Application of Derivatives: JEE Main Mathematics Previous Year Questions

274 previous year questions from Application of Derivatives. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. 1.If the tangent drawn at a point $P$ on the curve $y=3x^2-5x+7$ is parallel to its chord joining the points $\left(1\text{,}{y}_1\right)$ and…
2. 2.An angle between the curves $x^2-y^2=4$ and $x^2+y^2=4\sqrt{2}$ is
3. 3.For which value (s) of $a$ $f\text{(}x\text{)}=-x^3+4a{x}^2+2x-5$ is decreasing for every $x$ ?
4. 4.The rate of change of area of a circle with respect to its radius at $r=2\text{cms}$ is
5. 5.$m$ is the slope of a tangent to the curve $e^y=1+x^2$ at $x=1$ then $m=$
6. 6.The equation of the normal to the curve $\text{sin}y=\sqrt{3}x\text{sin}\text{⁡}(\frac{\pi }{6}+y)$ at $x=0$, is
7. 7.A sphere increases its volume at the rate of $\pi \text{cc}/s$. The rate at which its surface area increases when the radius is $1\text{cm}$ is
8. 8.If $f\text{(}x\text{)}=\text{(}2k+1\text{)}x-3-k{e}^{-x}+2e^x$ is monotonically increasing for all $x\text{∈}R$, then the least value of $k$ is
9. 9.If $p\text{(}x\text{)}$ be a polynomial of degree three that has a local maximum value $8$ at $x=1$ and a local minimum value $4$ at $x=2$ ; then…
10. 10.For the curve $4x^5=5y^4$, the ratio of the cube of the subtangent at a point on the curve to the square of the subnormal at the same point is
11. 11.The maximum value of $\frac{{\text{log}}_e\text{⁡}x}{x}$, if $x>0$ is
12. 12.The tangent of the angle between the curves $\text{xy}=1$ and $x^2+8y=0$, is
13. 13.If the surface area of a cube is increasing at a rate of $3.6{\text{cm}}^2/\text{sec}$ retaining its shape; then the rate of change of its volume (in…
14. 14.If $x=t^2$ and $y=2t$ are parametric equations of a curve, then equation of the normal to the curve at $t$ $=2$ is
15. 15.Let $f\text{(}x\text{)}=x^{2025}-x^{2000}\text{,}x\text{∈}\text{[}0\text{,}1\text{]}$ and the minimum value of the function $f\text{(}x\text{)}$ in the interval…
16. 16.The approximate value of $\text{cos}\text{⁡}{31}^{\circ }$ is (Take $1^{\circ }=0.0174$ )
17. 17.The real number k for which the equation, 2x3 + 3x + k = 0 has two distinct real roots in [0, 1]
18. 18.If the tangent at a point $P$ on the curve $y=4x^4+x$ is perpendicular to the tangent to the same curve at $\text{(}0\text{,}0\text{)}$, then the point $P$ is
19. 19.The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds,, it bec…
20. 20.If the tangent to the curve, $y=f\text{(}x\text{)}=x{\text{log}}_e\text{⁡}x\text{,}\text{(}x>0\text{)}$ at a point $\text{(}c\text{,}f\text{(}c\text{)}\text{)}$ is pa…
21. 21.The set of all a$\in$R for which the equation x |x-l| + |x + 2|+a = 0 has exactly one real root, is
22. 22.If $x=f\text{(}t\text{)}$ and $y=g\text{(}t\text{)}$ are differentiable functions of $t$, then $\frac{d^{2}y}{d{x}^2}$ is
23. 23.The equation of the tangent to the curve y = x + $\frac{4}{x^2}$, that is parallel to the x-axis,
24. 24.If $x=1$ is a critical point of the function $f\text{(}x\text{)}=\text{(}3x^2+\text{ax}-2-a\text{)}{e}^x$, then:
25. 25.Let $C$ be the locus of the mirror image of a point on the parabola $y^2=4x$ with respect to the line $y=x$. Thenthe equation of tangent to $C$ at…