CBSE Class 12 Calculus — practice questions
38 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice CBSE 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:Differential calculus grew from the problem of defining:Integral calculus grew from the problem of calculating:A function whose derivative is the given function is its:The formula giving all the anti derivatives is the:The process of finding anti derivatives is called:Knowing the velocity of an object at each instant, one can find its:How many anti derivatives does a function have?The constant C added to an anti derivative is called:The constant C in an indefinite integral is also called the constant of:Two functions with the same derivative differ by a:Varying C in an anti derivative traces out a:The two forms of the integral are the definite and the:The result linking indefinite and definite integrals is the:The definite integral is useful in science and:In an indefinite integral, x is called the variable of:Integration and differentiation are related as:An anti derivative is also known as a:Adding a different constant to an anti derivative gives:The family of anti derivatives of a function is written with:The problem of finding a function from its derivative leads to the:The problem of finding an area under a graph leads to the:A function whose derivative is zero throughout an interval is: