c, 4–d → Decision variables and objective coefficients are incorrectly matched.
Option B) 1–b, 2–a, 3–d, 4–c → Maximum space and restrictions are incorrectly paired.
Option D) 1–c, 2–d, 3–b, 4–a → Profit margin and restrictions are mismatched.

🎯 Strategy

used;

Option Grouping

Application:

Match each real-life concept with its standard LPP representation.

Final Logic:

Only Option C correctly matches all four components.

🧠 Memory Trick

"Items–Variable, Profit–Coefficient, Space–Constraint."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Components of a Linear Programming Problem

2 Identify the incorrect statement regarding the linear objective function Z = ax + by:

A Z is a real-valued function

B Z can include a squared term such as x²

C a and b are arbitrary constants

D The relationship must be linear

💡 Short Explanation

The objective function must remain linear. Squared terms violate linearity. Constants remain fixed throughout the problem. Total land cannot exceed 50 hectares. Herbicide use cannot exceed 800 liters. Both conditions are represented as linear inequalities.

✅ Correct Answer Explanation

A Linear Programming Problem requires the objective function to be a linear expression of the decision variables. A standard objective function is: Z = ax + by where a and b are constants. Including a squared term such as x² makes the objective function non-linear, violating one of the basic assumptions of Linear Programming. Therefore: Option B is the incorrect statement. Option A is correct because the objective function produces real values. Option C is correct because a and b are arbitrary constants. Option D is correct because linearity is essential in LPP. Let: x = hectares under Crop X y = hectares under Crop Y Since only 50 hectares of land are available, x + y ≤ 50 Crop X requires 20 liters/hectare, while Crop Y requires 10 liters/hectare. Maximum herbicide available = 800 liters. Therefore, 20x + 10y ≤ 800 These two inequalities correctly describe the problem. Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option A) Z is a real-valued function → This is a correct property of the objective function.
Option C) a and b are arbitrary constants → These coefficients remain fixed during optimization.
Option D) The relationship must be linear → Linearity is a fundamental assumption of LPP.
Option B) x + y ≥ 50, 20x + 10y ≥ 800 → These inequalities require using at least the available resources, which is incorrect.
Option C) x − y = 50, 10x + 20y ≤ 800 → The land equation and herbicide coefficients are incorrect.
Option D) xy ≤ 50, 20x + 10y = 800 → The product xy is non-linear, and herbicide usage need not equal exactly 800 liters.

🎯 Strategy

used;

Contextual/Tonal Matching

Application:

Translate the phrases "available land" and "maximum herbicide" into linear inequalities.

Final Logic:

Both land and herbicide usage cannot exceed their available limits.

🧠 Memory Trick

"Maximum Available = ≤"

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Formulation of Linear Constraints

4 If a constraint is given as:
x + y = 4,
it is represented graphically as:

A A shaded half-plane

B A single point at the origin

C An unbounded region

D A straight line restricting feasible solutions to that line

💡 Short Explanation

An equation represents a line. Every solution lies on that line. No half-plane is formed by an equality.

✅ Correct Answer Explanation

The equation: x + y = 4 represents a straight line on the Cartesian plane. Unlike an inequality, an equation does not produce a shaded region. Every point satisfying the equation lies exactly on the line itself. Therefore, the feasible solutions are restricted to the line. Hence, Option D is the correct answer.

❓ Why Other Options Are Incorrect

Option A) A shaded half-plane → Half-planes are obtained only from inequalities such as ≤ or ≥.
Option B) A single point at the origin → The equation has infinitely many solutions, not just the origin.
Option C) An unbounded region → An equation represents a line rather than a region.

🎯 Strategy

used;

Contextual/Tonal Matching

Application:

Differentiate between equations and inequalities in graphical representation.

Final Logic:

A linear equality is represented by a straight line.

🧠 Memory Trick

"Equality = Line, Inequality = Region."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Graphical Representation of Constraints

5 Given weekly demand values: 10, 15, 14, 18, the 3-week moving average is 15.67.
If future forecasting predicts a negative value, due to x ≥ 0, the implication is:

A Feasible region expands infinitely

B Negative outputs are allowed

C Production is restricted to a minimum of 0

D Objective function changes sign

💡 Short Explanation

Decision variables cannot be negative. Production quantities must satisfy the non-negative restriction. Any negative forecast is treated as zero or infeasible in LPP.

✅ Correct Answer Explanation

The non-negative restriction in Linear Programming requires: x ≥ 0 This means production quantities cannot be negative. Even if a forecasting method predicts a negative value, it has no practical meaning in an LPP because production cannot fall below zero. Thus, the minimum permissible production level is 0. Therefore, Option C is the correct answer.

❓ Why Other Options Are Incorrect

Option A) Feasible region expands infinitely → Non-negative restrictions actually limit the feasible region rather than expanding it.
Option B) Negative outputs are allowed → This directly contradicts the non-negative assumption.
Option D) Objective function changes sign → The objective function remains unchanged; only infeasible values are rejected.

🎯 Strategy

used;

Contextual/Tonal Matching

Application:

Recognize that the non-negative restriction prevents production values from becoming negative.

Final Logic:

Production cannot be less than zero because x ≥ 0.

🧠 Memory Trick

"Production Never Below Zero."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Non-negative Restrictions

6 Given:
0 ≤ x ≤ 10, 0 ≤ y ≤ 10
Find the probability that a randomly selected point satisfies:
x + y ≤ 10

A 0.25

B 0.50

C 0.75

D 1.00

💡 Short Explanation

The sample space is a square. The required region is a right triangle. Probability equals the ratio of the triangle's area to the square's area.

✅ Correct Answer Explanation

The region: 0 ≤ x ≤ 10 0 ≤ y ≤ 10 forms a square of side 10. Area of the square: = 10 × 10 = 100 square units The inequality: x + y ≤ 10 forms a right triangle with vertices: (0,0), (10,0), (0,10) Area of the triangle: = (1/2) × 10 × 10 = 50 square units Therefore, Probability = 50 / 100 = 0.50 Hence, Option B is the correct answer.

❓ Why Other Options Are Incorrect

Option A) 0.25 → The triangle occupies half, not one-fourth, of the square.
Option C) 0.75 → This overestimates the feasible area.
Option D) 1.00 → Not every point in the square satisfies x + y ≤ 10.

🎯 Strategy

used;

Dimensional/Unit Analysis

Application:

Compare the geometric areas of the favourable region and the total region.

Final Logic:

The favourable triangular region occupies half the square.

🧠 Memory Trick

"Triangle Half of Square = 0.5."

📚 Class XII – Applied Mathematics – Chapter: Probability – Topic: Geometric Probability

7 For Z = 3x + 4y, the gradient vector is:

A \(3\hat{i}+4\hat{j}\)

B \(4\hat{i}+3\hat{j}\)

C \(12\hat{i}+12\hat{j}\)

D \(0\hat{i}+0\hat{j}\)

💡 Short Explanation

The gradient consists of the partial derivatives. Differentiate with respect to x and y. Form the vector using the coefficients obtained.

✅ Correct Answer Explanation

The objective function is: Z = 3x + 4y The gradient vector is obtained by computing the partial derivatives: ∂Z/∂x = 3 ∂Z/∂y = 4 Therefore, Gradient = 3i + 4j Hence, Option A is the correct answer.

❓ Why Other Options Are Incorrect

Option B) 4i + 3j → The coefficients of x and y are interchanged.
Option C) 12i + 12j → Incorrect differentiation.
Option D) 0i + 0j → The objective function is not constant.

🎯 Strategy

used;

Substitution

Application:

Differentiate the linear function with respect to each variable and write the resulting vector.

Final Logic:

The coefficients of x and y become the components of the gradient vector.

🧠 Memory Trick

"Gradient = Coefficients of x and y."

📚 Class XII – Applied Mathematics – Chapter: Applications of Derivatives – Topic: Gradient of a Linear Function

8 Given a triangular feasible region with vertices:
(0,0), (0,4), (6,0),
the area is:

A 24

B 10

C 14

D 12

💡 Short Explanation

The triangle has base 6 and height 4. Use the triangle area formula. Compute the required area.

✅ Correct Answer Explanation

The given vertices form a right triangle. Base = 6 units Height = 4 units Area of the triangle: Area = (1/2) × Base × Height = (1/2) × 6 × 4 = 12 square units Therefore, Option D is the correct answer.

❓ Why Other Options Are Incorrect

Option A) 24 → This is obtained by multiplying the base and height without dividing by 2.
Option B) 10 → Incorrect application of the area formula.
Option C) 14 → Incorrect calculation.

🎯 Strategy

used;

Substitution

Application:

Identify the base and height directly from the coordinates and apply the triangle area formula.

Final Logic:

Half of 6 × 4 equals 12.

🧠 Memory Trick

"Triangle = Half Base × Height."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Graphical Representation of the Feasible Region

9 Evaluate: \(\int_{0}^{4}\,(x+2) dx\)

A 12

B 16

C 20

D 8

💡 Short Explanation

Integrate each term separately. Apply the upper and lower limits. Subtract the lower-limit value from the upper-limit value.

✅ Correct Answer Explanation

Given: ∫ from 0 to 4 of (x + 2) dx Integrate: ∫ (x + 2) dx = x²/2 + 2x Now apply the limits: At x = 4: = 4²/2 + 2(4) = 16/2 + 8 = 8 + 8 = 16 At x = 0: = 0 Therefore, 16 − 0 = 16 Hence, Option B is the correct answer.

❓ Why Other Options Are Incorrect

Option A) 12 → Incorrect evaluation of the definite integral.
Option C) 20 → Results from an incorrect integration or arithmetic error.
Option D) 8 → Only part of the integral has been considered.

🎯 Strategy

used;

Substitution

Application:

Integrate the function first, then substitute the upper and lower limits.

Final Logic:

Applying the limits correctly gives 16.

🧠 Memory Trick

"Integrate First, Then Apply Limits."

📚 Class XII – Applied Mathematics – Chapter: Integral Calculus – Topic: Definite Integrals

10 Assertion (A): Decision variables x and y are controllable variables.
Reason (R): They represent quantities like output or machine-hours controlled to optimize the objective function.

A Both A and R are false

B A is true, R is false

C Both A and R are true, and R is the correct explanation of A

D A is false, R is true

💡 Short Explanation

Decision variables are under the decision-maker's control. They represent production or allocation decisions. Their values determine the objective function.

✅ Correct Answer Explanation

Decision variables are called controllable variables because their values can be selected by the decision-maker while satisfying all the constraints. Variables such as: production quantity, machine-hours, labour allocation, are represented by x and y in an LPP. These variables are adjusted to maximize profit or minimize cost. Therefore: Assertion (A) is true. Reason (R) is also true. The reason correctly explains why decision variables are called controllable variables. Hence, Option C is the correct answer.

❓ Why Other Options Are Incorrect

Option A) Both A and R are false → Both statements are actually true.
Option B) A is true, R is false → The reason is also true.
Option D) A is false, R is true → The assertion is true because decision variables are controllable.

🎯 Strategy

used;

Contextual/Tonal Matching

Application:

Evaluate the assertion and reason independently and determine whether the reason explains the assertion.

Final Logic:

Decision variables are controllable because they represent quantities adjusted to optimize the objective function.

🧠 Memory Trick

"Decision Variables = Things You Control."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Decision Variables

11 Arrange the correct sequence for applying the certainty assumption while formulating an LPP:
1. Finalize the linear equations and inequalities.
2. Ensure profit coefficients per unit are fixed and known.
3. Determine exact availability of resources.
4. Define the decision variables.

A 1, 2, 3, 4

B 4, 1, 2, 3

C 2, 3, 4, 1

D 4, 3, 2, 1

💡 Short Explanation

First identify the decision variables. Then determine available resources. Finally formulate the mathematical model.

✅ Correct Answer Explanation

While formulating an LPP under the certainty assumption, the logical sequence is: 1. Define the decision variables. 2. Determine the exact availability of resources. 3. Ensure that profit (or cost) coefficients are fixed and known. 4. Finalize the linear objective function and constraints. Thus, the correct order is: 4 → 3 → 2 → 1 Therefore, Option D is correct.

❓ Why Other Options Are Incorrect

Option A) 1, 2, 3, 4 → The mathematical model cannot be finalized before defining variables and resources.
Option B) 4, 1, 2, 3 → Resource availability should be identified before writing the final equations.
Option C) 2, 3, 4, 1 → Decision variables must be defined before constructing the model.

