Class 11th

The examples of the probability include - flipping a coin, rolling a die, drawing a card from a deck, and picking a ball from a bag.

There are various applications of the probability in the real life. It is used to take informed decisions and risks in the following areas - insurance, weather forecasting, finance, business, sports, computer Science and gaming.

There are two basic rules for finding the Probability of two events A and B - Multiplication Rule and Addition Rule. 

There are four types of probability - Classical, Empirical, Subjective, and Axiomatic Probability. The classical probability is based on the logical and known outcomes, Empirical are based on data from actual experiments, and subjective is based on intuition, personal opinion, or experience.

Probability in Maths is used to calculate how an event is likely to occur. It is measured by dividing the favorable outcomes number by the number of possible outcomes. It is expressed from 0% to 100% or by either 0 (impossible) or 1 (certain).

Given   $F\propto \frac{1}{r^n}$

$m{\omega }^{2}R=\frac{K}{R^n}$

$?\frac{m.4{\pi }^{2}R}{T^2}=\frac{K}{R^n}$

$?T^2\propto R^{n+1}$

$T\propto R^{\frac{n+1}{2}}$

Angular momentum imparted to sprinkler per

$second=vr\frac{dm}{dt}=\frac{0.6}{60}*0.5*1=0.005N.m$

$?l\frac{d\omega }{dt}=0.005$

$?\frac{d\omega }{dt}=\frac{0.005}{500*{10}^{-7}}$

$=100\frac{rad}{s^2}$

Applying conservation of momentum for collision of blocks

$2mv+0=3m{v}^{\text{'}}$

$?v^{\text{'}}=\frac{2v}{3}\dots \left(1\right)$

Now, from conservation of energy

$\frac{1}{2}*3m*{v^{\text{'}}}^2=\frac{1}{2}k{x}_0^2$

$x_0=\sqrt[]{\frac{3m{v}^{\text{'}2}}{k}}=v\text{'}\sqrt[]{\frac{3m}{k}}$

$=\frac{2v}{3}\sqrt[]{\frac{3m}{k}}=v\sqrt[]{\frac{4m}{3k}}$

In NEET exam, there can be 1 to 2 questions from redox reactions, carrying 4-8 marks. The weightage is around 2% to 4%. In JEE Main, the weightage of this chapter is from 3.3% to 4-6%. You can expect nearly 1 to 2 questions from this chapter.

The applications of redox reactions include in cellular respiration, and batteries. In industries, these are used in the chemical production, metal extraction and water treatment.