List of top Engineering Mathematics Questions on Calculus

If \(y_{1}=x^{2}\) is a known solution of \[ x^{2}y^{\prime\prime}-3xy^{\prime}+4y=0, \] then the second independent solution \(y_{2}\) is

\[ \lim_{n\rightarrow\infty}\frac{5n^{2}+4}{7n^{2}+6n}= \]

If \[ \vec{v}=(x+y+1)\hat{i}+\hat{j}+(-x-y)\hat{k}, \] then the value of \[ \vec{v}\cdot(\nabla\times\vec{v}) \] is

\[ \lim_{n\rightarrow\infty}\frac{5n^{2}+4}{7n^{2}+6n}= \]

If \[ \vec{v}=(x+y+1)\hat{i}+\hat{j}+(-x-y)\hat{k}, \] then the value of \[ \vec{v}\cdot(\nabla\times\vec{v}) \] is

For the function \(f(x)=\log x\), the number \(c\) strictly between \(e^2\) and \(e^3\) that satisfies \(f'(c)=\dfrac{f(e^3)-f(e^2)}{e^3-e^2}\) is

Let A and B be real symmetric matrices of same size. Which one of the following options is correct?

A function f(x) is defined on the interval with values in R. It satisfies \( \int_0^2 f(x)[x-f(x)]dx = \frac{2}{3} \). Find the value of f(1).}

Find the order and degree of the following differential equation: \[ \frac{d^3 y}{dx^3} + \frac{d^2 y}{dx^2} + \frac{dy}{dx} + y = 0 \]

Solve the second-order differential equation: \[ y'' + 0.8 y' + 0.16 y = 0, \quad y(0) = 3, \quad y'(0) = 4.5 \]