COMEDK UGET 2026 Calculus Practice Questions with Solutions

Preparing COMEDK UGET 2026 Calculus Practice Questions with Solutions is a decisive step if you want to secure a strong score in Mathematics, as Calculus consistently contributes a significant number of questions in COMEDK UGET 2026 exam . As you work through practice questions with solutions, you gradually build conceptual clarity, speed, and confidence—three essentials for this time-bound exam. The most important portions from Calculus that you must focus on include Limits & Continuity, Differentiability, Applications of Derivatives (AOD), Indefinite and Definite Integrals, Area Under Curves, and Differential Equations. These topics not only carry high weightage but also allow for repeated practice with standard methods, making them scoring if prepared systematically.

When you analyze the type and nature of questions asked, you will notice that COMEDK favors concept-based, application-oriented MCQs rather than lengthy calculations. Questions from Limits and Continuity often test standard limits, graphical understanding, and continuity at a point. Differentiability questions usually involve checking differentiability using left-hand and right-hand derivatives or applying basic derivative rules. From Applications of Derivatives, expect questions on monotonicity, maxima–minima, tangents and normals, and increasing–decreasing functions. In Integral Calculus, previous years have frequently asked standard integrals, properties of definite integrals, and direct formula-based questions on Area Under Curves, while Differential Equations questions are generally straightforward, focusing on formation and solution of first-order differential equations.

To prepare this chapter effectively, you should start by strengthening your NCERT fundamentals, as most questions are directly or indirectly based on standard results and methods. Practice a wide variety of previous year–level questions topic-wise, and always analyze solutions to understand shortcuts and common traps. While solving practice sets, aim for accuracy first, then speed, especially in Differentiation and Integration. Maintaining a small formula notebook for limits, derivatives, standard integrals, and properties of definite integrals will help in quick revision. Finally, you should regularly attempt mixed Calculus practice tests so that you learn to switch between subtopics smoothly—this approach ensures you are fully prepared for any Calculus question that appears in COMEDK UGET 2026.

Also Check - Do or Die Chapters for COMEDK UGET 2026 Mathematics

COMEDK UGET 2026 Calculus Important Topics

The COMEDK UGET 2026 Mathematics syllabus features all the important topics based on which COMEDK question paper 2026 will be prepared. In the following table, we have provided the detailed Calculus topics for the entrance exam.

COMEDK UGET 2026 Calculus Expected Weightage

Calculus weightage will help you know the expected number of questions that will be asked in COMEDK UGET 2026 question paper. As per the trends from the past few years, the expected weightage of Calculus in COMEDK UGET 2026 is around 25%. You can check the detailed COMEDK UGET 2026 Calculus weightage below:

COMEDK UGET 2026 Calculus Practice Questions with Solutions

COMEDK Calculus practice questions will help you gain a better understanding of concepts and fundamentals. In the following section, we have listed down some of the most important COMEDK UGET 2026 Calculus practice questions with solutions:

Q1. Which of the following function is injective?

a. f(x) = |x +2|, x ∊ [ –2, ∞)

b. f(x) = x ² + 2, x ∊ (- ∞, ∞)

c. f(x) = 4x ² + 3x - 5, x ∊ (- ∞, ∞)

d. f(x) = (x - 4) (x - 5), x ∊ (- ∞, ∞)

Ans. a. f(x) = |x +2|, x ∊ [ –2, ∞)

Solution: Let's examine each option to check for injectivity. A function is injective (one-to-one) if different inputs always produce different outputs. In other words, for any two numbers a and b in the domain, if f(a) = f(b) then a = b.

Below is a breakdown of each option:

Option a: f(x) = |x +2|, x ∊ [ –2, ∞)

For x ≥ -2, the expression x + 2 is non-negative, so the absolute value function simplifies:

f(x) |x + 2| = x + 2

The function now is a linear function, f(x) = x + 2, which is strictly increasing over the domain [-2, ∞)

Because an increasing linear function never repeats the same output for different inputs, this function is injective. Thus option a is correct.

