Aspire's Library

A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations
  • CUET UG Mathematics Applied
    Previous Year Questions

CUET UG Mathematics Applied Previous Year Questions (PYQs)

CUET UG Mathematics Applied Differentiation PYQ

CUET UG Mathematics Applied PYQ
The second order derivative of which of the following functions is $5^x$?





Go to Discussion
CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2024 Mathematics PYQ

Solution

CUET UG Mathematics Applied PYQ
If $y=\left(\frac{1}{x}\right)^x$, then value of $e^e\left(\frac{d^2 y}{dx^2}\right)_{x=e}$ is:





Go to Discussion
CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2022 Applied Mathematics PYQ

Solution

Given

$y=\left(\frac{1}{x}\right)^x$

Rewrite:

$y=x^{-x}$

Taking log:

$\ln y=-x\ln x$

Differentiate:

$\frac{1}{y}\frac{dy}{dx}=-(\ln x+1)$

So,

$\frac{dy}{dx}=-x^{-x}(\ln x+1)$

Now differentiate again:

$\frac{d^2y}{dx^2}=x^{-x}\left[(\ln x+1)^2-\frac{1}{x}\right]$

Now put $x=e$

Since $\ln e=1$

$(\ln x+1)^2=(1+1)^2=4$

So,

$\frac{d^2y}{dx^2}\Big|_{x=e}=e^{-e}\left(4-\frac{1}{e}\right)$

Multiply by $e^e$:

$e^e\left(\frac{d^2y}{dx^2}\right)_{x=e}=4-\frac{1}{e}$
CUET UG Mathematics Applied PYQ
If $y=e^{nx}$, then $n^{\text{th}}$ derivative of $y$ is:





Go to Discussion
CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2022 Applied Mathematics PYQ

Solution

Given

$y=e^{nx}$

First derivative:

$\frac{dy}{dx}=n e^{nx}$

Second derivative:

$\frac{d^2y}{dx^2}=n^2 e^{nx}$

Continuing this pattern,

$n^{\text{th}}$ derivative:

$\frac{d^ny}{dx^n}=n^n e^{nx}$

Since $y=e^{nx}$,

$\frac{d^ny}{dx^n}=n^n y$
CUET UG Mathematics Applied PYQ
If $y=\log(\sec e^{x^2})$, then $\frac{dy}{dx}=$





Go to Discussion
CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2022 Applied Mathematics PYQ

Solution

$y=\log(\sec(e^{x^2}))$

Using property:

$\frac{d}{dx}\log(\sec u)=\tan u\cdot\frac{du}{dx}$

Let $u=e^{x^2}$

Then,

$\frac{du}{dx}=2xe^{x^2}$

Hence,

$\frac{dy}{dx}=2xe^{x^2}\tan(e^{x^2})$

CUET UG Mathematics Applied PYQ
If $t=e^{2x}$ and $y=ln(t^2)$, then $\frac{d^2y}{dx^2}$ is





Go to Discussion
CUET UG Mathematics Applied Previous Year PYQ CUET UG Mathematics Applied CUET UG 2024 Mathematics PYQ

Solution


CUET UG Mathematics Applied

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

Click Here to
View More

CUET UG Mathematics Applied

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

Click Here to
View More
Limited Seats
× Aspire MCA Promotion

Game Changer NIMCET Test Series 2026

Boost your preparation with mock tests, analysis and rank-focused practice.

JOIN NOW
Ask Your Question or Put Your Review.

loading...