Relations And Functions

01

PYQ 2020

medium

mathematics ID: mht-cet-

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

1

units

2

units

3

units

4

units

02

PYQ 2020

medium

mathematics ID: mht-cet-

The function is increasing for all:

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3

4

03

PYQ 2020

medium

mathematics ID: mht-cet-

If then the function is

1

an even function

2

an identity function

3

a constant function

4

an exponential function

04

PYQ 2020

medium

mathematics ID: mht-cet-

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

1

300

2

400

3

340

4

240

05

PYQ 2020

medium

mathematics ID: mht-cet-

If

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2

3

4

06

PYQ 2020

medium

mathematics ID: mht-cet-

The domain of the function is}

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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-

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

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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-

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

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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-

$The value of is$

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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-

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

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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-

$If and, then$

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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-

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

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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-

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

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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-

$The general solution of the differential equation is$

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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-

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

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2

3

4

Official Solution

Correct Option: (1)

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

High-Yield Trend

Chapter Questions
28 MCQs

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Relations And Functions

High-Yield Trend

Chapter Questions 28 MCQs

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Chapter Questions
28 MCQs