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Lesson Posted on 17/05/2021 Learn Tuition

CBSE CLASS 12 MATHS MATRICES INTROUCTION

Shoba

I worked as an assistant professor in engineering college, so I had experience in various area Like Handled...

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Comments Lesson Posted on 01/03/2021 Learn BSc Tuition

Experiment, Sample space and Events - Basics

Isha Patil

I have completed my Masters in Statistics a couple of years back. My love for teaching started when I...

Definition - (Experiment) An experiment is the process whose outcome is not predictable with certainty in advance. Example Tossing a coin once or several times Tossing a six-faced die Selecting a card or cards from a deck Obtaining blood types from a group of individuals Measuring (in hours)... read more

Definition - (**Experiment**) An experiment is the process whose outcome is not predictable with certainty in advance.

Example

- Tossing a coin once or several times
- Tossing a six-faced die
- Selecting a card or cards from a deck
- Obtaining blood types from a group of individuals
- Measuring (in hours) the lifetime of a transistor

Definition - (**Sample Space**) The set of all possible outcomes of an experiment is called the experiment's sample space and is denoted by S.

Example

- If the experiment is tossing a coin, then the outcomes will be head and tail, and hence the sample space is S = {H, T}.
- If the experiment consists of flipping two coins, then the outcomes will be heads, head and tail and both tails. So the sample space S consists of the following four points: S = {(H, H),(H, T),(T, H),(T, T)}.
- If the experiment consists of tossing a die, then the sample space is S = {1, 2, 3, 4, 5, 6}.
- If the experiment consists of tossing two dice, then the sample space consists of the 36 points S = {(i, j): i, j = 1, 2, 3, 4, 5, 6}, where the outcome (2, 5) means two appears in the first die and 5 on the other die.
- If the experiment consists of measuring (in hours) the transistor's lifetime, then the sample space consists of all nonnegative real numbers. That is, S = {x | 0 ≤ x < ∞}

Definition - (**Event**) Any subset E of the sample space S is known as an event. An event is called elementary or straightforward if it consists of a single outcome. If the experiment's outcome is contained in E, then we say that the event E has occurred.

Example

- In example 2, E = {(H, H),(H, T)} is the event that a head appears on the first coin. 2. In example 4, E1 = {(1, 5),(2, 4),(3, 3),(2, 4),(1, 5)} is the event that the sum of the dice equals 6. The Event E2 that the sum of dice equals 12 is the simple event as E2 = {(6, 6)} consists of only one outcome.
- In example 5 , E = {x | x ≥ 10} is the event that the transistor lasts at least 10 hours.

For any two events A and B of the sample space S, we can define the new events

• A ∪ B = {ω ∈ S | ω ∈ A or ω ∈ B} consists of all outcomes that are either in A or in B or A and B.

• A ∩ B = {ω ∈ S | ω ∈ A and ω ∈ B} consists of all outcomes that are both in A and B

• More generally, S∞ i=1 Ai = {ω ∈ S | ω ∈ Ai for some i} consists of all outcomes which lie in at least one event Ai and T∞ i=1 Ai = {ω ∈ S | ω ∈ Ai for all i} consists of all outcomes which lie in all events Ai

• Ac = {ω ∈ S | ω /∈ A} consists of all outcomes, not in A.

• An event that doesn't contain any outcome is referred to as a null event and is denoted by ∅.

• Sample space is also an event referred to as a specific or sure event.

**Definition: **(**Mutually Exclusive**) Two events A and B of the sample space S are said to be mutually exclusive if A ∩ B = ∅. i.e. if event A occurs, then event B doesn't occur, and vice versa.

**Example:** If S is the sample space of tossing a die, then the events A = {ω ∈ S | ω is even} and B = {ω ∈ S | ω is odd} are mutually exclusive.

**Definition:** Let A and B be two events of the sample space S. If A ⊂ B, then the occurrence of A necessarily implies the occurrence of B, i.e., the event B occurs whenever the event A occurs.

**Types of Events:**

**Elementary**event or simple event**Impossible**event**Sure**or**a specific**event**Mutually Exclusive**Events**The complement**of an event**Exhaustive**events

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Comments Lesson Posted on 28/07/2020 Learn BSc Tuition

Soma Sarkar

Was in research project and jn icse board school have experience of teaching bsc Biotech Students

It means making copies or duplication. In prokaryotes, it is performed in the cytoplasm, in Eukaryotes nucleus. It can be divided into three steps. Initiation Elongation Termination Many enzymes and proteins are needed like Helicase to break hydrogen bonds and unzip, RNA primer to initiate replication.DNA... read more

It means making copies or duplication.

In prokaryotes, it is performed in the cytoplasm, in Eukaryotes nucleus.

It can be divided into three steps.

Initiation

Elongation

Termination

Many enzymes and proteins are needed like

Helicase to break hydrogen bonds and unzip, RNA primer to initiate replication.DNA polymerase to add new nucleotides, as primer goes from 5 to 3 and new nucleotides add on three prime. so this strand is leading strand, and the opposite of it will be lagging as short Okazaki fragments are formed,

At last to stop exonuclease comes to remove primer and ligase joined all remaining points.

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Answered on 24/06/2020 Learn General Chemistry For Maths & Physics

Anand Choudhary

6+ years of experience in IIT-JEE,SAT,Physics ,NEET,Mathematics,English .

See, if you expand the function x|x|, you will get (square of x) in (0,∞). But (negative of the square of x)- in (-∞ ,0). so now if you plot the graph, the graph will be downward parabola in one part of the x-axis and another upward parabola. So, it is neither odd nor even. read more

See, if you expand the function x|x|, you will get (square of x) in (0,∞). But (negative of the square of x)- in (-∞ ,0). so now if you plot the graph, the graph will be downward parabola in one part of the x-axis and another upward parabola. So, it is neither odd nor even.

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Answers 4 Comments 3 Lesson Posted on 28/05/2020 Learn Principles of Inheritance and Variation

What is a Polymerase Chain Reaction (PCR)?

Alka Srivastava

I am doing my PhD in Botany from CSIR-National Botanical Research Institute. I have completed my...

It is a revolutionary method developed by Kary Mullis in the 1980s, used to synthesize a new strand of DNA complementary to the offered template strand. Components of PCR: 1. DNA template- the DNA strand that contains the target sequence which has to be multiplied. 2. DNA Polymerase enzyme- a type... read more

It is a revolutionary method developed by Kary Mullis in the 1980s, used to synthesize a new strand of DNA complementary to the offered template strand.

Components of PCR:

1. **DNA template**- the DNA strand that contains the target sequence which has to be multiplied.

2. **DNA Polymerase enzyme**- a type of enzyme that synthesizes new strands of DNA complementary to the target sequence. The first and most commonly used of these enzymes is *Taq DNA* polymerase (from *Thermus aquaticus*), whereas *Pfu*DNA polymerase (from *Pyrococcus furiosus*) is used widely because of its higher fidelity when copying DNA.

3. **Primers**- a short sequence of nucleotides that provides an initiation point for DNA synthesis.

4.** dNTPs(deoxynucleotides triphosphates)**- single units of the bases A, T, G, and C, which are essentially "building blocks" for new DNA strands.

Steps in PCR:

1. **Denaturation** (96°): Heat the reaction strongly to separate, or denature, the DNA strands. This provides a single-stranded template for the next step.

2. **Annealing** (55°C-65°C): Cool the reaction so the primers can bind to their complementary sequences on the single-stranded template DNA.

3.** The extension** (72°): Raise the reaction temperatures so *Taq* polymerase extends the primers, synthesizing new strands of DNA.

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Comments Lesson Posted on 04/05/2020 Learn BSc Tuition

Durga

ELECTRIC FIELD : The space or region around the charge in which its effect can be felt is called electric field. Electric field is denoted by 'E'. In other words, if we have a charge Q placed at the origin and an another charge q is placed at (1,0,0), then we have to... read more

**ELECTRIC FIELD** :

The space or region around the charge in which its effect can be felt is called electric field.

Electric field is denoted by 'E'. In other words, if we have a charge Q placed at the origin and an another charge q is placed at (1,0,0), then we have to check that upto which distance q charge is influenced by Q charge at origin.

Direction of electric field is from positive to negative charge same as force. Electric field is a vector quantity.

Mathematically, electri field is written as:

** **

**S.I. unit of electric field is N/C.**

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Lesson Posted on 22/04/2020 Learn Engineering Mathematics (M1)

Divergent And Curl of Vector Function

Sridhar Reddy Bijjula

I an Assistant Professor in Mathematics with 12+years of experiance in teaching in mathematics BSc, Bcom...

The following video gives clear and brief introduction about the Divergent and Curl of a vector function.

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Comments Answered on 02/06/2020 Learn BSc Tuition

Dr Kumud Sarin

30 years of experience across Research, Teaching, Writing, Management

Prolog means logic programming language related to artificial intelligence and computational symbolic linguistics with an application to define the functional objects leading to simulations and automation. Finite automata should have two arguments one input and other output and return to the states by... read more

Prolog means logic programming language related to artificial intelligence and computational symbolic linguistics with an application to define the functional objects leading to simulations and automation. Finite automata should have two arguments one input and other output and return to the states by which it passed through.

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Answers 25 Comments Answered on 24/06/2018 Learn BSc Tuition

Vishal Ranjan Verma

Cad Trainer

Time Management is key. Just you have to see that school and class time do not collide.

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Answers 9 Comments Take BSc Tuition from the Best Tutors

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Answered on 19/02/2017 Learn BSc Tuition

Swarniv C.

Physics Tuition

Value of pi is 3.14159 where as 22/7 equals to 3.142857. As it is clear that 22/7 is greater than the value of pi.

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