JEE Main Calculus — practice questions
112 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 $x=0$?$ in(180° - \theta)$ equals:$ in^2\theta + \cos^2\theta$ equals:$ in(A + B) = $$\cos 2\theta$ equals:If $ in\theta + \cos\theta = 1$, then $ in\theta \cdot \cos\theta$ equals:$\cos 3\theta$ equals: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:sin(0°) equals:cos(90°) equals:sin²θ + cos²θ equals:tan(45°) equals:In which quadrant is sin θ positive and cos θ negative?sec θ is defined as:sin(A + B) equals:cos(A + B) equals:sin(60°) cos(30°) + cos(60°) sin(30°) equals:If sin θ = 3/5 (θ in Q1), find cos θ:Find cos(75°) using cos(A + B):sin(2θ) equals:cos(2θ) equals:Find sin(15°):If tan θ = 1/2 (acute), find sin 2θ:For 0 ≤ θ < 2π, solutions of sin θ = 1/2:1 - cos²θ equals:sin(A) + sin(B) equals (sum-to-product):In a right triangle, if hypotenuse = 13 and one leg = 5, sin θ for angle θ opposite to that leg:tan(A + B) equals:sin(180° - θ) equals:In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states:If sin θ + cos θ = 1, then sin θ × cos θ equals:General solution of cos θ = 0:If tan θ + cot θ = 2, find sin 2θ:If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):Minimum value of sin²θ + cos⁴θ:If sin θ = 12/13 (acute), find tan(θ/2):In triangle with sides 7, 8, 9, find cos of the angle opposite to side 9 (use cosine rule):General solution of sin θ = sin α: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 In radian measure, $\pi$ radians equals:The identity $1 + \tan^2\theta$ equals:The period of the function $ in x$ is:The radian measure of $45^\circ$ is:The value of $ in\dfrac{\pi}{6}$ is:The expansion of $ in(A+B)$ is:The maximum value of $3 in\theta$ is:The value of $\cos 180^\circ$ is:An angle of $90^\circ$ in radians is:The value of $ in(\pi/4)$ is:The identity $ in 2A$ equals:The general solution of $\cos x = 1/2$ is:The angle 90° in radians is:The fundamental Pythagorean identity in trigonometry is:The exact value of cos 60° is:The double angle formula sin 2A equals:The general solution of sin θ = 1/2 is:The principal value range of sin⁻¹(x) is:In a triangle ABC, the Law of Sines states:The Law of Cosines, given sides a, b and included angle C, gives the third side c as:The function f(x) = tan x has vertical asymptotes at: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: