Uttarakhand Board Class 12 Calculus — practice questions
16 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice Uttarakhand Board Class 12 Calculus in the app →Find the order and degree of the differential equation $\dfrac{d^2y}{dx^2} + 3\left(\dfrac{dy}{dx}\right)^4 + The integrating factor of the linear differential equation $\dfrac{dy}{dx} + \dfrac{y}{x} = x^2$ is:To solve the homogeneous differential equation $\dfrac{dy}{dx} = \dfrac{x^2 + y^2}{xy}$, the appropriate substThe number of arbitrary constants in the general solution of a differential equation of order $n$ is:$\displaystyle\int x^n\,dx$ (where $n \ne -1$) equals:$\displaystyle\int \dfrac{1}{1+x^2}\,dx$ equals:$\displaystyle\int \dfrac{1}{ qrt{1 - x^2}}\,dx$ equals:$\displaystyle\int ec^2 x\,dx$ equals:$\displaystyle\int \tan x\,dx$ equals:Using integration by parts, $\displaystyle\int x e^x\,dx$ equals:In integration by parts $\displaystyle\int u\,dv$, the preferred order for choosing the first function $u$ is $\displaystyle\int \log x\,dx$ equals:$\displaystyle\int e^x\bigl(f(x) + f'(x)\bigr)\,dx$ equals:Using the substitution $t = 1 + x^2$, $\displaystyle\int \dfrac{x}{1 + x^2}\,dx$ equals:Using partial fractions, $\displaystyle\int \dfrac{1}{(x-1)(x-2)}\,dx$ equals:$\displaystyle\int \dfrac{1}{x^2 - a^2}\,dx$ (with $|x| > a > 0$) equals: