MHT-CET SERIES

Mathematics

Relations And Functions

28 previous year questions.

Volume: 28 Ques

Yield: High

High-Yield Trend

2025

2023

2020

Chapter Questions
28 MCQs

PYQ 2020

medium

mathematics ID: mht-cet-

The perimeter of the triangle whose vertices have the position vectors,, and is

units

units

units

units

PYQ 2020

medium

mathematics ID: mht-cet-

The function is increasing for all:

PYQ 2020

medium

mathematics ID: mht-cet-

If then the function is

an even function

an identity function

a constant function

an exponential function

PYQ 2020

medium

mathematics ID: mht-cet-

If,,,, where is the universal set and and are subsets of, then

300

400

340

240

PYQ 2020

medium

mathematics ID: mht-cet-

If

PYQ 2020

medium

mathematics ID: mht-cet-

The domain of the function is}

1

2

3

4

Official Solution

Correct Option: $(3)$

$Step 1: Analyze the domain of the function. For the function to be defined, we must have the following conditions: - (the square root must be non-negative). - must lie between -1 and 1 for to be valid. Step 2: Solve for the domain. We find that the domain of the function is . Step 3: Conclusion. The correct answer is (C) .$

07

PYQ 2020

medium

mathematics ID: mht-cet-

$If the function is continuous at, then$

1

$2$

2

$10$

3

$12$

4

$11$

Official Solution

Correct Option: $(3)$

$Step 1: Condition for continuity at . For continuity at, Step 2: Evaluate the limit. Step 3: Use standard limit. Using we get Step 4: Substitute value of . Thus,$

08

PYQ 2020

medium

mathematics ID: mht-cet-

$If,, then is {$

1

$an even function$

2

$not defined for all$

3

$a constant function$

4

$an odd function$

Official Solution

Correct Option: $(4)$

$Step 1: Find . Step 2: Substitute into the function. Step 3: Simplify. Step 4: Test for odd function. Step 5: Conclusion. Hence, is an odd function.$

09

PYQ 2020

medium

mathematics ID: mht-cet-

$Given, . If is a relation from to such that with, then the range of is$

1

2

3

4

Official Solution

Correct Option: $(1)$

$Step 1: Understand the relation. The relation consists of all ordered pairs such that Step 2: List possible pairs. For : all such that give valid pairs, so is included. For : values of satisfying exist (namely), so is included. For : there is no such that, so is excluded. Step 3: Determine the range. The range of a relation consists of all second elements of the ordered pairs. Hence,$

10

PYQ 2020

medium

mathematics ID: mht-cet-

$If is continuous at, then the value of is}$

1

2

3

4

Official Solution

Correct Option: $(1)$

$Step 1: Apply continuity condition at . For continuity, Step 2: Evaluate the limit. Using as, Step 3: Use the continuity value. Step 4: Solve for . Step 5: Conclusion. The value of is .$

11

PYQ 2020

medium

mathematics ID: mht-cet-

$If the angle between the lines given by the equation$

1

2

$10$

3

4

$2$

Official Solution

Correct Option: $(4)$

$Step 1: Using the formula for the angle between two lines. The general equation for the angle between two lines is given by: where and are the slopes of the lines. For the given quadratic equation, we use the condition for the angle between the lines and the discriminant method to find . Step 2: Finding the value of . After solving for, we get . Step 3: Conclusion. Thus, the value of is 2, which makes option (D) the correct answer.$

12

PYQ 2020

medium

mathematics ID: mht-cet-

$The radius of the circle passing through the points is$

1

$2 units$

2

$5 units$

3

$4 units$

4

$3 units$

Official Solution

Correct Option: $(2)$

$Step 1: Using the formula for the radius of the circle. The radius of a circle passing through three points is given by the formula: Step 2: Applying the formula. Using the points,, and, we calculate the radius to be 5 units. Step 3: Conclusion. Thus, the radius of the circle is 5 units, which makes option (B) the correct answer.$

13

PYQ 2020

medium

mathematics ID: mht-cet-

$The value of is$

1

2

3

4

Official Solution

Correct Option: $(3)$

$Step 1: Use the addition formula for arctangent. We can use the identity for the sum of two arctangents: We apply this identity sequentially to sum all four terms in the given expression. After performing the calculations, we find that the sum of these arctangents is . Step 2: Conclusion. Thus, the correct answer is, corresponding to option (C).$

14

PYQ 2020

medium

mathematics ID: mht-cet-

$If,, and,, then$

1

2

3

$3$

4

Official Solution

Correct Option: $(3)$

$Step 1: Composition of functions. To find, we first compute and then substitute the result into . Step 2: Compute . Substitute into : Step 3: Compute . Substitute into : Simplifying: Step 4: Conclusion. Thus,, and the correct answer is .$

15

PYQ 2020

medium

mathematics ID: mht-cet-

$The p.d.f. of a continuous r.v. is given by then is$

1

2

3

4

Official Solution

Correct Option: $(4)$

$Step 1: Write the cumulative distribution function. The cumulative distribution function (CDF) is the integral of the probability density function (PDF) from to : Step 2: Perform the integration. Perform the integration: Step 3: Conclusion. Thus, the correct answer is, corresponding to option (D).$

16

PYQ 2020

medium

mathematics ID: mht-cet-

$A line makes angles,, with the co-ordinate axes, then is equal to$

1

$2$

2

$-1$

3

$1$

4

$-2$

Official Solution

Correct Option: $(2)$

$Step 1: Use the property of the angles. For a line making angles,, with the co-ordinate axes, we use the identity: Step 2: Calculate the sum. Using the identity, we have: Step 3: Conclusion. The correct answer is .$

17

PYQ 2020

medium

mathematics ID: mht-cet-

$If and, then$

1

2

3

4

Official Solution

Correct Option: $(1)$

$Step 1: Equating the two functions. We are given, so Step 2: Simplify and solve for . After expanding and simplifying the equation, we get: Simplifying further gives: Solving this quadratic equation results in and . Step 3: Conclusion. The correct answer is (A) .$

18

PYQ 2020

medium

mathematics ID: mht-cet-

$If for, and for, then which of the following statements is true?$

1

$is continuous at$

2

3

4

$is discontinuous at$

Official Solution

Correct Option: $(4)$

$Step 1: Check the left-hand and right-hand limits. For, the function is either 1 or -1 depending on whether or . Step 2: Conclusion. Since the left-hand and right-hand limits of are not equal at, the function is discontinuous at . Therefore, the correct answer is (D) is discontinuous at .$

19

PYQ 2023

easy

mathematics ID: mht-cet-

$, . Find at$

1

$4$

2

$1$

3

$5$

4

$3$

Official Solution

Correct Option: $(3)$

$Step 1: Find : Given: Step 2: Find : Given: Step 3: Find : Substitute into : Step 4: Find : Substitute into : Step 5: Find : Substitute into : Step 6: Find : Substitute into : Step 7: Find : Substitute into : Final Answer: Therefore,$

20

PYQ 2023

easy

mathematics ID: mht-cet-

$Considering only the principal value of an inverse function, the set: A= { x \geq 0, tan -1 x + tan -1 6x =}, then A is...$

1

$an empty set$

2

$a singleton set$

3

$consists of two elements$

4

$contains more than two elements$

Official Solution

Correct Option: $(2)$

$We are tasked with finding the set that satisfies the equation: Let's solve this step by step. Step 1: Apply the sum identity for inverse tangents: Using the identity: we can rewrite the equation as: Step 2: Simplify the numerator and denominator: Simplifying the expression inside the inverse tangent: Step 3: Eliminate the inverse tangent: We take the tangent of both sides of the equation to eliminate the inverse tangent function: Since, we get: Step 4: Solve for : Multiply both sides of the equation by : Rearranging the equation: This is a quadratic equation in terms of . Step 5: Solve the quadratic equation: We can solve the quadratic equation using the quadratic formula: where,, and . Substituting these values into the formula: Simplifying: Step 6: Determine the valid solution: Since must be greater than or equal to 0 according to the set, we discard the negative solution. Thus, we take the positive root: Therefore, the set consists of the single element: Final Answer: The correct answer is (B) a singleton set.$

21

PYQ 2025

medium

mathematics ID: mht-cet-

$An ellipse has OB as semi-minor axis, S and S' are foci and angle SBS' is a right angle. Then the eccentricity of the ellipse is$

1

2

3

4

Official Solution

Correct Option: $(2)$

$Concept: For ellipse: Step 1: Use geometric condition. At point : Given : Step 2: Substitute. Step 3: Find eccentricity. Step 4: Conclusion.$

22

PYQ 2025

medium

mathematics ID: mht-cet-

1

2

3

4

Official Solution

Correct Option: $(1)$

$Step 1: Simplify the base Base . Step 2: Form As, base and exponent . Limit Step 3: Calculation Using change of base: . Exponent . Result . Final Answer: (A)$

23

PYQ 2025

medium

mathematics ID: mht-cet-

$Considering only the principal values of the inverse trigonometric function, the value of is$

1

2

3

4

Official Solution

Correct Option: $(4)$

$Step 1: Conversion Let . Then . Let . Then . Step 2: Formula We need . Step 3: Calculation . Wait, let's re-verify the values. If and, then . Checking the options: (C) is . Final Answer: (C)$

24

PYQ 2025

medium

mathematics ID: mht-cet-

1

2

3

4

Official Solution

Correct Option: $(2)$

$Step 1: Simplify Trigonometry . Step 2: Substitution Let . Integral . Step 3: Integration . Final Answer: (B)$

25

PYQ 2025

medium

mathematics ID: mht-cet-

$The general solution of the differential equation is$

1

2

3

4

Official Solution

Correct Option: $(2)$

$Step 1: Simplify Trigonometry . Step 2: Variable Separable . Step 3: Integration . Final Answer: (B)$

26

PYQ 2025

medium

mathematics ID: mht-cet-

$If a random variable has the p.d.f. then c.d.f. of X is$

1

2

3

4

Official Solution

Correct Option: $(3)$

$Concept: For a valid p.d.f., total probability must be 1: Step 1: Find constant . Step 2: Find c.d.f. . (for) Step 3: Conclusion.$

27

PYQ 2025

medium

mathematics ID: mht-cet-

$A plane passes through and is perpendicular to the planes and . The distance of the point from this plane is ________ units.$

1

$1$

2

3

4

Official Solution

Correct Option: $(2)$

$Concept: Plane perpendicular to two planes â normal is cross product of normals. Step 1: Normals. Step 2: Cross product. Step 3: Equation of plane. Step 4: Distance. Conclusion. Distance =$

28

PYQ 2025

medium

mathematics ID: mht-cet-

$In a triangle, with usual notations, if Then is$

1

2

3

4

Official Solution

Correct Option: $(1)$

$Concept: Use given ratios and cosine formula: Step 1: Assume common value. Let: Step 2: Solve for sides. Add all: Step 3: Find cosines. Step 4: Simplify ratio. Adjusting properly: Step 5: Conclusion.$

About Relations And Functions - MHT-CET

Relations And Functions is a vital chapter for MHT-CET aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.

By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.

Frequently Asked Questions

Why focus on Relations And Functions PYQs?

Analyzing PYQs for this specific chapter reveals the most frequently tested concepts and the typical complexity of questions, allowing you to tailor your study plan efficiently.

How to best use this analysis?

Review the topic breakdown to see which sub-topics within Relations And Functions carry the most weight. Then, tackle the questions iteratively to solidify your understanding.

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Relations And Functions

High-Yield Trend

Chapter Questions 28 MCQs

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About Relations And Functions - MHT-CET

Frequently Asked Questions

Why focus on Relations And Functions PYQs?

How to best use this analysis?

Chapter Questions
28 MCQs