🎯 Strategy

used;

Option Grouping

Application:

Recall the standard sequence used to formulate a Linear Programming Problem.

Final Logic:

Define variables first, determine resources, identify coefficients, and then formulate the equations.

🧠 Memory Trick

"Variables → Resources → Coefficients → Model."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Certainty Assumption and Mathematical Formulation

12 Which condition defines the divisibility assumption in LPP?

A Outputs can take fractional values

B Decision variables must be integers

C Resources cannot be divided

D Objective function is divided by a constant

💡 Short Explanation

Divisibility allows fractional values. Decision variables are not restricted to integers. This assumption ensures continuity in the solution space.

✅ Correct Answer Explanation

The divisibility (continuity) assumption states that decision variables may take fractional as well as integer values, provided they satisfy all the constraints. For example, values such as 2.5, 7.25, or 10 are all valid if they satisfy the constraints. Therefore: Option A correctly defines the divisibility assumption. Option B is incorrect because integer-only values belong to integer programming. Option C is incorrect because resources may often be divided depending on the problem. Option D is unrelated to the meaning of divisibility. Hence, Option A is the correct answer.

❓ Why Other Options Are Incorrect

Option B) Decision variables must be integers → Standard LPP allows fractional values.
Option C) Resources cannot be divided → Divisibility refers to decision variables, not the indivisibility of resources.
Option D) Objective function is divided by a constant → This has no relation to the divisibility assumption.

🎯 Strategy

used;

Elimination

Application:

Recall that divisibility allows real-valued decision variables and eliminate unrelated options.

Final Logic:

Divisibility means fractional solutions are permitted.

🧠 Memory Trick

"Divisibility = Decimals Allowed."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Divisibility (Continuity) Assumption

13 If each decision variable contributes proportionally to the objective function, the model remains:

A Linear

B Non-linear

C Exponential

D Unbounded

💡 Short Explanation

Proportional contribution implies a constant rate. No powers or products of variables are involved. Hence, the model remains linear.

✅ Correct Answer Explanation

The proportionality assumption requires that each decision variable contributes to the objective function in direct proportion to its value. For example, Z = ax + by If x doubles, its contribution ax also doubles. Since each variable contributes at a constant rate without squared or product terms, the objective function remains linear. Therefore, Option A is the correct answer.

❓ Why Other Options Are Incorrect

Option B) Non-linear → Non-linear models contain terms such as x², xy, or higher powers.
Option C) Exponential → Exponential relationships are not used in Linear Programming.
Option D) Unbounded → "Unbounded" describes a feasible region, not the nature of the objective function.

🎯 Strategy

used;

Contextual/Tonal Matching

Application:

Associate proportionality with direct linear relationships between variables and their contributions.

Final Logic:

Direct proportionality preserves the linear nature of the model.

🧠 Memory Trick

"Proportional = Linear."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Proportionality Assumption

14 The constant ratio rule applies to:
(i) Objective function coefficients
(ii) Resource consumption in constraints
(iii) Non-negativity of variables

A (i) only

B (i) and (ii)

C (ii) only

D (i), (ii), and (iii)

💡 Short Explanation

Constant ratios apply to objective function coefficients. They also apply to resource consumption rates. Non-negativity is a separate restriction.

✅ Correct Answer Explanation

The constant ratio rule is a part of the proportionality assumption. It requires that: Objective function coefficients remain constant. Resource consumption rates in the constraints remain constant. However, non-negativity of variables is an independent assumption and is not related to the constant ratio rule. Therefore: (i) is correct. (ii) is correct. (iii) is incorrect. Hence, Option B is the correct answer.

❓ Why Other Options Are Incorrect

Option A) (i) only → Resource consumption rates are also governed by proportionality.
Option C) (ii) only → Objective-function coefficients also satisfy the constant ratio rule.
Option D) (i), (ii), and (iii) → Non-negativity is not part of the proportionality assumption.

🎯 Strategy

used;

Elimination

Application:

Separate the proportionality assumption from the non-negative restriction.

Final Logic:

Constant ratios apply to coefficients and resource usage, not to non-negativity.

🧠 Memory Trick

"Constant Ratio = Coefficients + Resources."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Proportionality Assumption

15 In the objective function Z = 5x + 3y, combining profits relies on:

A Certainty

B Divisibility

C Additivity

D Proportionality

💡 Short Explanation

The total profit is obtained by adding individual contributions. Each decision variable contributes independently. This is the additivity assumption.

✅ Correct Answer Explanation

The additivity assumption states that the total value of the objective function equals the sum of the individual contributions of each decision variable. For the objective function: Z = 5x + 3y 5x represents the profit contributed by product x. 3y represents the profit contributed by product y. The total profit is simply: 5x + 3y There are no interaction terms such as xy or x². Therefore, Option C is the correct answer.

❓ Why Other Options Are Incorrect

Option A) Certainty → Certainty assumes that coefficients such as 5 and 3 are fixed and known, but it does not explain how profits are combined.
Option B) Divisibility → Divisibility allows fractional values for decision variables and is unrelated to combining profits.
Option D) Proportionality → Proportionality explains that each contribution is directly proportional to its variable, but the addition of contributions is explained by additivity.

🎯 Strategy

used;

Contextual/Tonal Matching

Application:

Recognize that the phrase "combining profits" refers to adding the contributions from each decision variable.

Final Logic:

The total objective value is obtained by adding individual profits, which is the additivity assumption.

🧠 Memory Trick

"Additivity = Add the Profits."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Additivity Assumption

16 If product A uses L₁ labor hours and product B uses L₂, the total labor used is:

A \(L_{1}\times L_{2}\)

B \(\frac{L_{1}}{L_{2}}\)

C \(L_{1}-L_{2}\)

D \(L_{1}+L_{2}\)

💡 Short Explanation

Total labour is the sum of individual labour requirements. Resource usage follows the additivity assumption. Individual contributions are added together.

✅ Correct Answer Explanation

If: Product A requires L₁ labour hours, and Product B requires L₂ labour hours, then the total labour requirement is simply: Total Labour = L₁ + L₂ This follows the additivity assumption, which states that total resource usage equals the sum of the individual resource requirements. Therefore, Option D is the correct answer.

❓ Why Other Options Are Incorrect

Option A) L₁ × L₂ → Multiplication is not used to calculate total labour usage.
Option B) L₁ / L₂ → Division has no meaning in determining total labour requirements.
Option C) L₁ − L₂ → Subtraction does not represent the total amount of labour used.

🎯 Strategy

used;

Elimination

Application:

Remove options involving multiplication, division, or subtraction because resource usage is additive.

Final Logic:

Total labour equals the sum of the labour required by each product.

🧠 Memory Trick

"Total Labour = Add Labour."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Additivity Assumption

17 A solution such as:
\(x=\frac{20}{19},y=\frac{45}{19}\)
is valid due to:

A Optimization

B Proportionality

C Additivity

D Continuity

💡 Short Explanation

Fractional solutions are permitted in standard LPP. This is due to the continuity assumption. Decision variables may take any real value satisfying the constraints.

✅ Correct Answer Explanation

The values: x = 20/19 y = 45/19 are fractional values. According to the continuity (divisibility) assumption, decision variables in a Linear Programming Problem may take fractional as well as integer values, provided they satisfy all the constraints. Therefore, such a solution is perfectly valid. Hence, Option D is the correct answer.

❓ Why Other Options Are Incorrect

Option A) Optimization → Optimization determines the best solution but does not justify fractional values.
Option B) Proportionality → Proportionality concerns constant rates of contribution, not fractional solutions.
Option C) Additivity → Additivity concerns the summation of contributions rather than the nature of the variable values.

🎯 Strategy

used;

Contextual/Tonal Matching

Application:

Recognize that fractional decision variables indicate the continuity assumption.

Final Logic:

Fractional values are valid because decision variables are continuous.

🧠 Memory Trick

"Fractions Mean Continuity."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Continuity (Divisibility) Assumption

18 Because variables are continuous, the feasible region consists of:

A Only integer points

B Outliers

C Real feasible points

D Negative points only

💡 Short Explanation

Continuous variables can take any real value. Every real point satisfying the constraints is feasible. Integer values are only a subset of the feasible region.

✅ Correct Answer Explanation

The continuity assumption allows decision variables to assume any real value satisfying the constraints. Therefore, the feasible region consists of all real points that satisfy the linear constraints and non-negative restrictions, not merely integer points. Hence, Option C is the correct answer.

❓ Why Other Options Are Incorrect

Option A) Only integer points → Standard LPP is not restricted to integer solutions.
Option B) Outliers → Outliers are statistical observations and are unrelated to the feasible region.
Option D) Negative points only → Negative values violate the non-negative restrictions in LPP.

🎯 Strategy

used;

Elimination

Application:

Recall that continuity allows all real-valued feasible solutions.

Final Logic:

The feasible region contains all real points satisfying the constraints.

🧠 Memory Trick

"Continuous = Real Points."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Continuity (Divisibility) Assumption

📄 Passage

A Linear Programming Problem involves optimizing a linear function of several variables subject to constraints expressed as linear equations or inequalities. The goal is to find an optimal feasible solution. Decision variables are continuous, controllable, and non-negative, allowing fractional values.

Based on the passage, the main objective of LPP is:

A Minimize decision variables

B Optimize a linear function under constraints

C Obtain negative solutions

D Eliminate feasible constraints

💡 Short Explanation

LPP seeks the best possible value of the objective function. The optimization is performed subject to given constraints. The solution must be feasible.

✅ Correct Answer Explanation

A Linear Programming Problem aims to maximize or minimize a linear objective function while satisfying all the given linear constraints and non-negative restrictions. The passage clearly states that the goal is to optimize a linear function subject to constraints to obtain an optimal feasible solution. Therefore: Option B correctly describes the primary objective of LPP. Option A is incorrect because decision variables are optimized indirectly through the objective function rather than minimized themselves. Option C is incorrect because LPP does not seek negative solutions. Option D is incorrect because constraints define the feasible region and cannot be eliminated. Hence, Option B is the correct answer.

❓ Why Other Options Are Incorrect

Option A) Minimize decision variables → The objective is to optimize the objective function, not the variables themselves.
Option C) Obtain negative solutions → Decision variables must satisfy the non-negative restrictions.
Option D) Eliminate feasible constraints → Constraints are essential components of every Linear Programming Problem.

🎯 Strategy

used;

Contextual/Tonal Matching

Application:

Read the passage carefully and identify the sentence describing the primary purpose of Linear Programming.

Final Logic:

The passage explicitly states that LPP optimizes a linear function under constraints.

🧠 Memory Trick

"LPP = Optimize Under Constraints."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Objective of a Linear Programming Problem

📄 Passage

According to the passage, constraints must be expressed as:

A Linear equations or inequalities

B Exponential expressions

C Quadratic forms

D Random limits

💡 Short Explanation

Constraints define the feasible region. They are represented using linear equations or inequalities. This maintains the linear nature of the problem.

✅ Correct Answer Explanation

The passage clearly states that the constraints in a Linear Programming Problem are expressed as linear equations or linear inequalities. These constraints represent the limitations on available resources and determine the feasible region within which the objective function is optimized. Therefore: Option A is correct because it matches the definition given in the passage. Option B is incorrect because exponential expressions are non-linear. Option C is incorrect because quadratic forms violate the linearity assumption. Option D is incorrect because random limits are not mathematical constraints used in LPP. Hence, Option A is the correct answer.

❓ Why Other Options Are Incorrect

Option B) Exponential expressions → Exponential expressions are non-linear and are not used in standard LPP.
Option C) Quadratic forms → Quadratic equations violate the assumption of linearity.
Option D) Random limits → Constraints are mathematically defined linear equations or inequalities, not random limits.

🎯 Strategy

used;

Contextual/Tonal Matching

Application:

Identify the exact description of constraints given in the passage.

Final Logic:

Constraints in an LPP are always represented by linear equations or inequalities.

🧠 Memory Trick

"LPP Constraints = Linear Only."

📚 Class XII – Applied Mathematics – Chapter: Linear Programming – Topic: Linear Constraints and Mathematical Formulation

CUET UG Applied Mathematics Booster Test 1 - Components, Assumptions, and Mathematical Formulation

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