Here are some shortcut methods and tricks to solve JEE Main/Advanced/CBSE Board Exam numericals:

JEE Main Numerical

• 1. Using the equation: $$v=\sqrt{2ax} $$where v is the final velocity, a is the acceleration, and x is the displacement, you can find the speed of the rod after it has moved 50 cm.

• 2. Use the formula: $$\epsilon=NAB\omega $$where ϵ is the emf induced in the coil, N is the number of turns in the coil, A is the area of the coil, B is the magnetic field strength, and ω is the angular velocity of the coil.

• 3. Use the formula: $$\frac{V_p}{N_p}=\frac{V_s}{N_s} $$where Vp and Vs are the voltages across the primary and secondary coils, respectively, and Np and Ns are the number of turns in the primary and secondary coils.

• 4. Use the formula: $$B=\mu_0nI,$$ where B is the magnetic field inside the solenoid, μ0 is the permeability of free space, n is the number of turns per unit length, and I is the current.

• 5. Use the formula: $$\tau=BIl\sin\theta$$ where τ is torque, B is the magnetic field strength, I is the current, l is the length of the conductor in the magnetic field, and θ is the angle between the conductor and the magnetic field.

JEE Advanced Numerical

• 1. Use Newton’s second law to find the equation of motion of the rod: $$ma = BIl - mg\sin\theta $$where m is the mass of the rod, a is the acceleration of the rod, B is the magnetic field strength, I is the current, l is the length of the rod in the magnetic field, g is the acceleration due to gravity, and θ is the angle between the rod and the horizontal.

• 2. Use the formula: $$\epsilon=\frac{d\Phi}{dt} $$ where ϵ is the emf induced in the coil, Φ is the magnetic flux through the coil, and t is time. To calculate the magnetic flux, use the formula $$\Phi=NBA\cos\theta $$ where N is the number of turns in the coil, B is the magnetic field strength, A is the area of the coil, and θ is the angle between the coil and the magnetic field. Then use $$P=I\epsilon $$ to find the average power dissipated.

• 3. Use the formula from question 3 of JEE Main Numerical.

• 4. Use the formula from question 4 of JEE Main Numerical.

• 5. Use the formula: $$\tau=BIl\sin\theta$$ where τ is torque, B is the magnetic field strength, I is the current, l is the length of the conductor in the magnetic field, and θ is the angle between the conductor and the magnetic field. To find the sensitivity, use the formula $$S=\frac{\theta}{I} $$ where S is the sensitivity, θ is the angle of deflection, and I is the current.

CBSE Board Exam Numerical

• 1. Using the equation: $$v=\sqrt{2ax} $$where v is the final velocity, a is the acceleration, and x is the displacement, you can find the speed of the rod after it has moved 20 cm.

• 2. Use the formula: $$\epsilon=NAB\omega $$where ϵ is the emf induced in the coil, N is the number of turns in the coil, A is the area of the coil, B is the magnetic field strength, and ω is the angular velocity of the coil.

• 3. Use the formula from question 3 of JEE Main Numerical.

• 4. Use the formula: $$B=\mu_0nI $$where B is the magnetic field inside the solenoid, μ0 is the permeability of free space, n is the number of turns per unit length, and I is the current.

• 5. Use the formula: $$\tau=BIl\sin\theta$$ where τ is torque, B is the magnetic field strength, I is the current, l is the length of the conductor in the magnetic field, and θ is the angle between the conductor and the magnetic field.