MCA NIMCET Continuity Previous Year Question Paper and Solution with PDF

Aspire's Library

A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations

MCA NIMCET
Previous Year Questions

MCA NIMCET
Previous Year Questions
MCA NIMCET

MCA NIMCET Previous Year Questions (PYQs)

MCA NIMCET Continuity PYQ

Qus : 1 MCA NIMCET PYQ

Test the continuity of the function at x = 2

$f(x)= \begin{cases} \frac{5}{2}-x & \text{ if } x<2 \\ 1 & \text{ if } x=2 \\ x-\frac{3}{2}& \text{ if } x>2 \end{cases}$

1
2
3
4
Go to Discussion

MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2020 PYQ

Solution

LHL ≠ f(2)

Qus : 2 MCA NIMCET PYQ

Let $f(x) = \lfloor x^2 - 3 \rfloor$ where $\lfloor \cdot \rfloor$ is the greatest integer function. Number of points in $(1,2)$ where $f$ is discontinuous:

1
2
3
4
Go to Discussion

MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2009 PYQ

Solution

Discontinuity occurs when $x^2 - 3$ is an integer

Let $x^2 - 3 = k \Rightarrow x = \sqrt{k+3}$

We need $1 < x < 2$ → square both sides: $1 < \sqrt{k+3} < 2$

$\Rightarrow 1 < k+3 < 4$

$\Rightarrow -2 < k < 1$

Possible integer values: $k = -1, 0$

So number of discontinuities = $2$

Qus : 3 MCA NIMCET PYQ

1
2
3
4
Go to Discussion

MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2012 PYQ

Solution

Qus : 4 MCA NIMCET PYQ

Let $f(x) = \begin{cases} \cos [x], & x\geq 0\\ |x| + a, & x< 0 \end{cases}$ where $[x]$ denotes the greatest integer $\leq x$. If f should be continuous at $x = 0$ then a must be:

1
2
3
4
Go to Discussion

MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2019 PYQ

Solution

Qus : 5 MCA NIMCET PYQ

$f(x)=x+|x|$ is continuous for

1
2
3
4
Go to Discussion

MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2022 PYQ

Solution

Qus : 6 MCA NIMCET PYQ

If $f\colon R\rightarrow R$ is defined by $f(x)=\begin{cases}{\frac{x+2}{{x}^2+3x+2}} & {,\, if\, x\, \in R-\{-1,-2\}} \\ {-1} & {,if\, x=-2} \\ {0} & {,if\, x=-1}\end{cases}$ , then f(x) is continuous on the set

1
2
3
4
Go to Discussion

MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2021 PYQ

Solution

Qus : 7 MCA NIMCET PYQ

If $ f(x)= \begin{cases} x \sin\left(\frac{1}{x}\right), & x \ne 0 \\ 0, & x = 0 \end{cases} $ then

1
2
3
4
Go to Discussion

MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2010 PYQ

Solution

Solution: lim_{x→0} x·sin(1/x) = 0 ⇒ f is continuous at 0. f'(0) = lim_{x→0} [x sin(1/x)]/x = sin(1/x) But sin(1/x) has no limit as x→0⁺ or x→0⁻. ⇒ Both f'(0+) and f'(0-) do not exist.

Qus : 8 MCA NIMCET PYQ

$f(x) = x + |x|$ is continuous for

1
2
3
4
Go to Discussion

MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2018 PYQ

Solution

Qus : 9 MCA NIMCET PYQ

Let $g:\mathbb{R}\rightarrow \mathbb{R}$ and $h:\mathbb{R}\rightarrow \mathbb{R}$, be two functions such that $h(x) = sgn(g(x))$. Then select which of the following is not true?( $\mathbb{R}$ denotes the set of all real numbers, sgn stands for signum function)

1
2
3
4
Go to Discussion

MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2025 PYQ

Solution

Let $g:\mathbb{R}\to\mathbb{R}$ and $h:\mathbb{R}\to\mathbb{R}$ be such that $h(x) = \operatorname{sgn}(g(x))$.

Recall: $\operatorname{sgn}(t) = \begin{cases} 1, & t>0\\ 0, & t=0\\ -1, & t<0 \end{cases}$

Check each statement:

1) "The domain of $h(x)$ is the same as the domain of $g(x)$." $\Rightarrow$ True, because $\operatorname{sgn}(g(x))$ is defined for every $x$ where $g(x)$ is defined.

2) "The domain of continuity of $h(x)$ equals the domain of continuity of $g(x) - \{x\in\mathbb{R} : g(x)=0\}$."

At points where $g(x)\neq 0$, $h(x)$ is locally constant ($1$ or $-1$), hence continuous there (provided $g$ itself is continuous).

At points where $g(x)=0$, $h(x)$ jumps from $-1$ to $1$, so it is discontinuous. $\Rightarrow$

This statement is true.

3) "The domain of $h(x)$ is different from the domain of $g(x)$ at the same point."

Since for every $x$ in the domain of $g$, $h(x)=\operatorname{sgn}(g(x))$ is defined, the domains are exactly the same; they never differ.

$\Rightarrow$ This statement is false.

4) " $h(x)$ is discontinuous at $g(x)=0$."

At any $x_0$ where $g(x_0)=0$, the left and right limits of $h(x)$ are $-1$ and $1$, not equal to $h(x_0)=0$.

$\Rightarrow$ $h$ is discontinuous there, so this statement is true.

Therefore, the statement which is **not true** is: $\boxed{\text{Option 3}}$

Qus : 10 MCA NIMCET PYQ

Consider the function $f$ defined by $f(x)=\begin{cases} x^2-1, & x<3 \ 2ax, & x\geq 3 \end{cases}$ for all real number $x$. If $f$ is continuous at $x=3$, then value of $a$ is

1
2
3
4
Go to Discussion

MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2016 PYQ

Solution

Qus : 11 MCA NIMCET PYQ

is a continuous function at x = 0, then the value of k is

1
2
3
4
Go to Discussion

MCA NIMCET Previous Year PYQ MCA NIMCET NIMCET 2020 PYQ

Solution

MCA NIMCET

Online Test Series,
Information About Examination,
Syllabus, Notification
and More.

Click Here to
View More

MCA NIMCET

Online Test Series,
Information About Examination,
Syllabus, Notification
and More.

Click Here to
View More

Ask Your Question or Put Your Review.

Please provide more information - at least 10 characters

Feedback

Info.

Information

Aspire's Library

MCA NIMCET Previous Year Questions (PYQs)

MCA NIMCET Continuity PYQ

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

MCA NIMCET

MCA NIMCET

Game Changer NIMCET Test Series 2026

Info.

Confirm Delete

Edit