문제 1
If $F(x) = \int_0^{x^2} \cos(\sqrt{t})\,dt$, what is the derivative $F'(x)$?
JEE Main Problem Solver Diagnostic Quiz
Ten advanced multiple choice questions covering calculus, coordinate geometry, rotational mechanics, and thermodynamics.
문제 2
What is the value of the definite integral $I = \int_0^{\pi/2} \frac{\sin^3(x)}{\sin^3(x) + \cos^3(x)}\,dx$?
문제 3
What is the distance between the parallel lines $3x + 4y - 9 = 0$ and $3x + 4y + 6 = 0$?
문제 4
What is the eccentricity of the ellipse $\frac{x^2}{25} + \frac{y^2}{16} = 1$?
문제 5
A uniform thin rod has mass $M$, length $L$, and moment of inertia $I_{\text{cm}} = \frac{1}{12}ML^2$ about its center. What is its moment of inertia about an axis through one end?
문제 6
If satellite orbital velocity near Earth's surface is $v_o$, what is the minimum launch velocity required for an object to escape Earth's gravity?
문제 7
An ideal monoatomic gas ($\gamma = \frac{5}{3}$) expands adiabatically to $8$ times its initial volume ($V_2 = 8V_1$). The final pressure $P_2$ is what fraction of initial pressure $P_1$?
문제 8
In a hydrogen atom, the ground state energy is $-13.6\text{ eV}$. What is the energy of the second excited state ($n = 3$)?
문제 9
What is the value of the limit $\lim_{x \to 0} \frac{1 - \cos(2x)}{x^2}$?
문제 10
Given vectors $\vec{a} = 2\hat{i} + 3\hat{j}$ and $\vec{b} = \hat{i} - 2\hat{j}$, what is the scalar projection of $\vec{a}$ onto $\vec{b}$?