Shortcut Methods
JEE Advanced
1. For calculating the time of flight in projectile motion, remember the equation:
$$Time = \frac{2(Final\ Velocity + Intial\ Velocity)\times\sin\theta}{g}$$
2. For quick calculation of the angle in projectile motion, just add 45° with half of the given angle.
3. When given the equation of the trajectory, the horizontal range is given by $$R = \frac{u^2\sin 2\theta}{g}$$
4. For quick calculations of the maximum height
$$H = \frac{u^2\sin^2\theta}{2g}$$
5. For easy estimation in a potentiometer experiment, remember that at the balancing point $$Length = \frac{e.m.f\ of\ Cell}{Potential\ Gradient}$$
6. For quick calculations of the drift velocity in a conductor $$v_d=\frac{ne\mu E}{m}$$
7. To find the angle between the magnetic field and the current carrying conductor for maximum magnetic force, just remember
$$B\perp I\Rightarrow\theta=90\degree$$
8. For easy calculations of the magnetic force on a moving charge, remember the formula
$$F=q(v\times B)\sin\theta$$
9. To find the frequency of revolution of a charged particle in a magnetic field, remember the equation:
$$f = \frac{qB}{2\pi m}$$
10. For quick calculations of the electric potential due to a point charge
$$V = \frac{1}{4\pi\epsilon_0}\cdot \frac{Q}{r}$$
11. To find the energy stored in a capacitor, just remember the equation:
$$E=\frac{1}{2}CV^2$$
12. To find the reactance of an inductor, use the formula:
$$X_{L} = 2\pi fL$$
13. To recall the equation for the capacitive reactance, remember the equation:
$$X_{C} = \frac{1}{2\pi fC}$$
CBSE Board Exams
1. For calculating the time of flight in projectile motion, remember the equation:
$$Time = \frac{2(Final\ Velocity + Intial\ Velocity)\times\sin\theta}{g}$$
2. For quick calculation of the angle in projectile motion, just add 45° with half of the given angle.
3. When given the equation of the trajectory, the horizontal range is given by $$R = \frac{u^2\sin 2\theta}{g}$$
4. For quick calculations of the maximum height
$$H = \frac{u^2\sin^2\theta}{2g}$$
5. For easy estimation in a potentiometer experiment, remember that at the balancing point
$$Length = \frac{e.m.f\ of\ Cell}{Potential\ Gradient}$$
6. To find the magnetic force on a current carrying conductor, just remember the formula:
$$F = BIL\sin\theta$$
7. For quick calculations of the electric potential due to a point charge
$$V = \frac{1}{4\pi\epsilon_0}\cdot \frac{Q}{r}$$
**8.**To find the energy stored in a capacitor, remember the equation:
$$E=\frac{1}{2}CV^2$$
9. To find the reactance of an inductor, use the formula:
$$X_{L} = 2\pi fL$$
10. To recall the equation for the capacitive reactance, remember the equation: $$X_{C} = \frac{1}{2\pi fC}$$