Q2. equals to:

a. -3/2

b. 1/2a ^3/2

c. 1/2

d. 2a ^-3/2

Ans. b. 1/2a ^3/2

Solution: The given limit is in the form of 0/0 as x →0. . To solve this, we will use the rationalization method.

Multiplying both numerator and denominator by the conjugate of the numerator, we get:

Now, we can directly substitute x = 0 into the expression, to get:

1/√[a(a+0)(√a+0 + √a)]

Simplifying the equation,

1/2a ^3/2

Q3. If Sin y = x(cos(a+y)), then find dy/dx when x = 0:

a. 1

b. Sec a

c. Cos a

d. -1

Ans. c. Cos a

Solutions: If Sin y = x(cos(a+y)), then find dy/dx when x = 0

Differentiating both sides of the equation with respect to x, we get

Cos ydy/dx = cos (a+y) + x(-sin(a+y)dy/dx

Cos y dy/dx + x sin (a+y)dy/dx = cos(a+y)

dy/dx(cos y + x sin(a+y)) = cos(a+y)

dy/dx = cos(a+y)/[cos y+xsin(a+y)]

When x = 0, we have

dy/dx = cos(a+y)/cos y

Since Sin y = xcos (a+y), when x = 0, we have sin y = 0. This implies y = 0 (since we are looking for the derivative at x =0)

Therefore, x = 0.

dy/dx = cos(a+0)/cos0 = Cos a.

Q4. The rate of change of the volume of a sphere with respect to its surface area S is?

a. 1/2√S/π

b. √S/π

c. 2/3√S/π

d. 1/4√S/π

Ans. d. 1/4√S/π

Solution: To find the rate of change of the volume of a sphere with respect to its surface area, we first need to express both the volume and the surface area in terms of the radius of the sphere.

The volume V of a sphere is given by the formula:

V = 4/3 πr ³

The surface area S of a sphere is given by the formula:

S = 4πr ²

We need to find the rate of change of V with respect to S, which is expressed as dV/dS. To do this, we use the chain rule:

dV/dS = dV/dr.dr/dS

First, we find dV/dr,

dV/dr = d/dr(4/3πr ³ ) = 4πr ²

Next, we find dS/dr,

dS/dr = d/dr(4πr ² ) = 8πr

Now, we need to find dr/dS. Since dS/dr = 8πr

we can write: dr/dS = 1/8πr

Finally, we substitute, dV/dr and dr/dS back into the chain rule expression:

dV/dS = (4πr ² ).(1/8πr) = r/2

We know from the surface area formula that S = 4πr ² . Solving for r in terms of S, we get:

r ² = S/4π = √S/4π

Substituting this back into dV/dS, we get:

dV/dS = 2/s√S/4π = 1/2.1/2√S/π = 1/4√S/π

Q5. The area enclosed by the pair of lines x = 0, the line x - 4 = 0 and y + 5 = 0 is

a. 10 square unit

b. 20 square unit

c. 50 square unit

d. 5/4 square unit

Ans. b. 20 square unit

Solution: We have,

xy = 0, x - 4 = 0, y + 5 = 0

x = 0, y = 0, x = 4, y = -5

So, area enclosed = Area of rectangle of OABC

AB X BC

5 X 4 = 20 square unit.

You should also revise Calculus equations and formulas from COMEDK 2026 Mathematics formula sheet to tackle the questions easily and promptly, thus saving valable time in the exam hall.

Important Portions from Calculus & How You Should Study Them

Candidates can check the below table to know how they can study the important portions from Calculus.

Topic-wise Question Distribution & Pattern

Check the distribution of questions from the below table.

Number of Questions Asked from Calculus in Last 6 Years

You can get an overall idea how important this chapter is by knowing the no of questions that were asked in the last 6 years.

Common Traps in Calculus

Make sure you do not fall in the below mentioned traps.

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