NIMCET Limit Previous Year Question Paper and Solution with PDF

$\lim _{{n}\rightarrow\infty}\frac{({1}^a+{2}^a+{\ldots+{n}^a})}{{(n+1)}^{a-1}\lbrack(na+1)(na+b)\ldots(na+n)\rbrack}=\frac{1}{60}$ . Then one of the value of

$a$ is

1
2
3
4
Go to Discussion

NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution

Qus : 8NIMCET PYQ 2024

The value of

${{Lt}}_{x\rightarrow0}\frac{{e}^x-{e}^{-x}-2x}{1-\cos x}$ is equal to

1
2
3
4
Go to Discussion

NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution

Evaluate:

$\lim_{x \to 0} \frac{e^x - e^{-x} - 2x}{1 - \cos x}$

Step 1: Apply L'Hôpital's Rule (since it's 0/0):

First derivative:

$\frac{e^x + e^{-x} - 2}{\sin x}$

Still 0/0 → Apply L'Hôpital's Rule again:

$\frac{e^x - e^{-x}}{\cos x}$

Now,

$\lim_{x \to 0} \frac{1 - 1}{1} = 0$

Final Answer:

$\boxed{0}$

Qus : 9NIMCET PYQ 2021

$\lim_{x\to \infty} (\frac{x+7}{x+2})^{x+5}$ equal to

1
2
3
4
Go to Discussion

NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution

Qus : 10NIMCET PYQ 2017

Let f(x) be a polynomial of degree four, having extreme value at x = 1 and x = 2. If

$\lim _{{x}\rightarrow0}[1+\frac{f(x)}{{x}^2}]=3$ , then f(2) is

1
2
3
4
Go to Discussion

NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

Given it has extremum values at x=1 and x=2
⇒f′(1)=0 and f′(2)=0
Given f(x) is a fourth degree polynomial
Let

$f(x)=a{x}^4+b{x}^3+c{x}^2+dx+e$

Given

$\lim _{{x}\rightarrow0}[1+\frac{f(x)}{{x}^2}]=3$

$\lim _{{x}\rightarrow0}\lbrack1+\frac{a{x}^4+b{x}^3+c{x}^2+\mathrm{d}x+e}{{x}^2}\rbrack=3$

$\lim _{{x}\rightarrow0}\lbrack1+a{x}^2+bx+c+\frac{d}{x}+\frac{e}{{x}^2}\rbrack=3$

For limit to have finite value, value of 'd' and 'e' must be 0

⇒d=0 & e=0

Substituting x=0 in limit

⇒ c+1=3

⇒ c=2

$f^{\prime}(x)=4a{x}^3+3b{x}^2+2cx+d$

$x=1$ and

$x=2$ are extreme values,

⇒

$f^{\prime}(1)=0$ and $f^{\prime}(2)=0

⇒

$4a+3b+4=0$ and

$32a+12b+8=0$

By solving these equations

we get,

$a=\frac{1}{2}$ and

$b=-2$

So,

$f(x)=\frac{x^{4}}{2}-2x^{3}+2x^{2}$

⇒

$f(x)=x^{2}(\frac{x^{2}}{2}-2x+2)$

⇒

$f(2)=2^{2}(2-4+2)$

⇒

$f(2)=0$

Qus : 11NIMCET PYQ 2015

The value of

$\lim_{x\to a} \frac{\sqrt{a+2x}-\sqrt{3x}}{\sqrt{3a+x}-2\sqrt{x}}$

1
2
3
4
Go to Discussion

NIMCET Previous Year PYQNIMCET NIMCET 2015 PYQ

Solution

Qus : 12NIMCET PYQ 2017

1
2
3
4
Go to Discussion

NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

Function is the form of

therefore using by L'Hospital rule

Again apply L'Hospital Rule,

Putting x = 0, we get

Qus : 13NIMCET PYQ 2020

Find

1
2
3
4
Go to Discussion

NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution

Qus : 14NIMCET PYQ 2023

$f(x)=\lim _{{x}\rightarrow0}\, \frac{{6}^x-{3}^x-{2}^x+1}{\log _e9(1-\cos x)}$ is a real number then

$\lim _{{x}\rightarrow0}\, f(x)$

1
2
3
4
Go to Discussion

NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

Solution

NIMCET

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

Click Here to
View More

NIMCET

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

Click Here to
View More

Ask Your Question or Put Your Review.

Feedback

Info.

Information

Aspire's Library

NIMCET Previous Year Questions (PYQs)

NIMCET Limit PYQ

Solution

Solution

Quick DL Method Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

Solution

NIMCET

NIMCET

Info.

Confirm Delete

Edit