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IPMAT Limits, Continuity and Functions Questions 2026
IPMAT Limits, Continuity and Functions questions are an important part of the IPMAT Quant section. These questions check how well you understand the basic ideas of limits, continuity, and functions. You may get questions on finding limits, checking whether a function is continuous, finding the domain and range, and solving simple function-based questions.
These questions may be asked directly or may come as part of a longer question. The good thing is that this topic becomes much easier when your basics are clear. You do not need very advanced maths for this chapter. You only need clear concepts, regular practice, and careful solving.
In this blog, you will find a simple formula PDF, a set of practice questions with answers, and some extra questions to solve on your own. You will also learn about common mistakes students make and a few easy tips to save time in the exam.
Important Formulas for IPMAT Limits, Continuity and Functions Questions
You only need a few basic formulas and rules to solve most Limits, Continuity and Functions questions in IPMAT. These formulas help you find limits, check continuity, and solve function-based questions more easily.
You can download the full formula PDF from the link above. Here is a quick look at some of the main formulas:
Concept | Formula / Meaning |
Function | A function gives one output for one input |
Limit at x = a | lim x→a f(x) |
Limit of a constant | lim x→a c = c |
Limit of x | lim x→a x = a |
Sum rule | lim x→a [f(x) + g(x)] = lim x→a f(x) + lim x→a g(x) |
Difference rule | lim x→a [f(x) - g(x)] = lim x→a f(x) - lim x→a g(x) |
Product rule | lim x→a [f(x) × g(x)] = lim x→a f(x) × lim x→a g(x) |
Quotient rule | lim x→a [f(x) / g(x)] = lim x→a f(x) / lim x→a g(x), if g(x) is not 0 |
Power rule | lim x→a [f(x)]ⁿ = [lim x→a f(x)]ⁿ |
Continuity at x = a | A function is continuous at x = a if the function value exists, the limit exists, and both are equal |
Domain of a function | All values of x that are allowed |
Range of a function | All values that come as output |
Polynomial function | A function like ax² + bx + c |
Rational function | A function in the form p(x) / q(x), where q(x) is not 0 |
Modulus function | f(x) = |x| |
Greatest Integer Function | f(x) = [x], the greatest integer less than or equal to x |
Identity function | f(x) = x |
Constant function | f(x) = c |
One-one function | Different inputs give different outputs |
Onto function | Every output value in the codomain is used |
These formulas are useful for solving questions on limits, continuity, domain, range, and different types of functions that often come in IPMAT.
Top 5 Common Mistakes to Avoid in IPMAT Limits, Continuity and Functions Questions
Not understanding the basic concepts: First make sure you understand what function, limit, continuity, domain, and range mean.
Using direct substitution in every limit question: In some questions, direct substitution gives 0/0. In such cases, you should simplify the expression first.
Not checking where the function is not defined: Always check where the denominator becomes 0 or where the value inside the square root becomes negative.
Confusing limit with continuity: A limit may exist at a point, but the function may still not be continuous there.
Making small calculation mistakes: Many students know the correct method but lose marks because of simple mistakes in signs or simplification.
List of IPMAT Limits, Continuity and Functions Questions
Here is a short set of IPMAT-style Limits, Continuity and Functions questions to help you practise. These include common types of questions based on limits, continuity, domain, range, and functions. Practise them regularly to become faster and more confident before your IPMAT exam.
Question 1
Let A and B be two sets such that the Cartesian product $$A \times B$$ consists of four elements. If two elements of $$A \times B$$ are (1, 4) and (4, 1), then
correct answer:- 2
Question 2
The inequality $$\log_{a} f(x)<\log_{a} g(x)$$ implies that
correct answer:- 1
Question 3
The function $$f(x) = \dfrac{x^{3} - 5x^{2} - 8x}{3}$$ is
correct answer:- 3
Question 4
Let f and g be two functions defined by $$f(x) = \mid x + \mid x \mid \mid$$ and $$g(x) = \frac{1}{x}$$ for $$x \neq 0$$. If $$f(a) + g(f(a)) = \frac{13}{6}$$ for some real a, then the maximum possible value of $$f(g(a))$$ is:
correct answer:- 6
Question 5
Given $$f(x) = x^2 + \log_{3} x$$ and $$g(y) = 2y + f(y)$$, the value of g(3) equals
correct answer:- 1
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Question 6
A real-valued function f satisfies the relation f(x)f(y) = f(2xy + 3) + 3f(x + y) - 3f(y) + 6y, for all real numbers x and y, then the value of f(8) is.
correct answer:- 19
Question 7
A set of all possible values the function $$f(x)=\frac{x}{|x|}$$, where $$x \neq 0$$ takes is,
correct answer:- 2
Question 8
Let P(X) denote power set of a set X. If A is the null set, then the number of elements in P(P(P(P(A)))) is
correct answer:- 16
Question 9
Let A = {1, 2, 3} and B = {a, b}. Assuming all relations from set A to set B are equally likely, what is the probability that a relation from A to B is also a function?
correct answer:- 2
Question 10
If $$f(x^{2} + f(y)) = xf(x) + y$$ for all non-negative integers x and y, then the value of $$[f(0)]^{2} + f(0)$$ equals________.
correct answer:- 1
Question 11
Let the set $$P = \{2,3,4, \dots, 25\}$$. For each $$k \in P$$, define $$Q(k) = \{x \in P$$ such that $$x > k$$ and $$k$$ divides $$x\}$$. Then the number of elements in the set $$P - {\bigcup}_{k = 2}^{25} Q(k)$$ is
correct answer:- 9
Question 12
Suppose that a real-valued function f(x) of real numbers satisfies f(x + xy) = f(x) + f(xy) for all real x, y, and that f(2020) = 1. Compute f(2021)
correct answer:- 1
Question 13
If f(1) = 1 and f(n) = 3n - f(n - 1) for all integers n > 1 , then the value of f(2023) is _________
correct answer:- 3034
Question 14
If a function f(a) = max (a, 0) then the smallest integer value of x for which the equation f(x — 3) + 2𝑓(x + 1) = 8 holds true is _______________.
correct answer:- 3
Question 15
If f(n)= 1 + 2 + 3 +∙∙∙+(n+1) and $$g(n)$$ = $$\sum_{k=1}^{k=n}\frac{1}{f(k)}$$ then the least value of $$n$$ for which $$g(n)$$ exceeds the value $$\frac{99}{100}$$ is ____________.
correct answer:- 199
