JEE Main Calculus — practice questions
33 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Main Calculus in the app →According to the second derivative test, if $f'(c)=0$ and $f''(c)>0$, then $x=c$ isSuppose $f$ is continuous on $[a,b]$ and differentiable on $(a,b)$. If $f'(x)>0$ for every $x\in(a,b)$, then $If a curve has slope $m$ at a point, then the slope of the normal at that point isWhich set of conditions is required in Rolle's theorem on $[a,b]$?If $y=f(x)$ and $\Delta x$ is small, the differential approximation for the corresponding small change in $y$ If $x$ and $y$ are given parametrically in terms of $t$, then $\dfrac{dy}{dx}$ isIf $y=f(g(x))$, then by the chain rule $\dfrac{dy}{dx}$ equalsWhich of the following standard limits is equal to $1$?Using standard limits, evaluate $\lim_{x\to 0}\dfrac{a^x-1}{x}$ for $a>0$.The derivative of $a^x$ for $a>0$ and $a\neq 1$ isWhich statement is always true for a differentiable function at a point?If $f$ and $g$ are continuous at $x=0$ and $g(0)\neq 0$, which of the following is necessarily continuous at $Which condition correctly states that a function $f(x)$ is continuous at $x=0$?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:Consider the ratio $r = \frac{1-a}{1+a}$ to be determined by measuring a dimensionless quantity $a$. If the erA physical quantity $X$ is given by $X = \frac{q^3 b^2}{c qrt{d}}$. The percentage error in $X$ is (given $\DThe error in the measurement of radius of a sphere is 2%. The error in the measurement of volume is:The percentage errors in the measurement of mass and speed are 2% and 3% respectively. The maximum percentage