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NIMCET Previous Year Questions (PYQs)

NIMCET Differentiation PYQ

NIMCET PYQ
$$ \frac{d^{2}x}{dy^{2}} \; = \; ? $$

$ (a) -\left(\dfrac{d^{2}y}{dx^{2}}\right)^{-1}\left(\dfrac{dy}{dx}\right)^{-3} $
$ (b) \left(\dfrac{d^{2}y}{dx^{2}}\right)\left(\dfrac{dy}{dx}\right)^{-2} $
$ (c) -\left(\dfrac{d^{2}y}{dx^{2}}\right)\left(\dfrac{dy}{dx}\right)^{-3} $
$ (d) \left(\dfrac{d^{2}y}{dx^{2}}\right)^{-1} $





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NIMCET Mathematics PYQ NIMCET Differentiation (Disha JEE) PYQ

Solution

NIMCET PYQ
If x = a cos t, y = b sin t, then $\frac{d^{2}y}{dx^{2}}$ is





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NIMCET Previous Year PYQ NIMCET NIMCET 2013 PYQ

Solution

NIMCET PYQ
The function $f(x)=\begin{cases}{{(1+2x)}^{1/x}} & {,x\ne0} \\ {{e}^2} & {,x=0}\end{cases}$, is





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NIMCET Previous Year PYQ NIMCET NIMCET 2022 PYQ

Solution

NIMCET PYQ
If $x^my^n$=$(x+y)^{m+n}$, then $\frac{dy}{dx}$ is





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NIMCET Previous Year PYQ NIMCET NIMCET 2022 PYQ

Solution

NIMCET PYQ
If $y={\tan }^{-1}\lgroup{\frac{3x-{x}^3}{1-3{x}^2}}\rgroup\, ,\, \frac{-1}{\sqrt[]{3}}{\lt}x{\lt}\frac{1}{\sqrt[]{3}}$ then $\frac{dy}{dx}$ is





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NIMCET Previous Year PYQ NIMCET NIMCET 2021 PYQ

Solution

Incorrect question
NIMCET PYQ
If $y=\sin ^{-1}(\frac{{x}^2+1}{\sqrt[]{1+3{x}^2+{x}^4}}),\, (x>0),$ then  $\frac{dy}{dx}$=





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NIMCET Previous Year PYQ NIMCET NIMCET 2021 PYQ

Solution

NIMCET PYQ
Differential coefficient of  with respect to  to





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NIMCET Previous Year PYQ NIMCET NIMCET 2018 PYQ

Solution

NIMCET PYQ
If y = cos2 x2 , find dy/dx





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NIMCET Previous Year PYQ NIMCET NIMCET 2017 PYQ

Solution

Let $y = [\cos(x^2)]^2$. Using the chain rule: 

 \[ \frac{dy}{dx} = 2\cos(x^2)\cdot \frac{d}{dx}\big(\cos(x^2)\big) \]  \[      = 2\cos(x^2)\cdot\big(-\sin(x^2)\cdot 2x\big) \] \[= -4x\,\cos(x^2)\sin(x^2). \] Using $\;2\sin u\cos u=\sin(2u)$ with $u=x^2$: \[ \frac{dy}{dx} = -2x\,\sin\!\big(2x^2\big). \]

Answer: ${\dfrac{dy}{dx}=-4x\,\sin\!\big(x^2\big) \cos (x^2)}$

NIMCET PYQ
The derivative of (x3 + ex + 3x + cotx) with respect to x is





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NIMCET Previous Year PYQ NIMCET NIMCET 2017 PYQ

Solution

$\dfrac{d}{dx}(x^3) = 3x^2$

$\dfrac{d}{dx}(e^x) = e^x$

$\dfrac{d}{dx}(3x) = 3$

$\dfrac{d}{dx}(\cot x) = -cosec^2 x$

Therefore, total derivative $= 3x^2 + e^x + 3 - cosec^2 x$

Answer: $\boxed{3x^2 + e^x + 3 - cosec^2 x}$ ✅

NIMCET PYQ
Differentiate [- log(log x),  x > 1] with respect to x





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NIMCET Previous Year PYQ NIMCET NIMCET 2017 PYQ

Solution

Let $y=-\log(\log x)$

$\dfrac{dy}{dx}=-\dfrac{d}{dx}[\log(\log x)]$

$\dfrac{d}{dx}[\log(\log x)]=\dfrac{1}{\log x}\cdot\dfrac{1}{x}$

Therefore, $\dfrac{dy}{dx}=-\dfrac{1}{x\log x}$

Answer: $\boxed{-\dfrac{1}{x\log x}},\; x>1$ ✅

NIMCET PYQ
With the usual notation $\frac{d^{2}x}{dy^{2}}$





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NIMCET Previous Year PYQ NIMCET NIMCET 2015 PYQ

Solution


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