AMU MCA Application of Derivatives Previous Year Question Paper and Solution with PDF

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AMU MCA Previous Year Questions (PYQs)

AMU MCA Application Of Derivatives PYQ

Qus : 1 AMU MCA PYQ

The kinetic energy of a body is twice its rest mass energy. What is the ratio of relativistic mass to rest mass?

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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2020 PYQ

Solution

Given: $K = 2m_0c^2$

Total energy $E = K + m_0c^2 = 3m_0c^2$

$E=\gamma m_0 c^2$

$\gamma=3$

Relativistic mass $=\gamma m_0=3m_0$

Ratio $=\frac{m}{m_0}=3$

Qus : 2 AMU MCA PYQ

The value of the integral $I=\iint_R e^{x^2+y^2},dy,dx$ where $R$ is the semicircular region bounded by the $x$-axis and the curve $y=\sqrt{1-x^2}$ is

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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2022 PYQ

Solution

Qus : 3 AMU MCA PYQ

The derivative of $f(x,y)=x^2+xy$ at $P_0(1,1)$ in the direction of unit vector $\vec{u}=\left(\frac{1}{\sqrt{2}}\right)\hat{i}+\left(\frac{1}{\sqrt{2}}\right)\hat{j}$ is

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AMU MCA Previous Year PYQ AMU MCA AMU MCA 2021 PYQ

Solution

$\nabla f=(2x+y, x)$ At $(1,1)$: $\nabla f=(3,1)$ Directional derivative: $D_{\vec{u}}f=(3,1)\cdot\left(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}\right)$ $=\frac{3+1}{\sqrt{2}}=\frac{4}{\sqrt{2}}=2\sqrt{2}$