SATHEE: Neet

Shortcut Methods

January 1, 0001 read

Shortcut Methods

January 1, 0001 read

Shortcut Methods

For a point charge of 1 micro-coulomb, what is the magnitude of the electric field 1 meter away from the charge?

Shortcut: Use the formula $$E=\frac{kQ}{r^2}$$

Calculation: $$E=\frac{(9\times10^9\text{ N}\cdot\text{m}^2/\text{C}^2)(1\times10^{-6}\text{ C})}{(1\text{ m})^2}=9\times10^3\text{ N/C}$$

Final Answer: $$9\times10^3\ N/C$$

A charge of 2 micro-coulombs is placed at the origin. What is the electric field at a distance of 3 meters along the positive z-axis?

Shortcut: Use the formula $$E=kq/r^2$$, and the unit vector in the z-direction $$\hat{z}$$

January 1, 0001 read

Shortcut Methods

CBSE Class 11 and Class 12 Exams

Coefficient of x^2 = 3 Coefficient of x = -2 Constant term = 5 Discriminant D>0 (Since roots are real)

The quadratic equation is $$3x^2-2x+5=0$$

As per hit-and-trial method, the values of a, b, and c are determined as $$a=3, \ b=-2, \ and \ c=5$$ So, we can write it as $$3x^2-3x+x+5=0$$ $$3x(x-1)+(x+5)=0$$ Taking 3x common from the first two terms, and 1 common from the last two terms, we get $$3x(x-1)+1(x+5)=0$$ $$(x+5)(3x-1)=0$$ $$\therefore x=\frac{-5}{3}, and \ \frac{1}{3}$$ Hence, the roots are -5/3 and 1/3 which are real and distinct.

January 1, 0001 read

Shortcut Methods

NEET Level:

Lens Formula: $$\frac{1}{u}+\frac{1}{v} = \frac{n_2 - n_1}{R}$$ where,
u = distance of the object from the spherical surface
v = distance of the image from the spherical surface
R = radius of curvature of the spherical surface
n1 = refractive index of the medium in which the object is placed
n2 = refractive index of the medium in which the image is formed
Focal Length of a Concave Spherical Surface: $$f = \frac{R}{2}$$ where,

January 1, 0001 read

Shortcut Methods

1. Refractive Index (n):

Typical values of the refractive index (n) for different materials:
- Air: n ≈ 1.0003 (at room temperature and pressure)
- Water: n ≈ 1.33
- Glass: n ≈ 1.5 (varies depending on the type of glass)
- Diamond: n ≈ 2.42

2. Angle of Refraction (r):

Snell’s Law: n1 sin i = n2 sin r
- n1: refractive index of medium 1
- n2: refractive index of medium 2
- i: angle of incidence
- r: angle of refraction

3. Critical Angle (c):

The critical angle (c) is the angle of incidence beyond which light is entirely reflected back into the first medium.
sin c = n2/n1

4. Total Internal Reflection:

Occurs when light strikes a boundary between two media at an angle greater than the critical angle.
Used in various optical devices such as prisms, fiber optic cables, and mirrors.

5. Prisms:

Triangular-shaped optical components that refract light.
Angle of deviation (δ): δ = (n - 1)A
- n: refractive index of the prism material
- A: apex angle of the prism

6. Lenses:

Curved optical components that converge (convex lenses) or diverge (concave lenses) light rays.
Focal length (f): distance between the lens and the point where light rays converge or appear to diverge.

neet/CBSE Numerical Values and Concepts:

Determine refractive indices of materials using Snell’s Law.
Calculate critical angles for pairs of materials.
Understand total internal reflection and applications.
Analyze the behavior of light through prisms and calculate angles of deviation.
Understand the concept and determination of focal length for different lenses.
Analyze image formation by lenses, image distances, and magnification.
Solve numerical problems involving Snell’s Law, lens equations, and optical phenomena.
Interpret graphs and diagrams related to refraction and optical instruments.

Note: The numerical values and concepts covered may vary in neet/CBSE exams, so a comprehensive understanding of the underlying principles is essential.

January 1, 0001 read

Shortcut Methods

1. Refractive Index (n):

Typical values of the refractive index (n) for different materials:
- Air: n ≈ 1.0003 (at room temperature and pressure)
- Water: n ≈ 1.33
- Glass: n ≈ 1.5 (varies depending on the type of glass)
- Diamond: n ≈ 2.42

2. Angle of Refraction (r):

Snell’s Law: n1 sin i = n2 sin r
- n1: refractive index of medium 1
- n2: refractive index of medium 2
- i: angle of incidence
- r: angle of refraction

3. Critical Angle (c):

The critical angle (c) is the angle of incidence beyond which light is entirely reflected back into the first medium.
sin c = n2/n1

4. Total Internal Reflection:

Occurs when light strikes a boundary between two media at an angle greater than the critical angle.
Used in various optical devices such as prisms, fiber optic cables, and mirrors.

5. Prisms:

Triangular-shaped optical components that refract light.
Angle of deviation (δ): δ = (n - 1)A
- n: refractive index of the prism material
- A: apex angle of the prism

6. Lenses:

Curved optical components that converge (convex lenses) or diverge (concave lenses) light rays.
Focal length (f): distance between the lens and the point where light rays converge or appear to diverge.

neet/CBSE Numerical Values and Concepts:

Determine refractive indices of materials using Snell’s Law.
Calculate critical angles for pairs of materials.
Understand total internal reflection and applications.
Analyze the behavior of light through prisms and calculate angles of deviation.
Understand the concept and determination of focal length for different lenses.
Analyze image formation by lenses, image distances, and magnification.
Solve numerical problems involving Snell’s Law, lens equations, and optical phenomena.
Interpret graphs and diagrams related to refraction and optical instruments.

Note: The numerical values and concepts covered may vary in neet/CBSE exams, so a comprehensive understanding of the underlying principles is essential.

January 1, 0001 read

Shortcut Methods

1. Menstrual Cycle:

Typical Lengths:
Menstrual cycle: 28 days (average)
Follicular phase: 14 days (approximately)
Luteal phase: 14 days (approximately)
Fertile Window Calculation:
If the menstrual cycle is 28 days, ovulation typically occurs 14 days before the next period. Therefore, the fertile window is roughly between days 10 and 17 of the cycle.

2. Gamete Production:

Primary Spermatocytes:
To produce 128 mature sperm cells, 64 primary spermatocytes are required. (Each primary spermatocyte undergoes two meiotic divisions to produce four haploid sperm cells.)

January 1, 0001 read

Shortcut Methods

1. Number of Seeds Produced

Given: 100 flowers, 100 pollen grains per flower, 5% pollen reach the stigma, 1% fertilization rate.
Calculation:
- Number of pollen grains reaching stigma = 100 flowers x 100 pollen/flower x 5% = 500
- Number of ovules fertilized = 500 x 1% = 5

2. Number of Pollen Grains Required

Given: Pollen viability 85%, stigma receptivity 70%, 1000 pollen grains per flower, 100 ovules.
Calculation:
- Number of viable pollen grains = 1000 x 85% = 850

January 1, 0001 read

Shortcut Methods

CBSE Board Exams

Circular Disc (Rotating): Angular Momentum = $$20 kg.m^2/s$$ Use $$ I=\frac{1}{2}MR^2$$, angular momentum equation: $$ L=I\omega $$

Solid Cylinder (Rolling): Angular Momentum = $$4.24 kg.m^2/s$$ _Use $$ I=\frac{1}{2}MR^2 $$angular momentum equation: $$ L=I\omega $$ _

Two Particles (Rotating): Angular Momentum = $$2.5 kg.m^2/s$$ Use $$ I = m_1r_1^2 + m_2r_2^2 +…$$, angular momentum equation: $$ L=I\omega$$

January 1, 0001 read

Shortcut Methods

I. Kinematics

1. Uniform Circular Motion: To find the tangential velocity (v) of a point on the rim of a rotating disk, simply multiply the angular velocity (\omega) by the radius (r) of the disk.

$$v = \omega r$$

2. Uniform Angular Acceleration: To find the angular displacement (\theta) of a rotating wheel that starts from rest and accelerates uniformly, use the following formula:

$$ \theta = \frac{1}{2} \alpha t^2 $$

January 1, 0001 read

Shortcut Methods

**1.$$ An alpha particle (helium nucleus) of energy 5.5 MeV is scattered through 180° by a gold nucleus. The distance of the closest approach is: Shortcut: The distance of closest approach is given by: $$b = \frac{2Z_1Z_2e^2}{K}$$

Where:

(Z_1) and (Z_2) are the atomic numbers of the two nuclei.
(e) is the elementary charge.
(K) is the kinetic energy of the alpha particle.

Substituting the given values, we get:

$$b = \frac{2(2)(79)(1.6 \times 10^{−19} \text{ C})^2}{5.5 \times 10^6 \text{ eV}}$$ $$b = 30 \times 10^{−15} \text{ m}$$ $$b = 30 \text{ fm}$$

January 1, 0001 read

Shortcut Methods

CBSE Class 11 and Class 12 Exams

Shortcut Methods

NEET Level:

Shortcut Methods

1. Refractive Index (n):

2. Angle of Refraction (r):

3. Critical Angle (c):

4. Total Internal Reflection:

5. Prisms:

6. Lenses:

neet/CBSE Numerical Values and Concepts:

Shortcut Methods

1. Refractive Index (n):

2. Angle of Refraction (r):

3. Critical Angle (c):

4. Total Internal Reflection:

5. Prisms:

6. Lenses:

neet/CBSE Numerical Values and Concepts:

Shortcut Methods

I. Kinematics

Shortcut Methods

Shortcut Methods

Shortcut Methods

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

Shortcut Methods

Shortcut Methods

Shortcut Methods

Shortcut Methods

CBSE Class 11 and Class 12 Exams#

Shortcut Methods

NEET Level:#

Shortcut Methods

1. Refractive Index (n):#

2. Angle of Refraction (r):#

3. Critical Angle (c):#

4. Total Internal Reflection:#

5. Prisms:#

6. Lenses:#

neet/CBSE Numerical Values and Concepts:#

Shortcut Methods

1. Refractive Index (n):#

2. Angle of Refraction (r):#

3. Critical Angle (c):#

4. Total Internal Reflection:#

5. Prisms:#

6. Lenses:#

neet/CBSE Numerical Values and Concepts:#

Shortcut Methods

Shortcut Methods

Shortcut Methods

Shortcut Methods

I. Kinematics#

Shortcut Methods

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Mentorship

NCERT Exercise Video Solution

Forum

For International Students

Get In Touch

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CBSE Class 11 and Class 12 Exams

NEET Level:

1. Refractive Index (n):

2. Angle of Refraction (r):

3. Critical Angle (c):

4. Total Internal Reflection:

5. Prisms:

6. Lenses:

neet/CBSE Numerical Values and Concepts:

1. Refractive Index (n):

2. Angle of Refraction (r):

3. Critical Angle (c):

4. Total Internal Reflection:

5. Prisms:

6. Lenses:

neet/CBSE Numerical Values and Concepts:

I. Kinematics