SATHEE: Neet

Shortcut Methods

1. Genetically Modified Crops:

To calculate the percentage increase in crop yield achieved by introducing a GM trait:

Increase in yield (%) = [(Yield of GM crop - Yield of conventional crop) / Yield of conventional crop] x 100
To determine the economic benefits gained from cultivating a GM crop:

Economic benefit = (Increased productivity x Crop value) - (Reduced production costs)

2. Tissue Culture:

To calculate the number of plantlets that can be produced from a single explant:

January 1, 0001 read

Shortcut Methods

1. Electric Field due to a Charged Conducting Sphere:

Gauss’s Law Equation: $$∮\overrightarrow{E}⋅d\overrightarrow{A}=\frac{Q_{inside}}{\epsilon_0}$$
Electric Field Inside the Sphere: $$E_{in}=0$$
Electric Field Outside the Sphere: $$E_{out}=\frac{Q}{\epsilon_0 r^2}$$
Potential at the Surface of the Sphere: $$V=\frac{1}{4\pi\epsilon_0}\cdot\frac{Q}{R}$$
Charge Density on the Surface of the Sphere: $$\sigma=\frac{Q}{4\pi R^2}$$

2. Electric Field due to a Charged Thin Rod:

Gauss’s Law Equation: $$∮\overrightarrow{E}⋅d\overrightarrow{A}=\frac{Q_{inside}}{\epsilon_0}$$
Electric Field at a Point on the Axis of the Rod:** $$E=\frac{1}{4\pi\epsilon_0}\frac{2\lambda}{x\sqrt{x^2+R^2}}$$
Potential at a Point near the End of the Rod: $$V=\frac{1}{4\pi\epsilon_0}\cdot\frac{2k\lambda}{R}\ln\left(\frac{L+R}{R}\right)$$

January 1, 0001 read

Shortcut Methods

Hollow Conducting Sphere Electric Field:

(i) Inside the sphere (r < R) $$E=0$$

(ii) Outside the sphere (r > R) $$E=\dfrac{1}{4\pi \epsilon_0}\dfrac{Q}{r^2}$$

Solid Conducting Sphere Electric Field:

(i) Inside the sphere (r < R) $$E=\dfrac{1}{4\pi \epsilon_0}\dfrac{Qr}{R^3}$$

(ii) Outside the sphere (r > R) $$E=\dfrac{1}{4\pi \epsilon_0}\dfrac{Q}{r^2}$$

Concentric Conducting Spheres Electric Field:

(i) Inside the inner sphere (r < R1) $$E=0$$

(ii) Between the spheres (R1 < r < R2) $$E=\dfrac{1}{4\pi \epsilon_0}\dfrac{Q_1}{r^2}$$

January 1, 0001 read

Shortcut Methods

Tricks and Shortcuts

1. Binomial Theorem

1. Formula:

$$(a+b)^n=\sum_{r=0}^n {}^nC_r a^{n-r}b^{r}$$

(n) choose (r), where (n\ge r), or,

$${}^n C_r=\frac{n!}{r!(n-r)!}$$

2. Binomial Coefficients:

$${}^nC_r= {}^nC_{n-r} $$

$${}^nC_0 = {}^nC_n=1$$

If n = 2k, the middle coefficient is

$$= ^{n}C_{k} = \frac {(2k)!} {(k!)^2}$$

##3. Summations/Identities

$$\sum_{i=0}^n {}^nC_i = 2^n$$

$$\sum_{i=0}^n {}^nC_i r^i = (1+r)^n$$

$$\sum_{i=0}^n{}^nC_ir^{n-i}=(1+r)^n$$

Product of two Binomials:

$$ (a+b)(c+d) = ac+ad+bc+bd $$

January 1, 0001 read

Shortcut Methods

1. Antibiotic Resistance

Percentage rise in antibiotic resistance:
- Calculate the initial population of bacteria before antibiotic exposure.
- Count the number of resistant bacteria after antibiotic exposure.
- Use the formula: % Increase in resistance (%) = ((Number of resistant bacteria - Initial bacterial population) / Initial bacterial population) * 100
Rate of mutation:
- Count the number of resistant bacteria after several generations.
- Calculate the total number of bacteria after several generations.
- Use the formula: Rate of mutation (per generation) = (Number of mutations / Total bacterial population)

2. Probiotics and Prebiotics:

Minimum daily intake of probiotics:

January 1, 0001 read

Shortcut Methods

January 1, 0001 read

Shortcut Methods

Tricks and Shortcuts

1. Binomial Theorem

2. Binomial Coefficients:

Shortcut Methods

1. Antibiotic Resistance

2. Probiotics and Prebiotics:

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Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Mentorship

NCERT Exercise Video Solution

Forum

For International Students

Get In Touch

Shortcut Methods

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Shortcut Methods

Tricks and Shortcuts#

1. Binomial Theorem#

2. Binomial Coefficients:#

Shortcut Methods

1. Antibiotic Resistance#

2. Probiotics and Prebiotics:#

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

Tricks and Shortcuts

1. Binomial Theorem

2. Binomial Coefficients:

1. Antibiotic Resistance

2. Probiotics and Prebiotics: