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Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable Mock Test for JEE

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Part of Limit, Continuity and Differentiability in JEE Main Mathematics.

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Q1MathsUnit 7: Limit, Continuity and Differentiability
If the radius of a sphere is measured as 9cm9 \mathrm{cm} with an error of 0.03cm0.03 \mathrm{cm} then, find the approximate error in calculating its volume
Q2MathsUnit 7: Limit, Continuity and Differentiability
If the ratio of base radius and height of a cone is 1: 2 and percentage error in radius is λ%,\lambda \%, then the error in its volume is
Q3MathsUnit 7: Limit, Continuity and Differentiability
Function f(x)=(x+2)e−x\boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}+\mathbf{2}) \boldsymbol{e}^{-\boldsymbol{x}} is
Q4MathsUnit 7: Limit, Continuity and Differentiability
The two curves x3−3xy2+2=0x^{3}-3 x y^{2}+2=0 and 3x2y−y3−2=0\mathbf{3} \boldsymbol{x}^{2} \boldsymbol{y}-\boldsymbol{y}^{3}-\boldsymbol{2}=\mathbf{0}
Q5MathsUnit 7: Limit, Continuity and Differentiability
Equation of normal drawn to the graph of the function defined as f(x)=sin⁡x2xf(x)=\frac{\sin x^{2}}{x} x≠0\boldsymbol{x} \neq \mathbf{0} and f(0)=0\boldsymbol{f}(\mathbf{0})=\mathbf{0} at the origin is?
Q6MathsUnit 7: Limit, Continuity and Differentiability
The point on the curve y=x2y=x^{2} which is nearest to (3,0) is
Q7MathsUnit 7: Limit, Continuity and Differentiability
For x∈R\boldsymbol{x} \in \boldsymbol{R} let f(x)=∣sin⁡x∣\boldsymbol{f}(\boldsymbol{x})=|\sin \boldsymbol{x}| and g(x)=∫0xf(t)dt.g(x)=\int_{0}^{x} f(t) d t . Let p(x)=g(x)−2πxp(x)=g(x)-\frac{2}{\pi} x Then
Q8MathsUnit 7: Limit, Continuity and Differentiability
The normals to the curve y=x2−x+y=x^{2}-x+ 1, drawn at the points with the abscissa x1=0,x2=−1\boldsymbol{x}_{1}=\mathbf{0}, \boldsymbol{x}_{2}=-\mathbf{1} and x3=52\boldsymbol{x}_{3}=\frac{\mathbf{5}}{\mathbf{2}}
Q9MathsUnit 7: Limit, Continuity and Differentiability
For a curve at which the tangent lines at two distinct points coincide, then the curve cannot be
Q10MathsUnit 7: Limit, Continuity and Differentiability
Mark the correct alternative of the following. f(x)=1+2sin⁡x+3cos⁡2x,0≤x≤f(x)=1+2 \sin x+3 \cos ^{2} x, 0 \leq x \leq 2π3\frac{2 \pi}{3} is?
Q11MathsUnit 7: Limit, Continuity and Differentiability
If the percentage error in the edge of a cube is 1,1, then error in its volume is
Q12MathsUnit 7: Limit, Continuity and Differentiability
Assertion (A):(A): If f(x)=∣x∣,f(x)=|x|, then ff has minimum value at x=0x=0 Reason (R): A function f(x) has minimum value at x=ax=a if f′(a)=0f^{\prime}(a)=0 and f′′(a)>0\mathbf{f}^{\prime \prime}(\mathbf{a})>\mathbf{0}
Q13MathsUnit 7: Limit, Continuity and Differentiability
If there is an error of 2%2 \% in measuring the length of a simple pendulum, then percentage error in its period is
Q14MathsUnit 7: Limit, Continuity and Differentiability
f(x)=tan⁡−1x−xf(x)=\tan ^{-1} x-x is −1_{-1} R\boldsymbol{R}
Q15MathsUnit 7: Limit, Continuity and Differentiability
Let f(x)=(x−p)2+(x−q)2+(x−\boldsymbol{f}(\boldsymbol{x})=(\boldsymbol{x}-\boldsymbol{p})^{2}+(\boldsymbol{x}-\boldsymbol{q})^{2}+(\boldsymbol{x}- r)2.\boldsymbol{r})^{2} . Then f(x)\boldsymbol{f}(\boldsymbol{x}) has a minimum at x=λ\boldsymbol{x}=\boldsymbol{\lambda} where λ\lambda is equal to

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