Shortcut Methods

NEET

1. Resonance Formula

$$f_0=\frac{1}{2\pi\sqrt{LC}}$$

Where:

$$f_0$$ is the resonant frequency in Hz
$$L$$ is the inductance in Henry
$$C$$ is the capacitance in Farads

2. Time Period Formula

$$T_0=\frac{2\pi\sqrt{LC}}{1}$$

Where:

$$T_0$$ is the time period in seconds
$$L$$ is the inductance in Henry
$$C$$ is the capacitance in Farads

3. Energy Storage Formula

The total energy stored in an LC circuit at any instant is given by:

January 1, 0001 read

Shortcut Methods

NEET

Find the value of log10(2018!) - log10(2017!).

Shortcut method:

Use the fact that log10(n!) = log10(1×2×3…n) = log10(1) + log10(2) + log10(3) + … + log10(n).
Therefore, log10(2018!) - log10(2017!) = [log10(1) + log10(2) + log10(3) + … + log10(2018)] - [log10(1) + log10(2) + log10(3) + … + log10(2017)] = log10(2018).

Trick:

Notice that the sum of the first 2017 positive integers is given by the formula: 1+2+3+4+…+2017= 2017×(2018)/2 = 2035896.
Therefore, log10(2018!) - log10(2017!) = log10(2018) - log10(2035896) = log10(2018/2035896) = log10(1/1016) = -3.

Solve the equation log2(x+2) + log2(x-2) = 3.

Shortcut method:

January 1, 0001 read

Shortcut Methods

CBSE Board Level:

Magnetic field due to a long straight wire:

$$B = \frac{\mu_0 I}{2\pi d}$$

Where:

B is the magnetic field (in Tesla)
I is the current (in Ampere)
d is the distance from the wire (in meters)
µ0 is the permeability of vacuum (( 4\pi \times 10^{-7}) H/m)

Magnetic field at the center of a circular loop:

$$B = \frac{\mu_0 I}{2R}$$

Where:

B is the magnetic field (in Tesla)
I is the current (in Ampere)
R is the radius of the loop (in meters)

Magnetic field inside a solenoid:

$$B = \mu_0 nI$$

January 1, 0001 read

Shortcut Methods

1. Particle Motion:

De Broglie Wavelength (λ): $$λ = \frac{h}{mv}$$ where h is Planck’s constant (6.626 x 10^-34 Js), m is the particle’s mass, and v is its velocity.

2. Photoelectric Effect:

Maximum Kinetic Energy (KE_max): $$ KE_{max} = hf - \varphi $$ where h is Planck’s constant, f is the frequency of light, and φ is the work function of the metal surface.

3. Quantum Mechanics:

Schrödinger Equation: $$-\frac{\hbar^2}{2m} \frac{d^2\psi(x)}{dx^2} + V(x)\psi(x) = E\psi(x)$$ where Ψ is the wave function, ħ is the reduced Planck constant, m is the particle’s mass, V is the potential energy function, E is the total energy, and x is the position.

4. Nuclear Reactions:

January 1, 0001 read

Shortcut Methods

#CBSE Board Exam: There are no additional shortcut methods or tricks mentioned for solving numerical problems related to moments of inertia.

January 1, 0001 read

Shortcut Methods

1. Mirror Formula (for spherical mirrors):

Object distance (u): Typically ranges from a few centimeters to infinity (∞).
Image distance (v): Can be positive (for real images) or negative (for virtual images).
Focal length (f): Typically ranges from a few centimeters to a few meters.

2. Magnification (for spherical mirrors):

Lateral magnification (m): Can be positive (enlarged image) or negative (diminished image).
Values for lateral magnification can range from less than 1 (diminished image) to greater than 1 (enlarged image).

3. Mirror Equation:

Relation between object distance (u), image distance (v), and focal length (f) is given by 1/u + 1/v = 1/f.

4. Laws of Reflection:

Angles of incidence (i) and reflection (r) are typically measured in degrees and their values are equal, i.e., i = r.

5. Ray Tracing Diagrams:

Construction of ray diagrams for spherical mirrors involves drawing incident rays parallel to the principal axis, rays through the center of curvature, and rays toward the focus.

6. Sign Conventions:

Standard sign conventions are used for distances and heights:
Distances are positive for real objects and negative for virtual objects.
Heights are positive for images above the principal axis and negative for images below the principal axis.

7. Focal Length Measurements:

The focal length of a spherical mirror can be experimentally determined using the object-image distance relationship or the thin lens equation.

8. Types of Images:

Real images are formed by the actual convergence of reflected light rays, while virtual images appear to form behind the mirror due to the divergence of reflected rays.

Note:

These numerical values are approximate and can vary depending on the specific problem or scenario.

January 1, 0001 read

Shortcut Methods

Double-Slit Interference

Fringe width: $$\beta = \frac{\lambda D}{d},$$ where (\beta) is the fringe width, (\lambda) is the wavelength of light, (D) is the distance from the slits to the screen, and (d) is the slit separation.
Separation of bright fringes: $$\Delta x = \frac{\lambda D}{d}$$
Intensity distribution: $$I = I_0 \cos^2 \left(\frac{\pi d}{\lambda D}x\right),$$ where (I_0) is the maximum intensity and (x) is the distance from the central fringe.

Michelson Interferometer

Wavelength of light $$\lambda = \frac{2D}{N},$$ where (D) is the path difference and (N) is the number of fringes observed.
Coherence Length $$l_c = \frac{\lambda}{2(\Delta \lambda)},$$ where (l_c) is the coherence length and (\Delta \lambda) is the spectral bandwidth of the light source.

Young’s Double-Slit Experiment

Fringe spacing $$x = \frac{\lambda D}{d},$$ where (x) is the fringe spacing, (\lambda) is the wavelength of light, (D) is the distance to the screen, and (d) is the slit separation.
Fringe width $$\beta = \frac{2\lambda D}{d},$$ where (\beta) is the fringe width.
Total Number of fringes: $$N = \frac{D}{\beta}=\frac{d}{2\lambda}$$

Coherence and Incoherence

Coherent sources: Emit waves with the same frequency, constant phase difference, and a definite phase relation.
Incoherent sources: Emit waves with random phase differences and no definite phase relation.

Thin Film Interference

Condition for constructive interference: $$2tn = m\lambda, \quad m=0, 1, 2, 3,…$$
Condition for destructive interference: $$2tn = (m+\frac{1}{2})\lambda, \quad m=0, 1, 2, 3,…$$ where (t) is the film thickness, (n) is the refractive index of the film, (\lambda) is the wavelength of light, and (m) is the order of interference.

January 1, 0001 read

Shortcut Methods

1. Mirror Formula (for spherical mirrors):

Object distance (u): Typically ranges from a few centimeters to infinity (∞).
Image distance (v): Can be positive (for real images) or negative (for virtual images).
Focal length (f): Typically ranges from a few centimeters to a few meters.

2. Magnification (for spherical mirrors):

Lateral magnification (m): Can be positive (enlarged image) or negative (diminished image).
Values for lateral magnification can range from less than 1 (diminished image) to greater than 1 (enlarged image).

3. Mirror Equation:

Relation between object distance (u), image distance (v), and focal length (f) is given by 1/u + 1/v = 1/f.

4. Laws of Reflection:

Angles of incidence (i) and reflection (r) are typically measured in degrees and their values are equal, i.e., i = r.

5. Ray Tracing Diagrams:

Construction of ray diagrams for spherical mirrors involves drawing incident rays parallel to the principal axis, rays through the center of curvature, and rays toward the focus.

6. Sign Conventions:

Standard sign conventions are used for distances and heights:
Distances are positive for real objects and negative for virtual objects.
Heights are positive for images above the principal axis and negative for images below the principal axis.

7. Focal Length Measurements:

The focal length of a spherical mirror can be experimentally determined using the object-image distance relationship or the thin lens equation.

8. Types of Images:

Real images are formed by the actual convergence of reflected light rays, while virtual images appear to form behind the mirror due to the divergence of reflected rays.

Note:

These numerical values are approximate and can vary depending on the specific problem or scenario.

January 1, 0001 read

Shortcut Methods

Linear Motion in a Plane (1D Motion)

Speed: Speed can be calculated by dividing the distance traveled by the time taken. To quickly calculate speed when distance is given in kilometers and time in hours, multiply the distance by 1000/3600. For example, if a car travels 120 kilometers in 2 hours, its speed is (120 x 1000/3600) = 33.33 m/s.
Acceleration: Acceleration can be determined by dividing the change in velocity by the time interval. To simplify calculations when acceleration is given in m/s² and time in seconds, multiply acceleration by the time squared. For instance, if an object starts from rest and accelerates at 5 m/s² for 10 seconds, its final velocity is 5 x (10²) = 50 m/s.

January 1, 0001 read

Shortcut Methods

Work Done:

$$W= F \times d$$ where

W = work done (in joules)
F = force applied (in newtons)
d = displacement (in meters)

In this case, the force is 5 N and the displacement is 20 m, so the work done is: $$W= 5 \text{ N} \times 20 \text{ m} = 100 \text{ J}$$ Therefore, the work done on the particle is 100 J.

Potential Energy (Spring):

$$PE = (1/2) kx^2$$ where,

January 1, 0001 read

Shortcut Methods

January 1, 0001 read

Shortcut Methods

1. To find the inverse of a matrix, you can use the adjoint formula. The adjoint of a matrix is the transpose of its cofactor matrix. For the given matrix $$A$$, the adjoint is: $$A^{adj} = \begin{bmatrix} 3 & -6 & 3 \\ -4 & 8 & -4 \\ 1 & -2 & 1 \end{bmatrix}$$ Therefore, the inverse of $$A$$ is: $$A^{-1} = \frac{A^{adj}}{|A|}$$ where $$|A|$$ is the determinant of $$A$$. In this case, the determinant is $$|A| = 0$$, so the matrix is not invertible.

January 1, 0001 read

Shortcut Methods

NEET#

Shortcut Methods

Shortcut Methods

CBSE Board Level:#

Shortcut Methods

Shortcut Methods

Shortcut Methods

1. Mirror Formula (for spherical mirrors):#

2. Magnification (for spherical mirrors):#

3. Mirror Equation:#

4. Laws of Reflection:#

5. Ray Tracing Diagrams:#

6. Sign Conventions:#

7. Focal Length Measurements:#

8. Types of Images:#

Note:#

Shortcut Methods

Double-Slit Interference#

Michelson Interferometer#

Young’s Double-Slit Experiment#

Coherence and Incoherence#

Thin Film Interference#

Shortcut Methods

1. Mirror Formula (for spherical mirrors):#

2. Magnification (for spherical mirrors):#

3. Mirror Equation:#

4. Laws of Reflection:#

5. Ray Tracing Diagrams:#

6. Sign Conventions:#

7. Focal Length Measurements:#

8. Types of Images:#

Note:#

Shortcut Methods

Shortcut Methods

Shortcut Methods

Shortcut Methods

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Mentorship

NCERT Exercise Video Solution

Forum

For International Students

Get In Touch

Menu

NEET

CBSE Board Level:

1. Mirror Formula (for spherical mirrors):

2. Magnification (for spherical mirrors):

3. Mirror Equation:

4. Laws of Reflection:

5. Ray Tracing Diagrams:

6. Sign Conventions:

7. Focal Length Measurements:

8. Types of Images:

Note:

Double-Slit Interference

Michelson Interferometer

Young’s Double-Slit Experiment

Coherence and Incoherence

Thin Film Interference

1. Mirror Formula (for spherical mirrors):

2. Magnification (for spherical mirrors):

3. Mirror Equation:

4. Laws of Reflection:

5. Ray Tracing Diagrams:

6. Sign Conventions:

7. Focal Length Measurements:

8. Types of Images:

Note: