#properties of logarithmic logarithm class 11 maths

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What Are The Important Topics For IIT JEE In 11th And 12th Standard?

With the passion to pursue engineering from a premier institute like IIT, a lot of students aim at cracking the IIT JEE to live this dream right from their 11th standard. Every year, about 1.2 million candidates appear for the JEE Main exam, out of which, a fraction of students qualify to appear for the JEE Advanced exam.  Considered as one of the most difficult entrance exams across the globe, not many know how to prepare for JEE and lack correct guidance. ISS coaching in Lucknow will discuss in this article, how one needs to divide and dedicate time for important topics in 11th standard to score maximum marks in IIT JEE.

IIT JEE consists of thirty multiple choice questions from Maths, Physics and Chemistry. With equal weightage given to all three subjects, one should know how to prepare for IIT and what topics to emphasize on to be able to answer most questions correctly in the assigned time.

To help students understand and prepare better, we have curated a list of important topics for JEE Mains from each subject for them to prioritize topics based on it.. Have a look.

Mathematics

Generally, the weightage of topics of class 11 mathematics is 40% to 50% in JEE.

·         Probability: Being one of the most important topics, one needs to cover Conditional Probability, Law of Total Probability and Bayes theorem in detail to score maximum marks in this subject.

·         Coordinate Geometry: One needs to be thorough with Circle

·         Logarithm: Basic Logarithm questions are only asked

·         Permutation and Combination: Important topics to cover here are circular permutation, Integral solution of linear equation and Division/ Arrangement of Groups

·         Quadratic Equation: One needs to focus on roots of an equations coefficients and most importantly on roots of an equation.

·         Complex Number

·         Conic Section

·         Circle

·         Calculus

·         Vector & 3 D

·         Trigonometric Equation

·         Properties of Triangles

·         Quadratic Equation

·         Sequence and Series

 Physics

In Physics, the weightage of the syllabus of class 11 and 12 is almost equal -- it is around 50% for each. Some important chapters of Physics in class 11 include Waves, Simple Harmonic Motion, Units and Dimensions, Rotational Motion, and Newton’s Laws of Motion. The class 12 Physics topics that carry heavy weightage in JEE include Electrostatics, Magnetism, Current Electricity, Optics, Modern Physics.

·         Units & Dimension: All concepts under this topic needs to be covered.

·         Rotational Motion: One should draw their focus on the concept of rigid body dynamics.

·         Kinematics of SHM: Questions asked on this are to test the understanding of Simple Harmonic Motion and one can expect around 3 questions from this concept.

·         Newton s Law of Motion: Application of the three laws of motion needs to be understood and effectively used in solving the questions.

Chemistry

In JEE chemistry, generally, the weightage of the class 12 syllabus is more than that of class 11. Generally, the weightage of the class 11 chemistry syllabus in JEE is around 30% to 40%. Many topics that are taught in class 11 are the basic ones and serve as a foundation for a deeper understanding of many class 12 topics. So, even though the weightage of the class 11 syllabus is slightly on the lower side, the topics taught in class 11 should not be ignored or taken for granted.

·         Chemical Equilibrium: One needs to focus on concepts like Law of Mass Action, Acids and Bases and Solubility product.

·         Atomic Structure: Atomic structure preparation and atomic mass concepts are important . Theories like the Thomson, Bohr and Rutherford should be concentrated on.

·         Stoichiometry: Focusing on topic like the Mole and equivalent concept is very important in class 11th.

·         Gaseous State: States of matter, compressibility factor and van der Waals equation are concepts to be focused on.

·         Chemical Bonding: One should focus on periodicity concept.

·         Organic Chemistry: Basic concepts of Organic Chemistry from 11th standard is usually asked. Hence one shouldn’t t ignore it and emphasize on the basics.

·         Electrochemistry

·         Coordination compound

·         Salt analysis

·         Ionic equilibrium

·         Thermodynamics & thermochemistry

·         Aldehydes and ketones

·         Aromatic hydrocarbons

·         GOC isomerism

·         Liquid solutions

·         Alkyl halides and aryl halides

JEE Main Important Topics 2021- Best Books to Cover

Students should cover all the JEE Mains 2021 important topics and chapters from the below best-recommended books by various subject experts, previous year JEE Main toppers and many test takers. Students are advised to follow only one or two books for each subject and do not refer to so many books. Beside all the recommendations, NCERT books is highly recommended for JEE Main preparation.

JEE Main Best Books 2021

I.        Subject : Mathematics

Recommended Books:

1)     NCERT Class 11 and 12 Textbooks

2)     Differential and Integral Calculus by Amit M Aggarwal

3)     Trigonometry and Coordinate Geometry by SL Loney

4)     Complete Mathematics for JEE Main by TMH Publication

5)     Algebra by Dr.SK Goyal

 II.     Subject : Physics

Recommended Books:

1)      NCERT Class 11 and 12 Textbooks

2)      Concepts of Physics by HC Verma (Volume 1 and 2)

3)      Fundamentals of Physics by Halliday, Resnick & walker

4)      Problems in General Physics by I.E Irodov

 III.   Subject : Chemistry

Recommended Books:

1)       NCERT Class 11 and 12 Textbooks

2)       Organic Chemistry by OP Tandon

3)       Physical Chemistry by P Bahadur

4)       Inorganic Chemistry by JD Lee

5)       Modern Approach to Chemical Calculations by RC Mukherjee

 JEE is a very tough competition, where the difference of even 1 mark can cause a lot of damage to one’s rank. Hence, it is important to be equally proficient in all the topics, both from class 11 and class 12. Even though it may seem like that a majority of JEE questions are from the class 11 syllabus, however, you must notice that JEE questions generally involve a mix of several concepts, and hence, you should be comfortable with all the concepts involved to apply them in a single question. Generally, in class 11, the foundations of several advanced concepts are laid. Hence, you should pay equal attention to the syllabus of class 11 and 12, both.

We advice students to be through with all three subjects mentioned above and give additional attention to these important topics of class 11 for IIT JEE mains to score maximum marks. Good Luck!

[shilkaren]

Python Numbers

In this article, you'll find out about the various numbers utilized in Python, how to change over from one data type to the next, and the numerical tasks upheld in Python.

Number Data Type in Python

Python upholds integers, floating-point numbers and complex numbers. They are defined as int, buoy, and complex classes in Python.

Integers and floating points are isolated by the presence or nonappearance of a decimal point. For instance, 5 is an integer though 5.0 is a floating-point number.

Complex numbers are written in the structure, x + yj, where x is the genuine part and y is the imaginary part.

We can utilize the type() capacity to realize which class a variable or a worth has a place with and isinstance() capacity to check in the event that it has a place with a specific class.

How about we take a gander at a model:

a = 5

print(type(a))

print(type(5.0))

c = 5 + 3j

print(c + 3)

print(isinstance(c, complex))

At the point when we run the above program, we get the following yield:

<class 'int'>

<class 'float'>

(8+3j)

Valid

While integers can be of any length, a floating-point number is exact simply up to 15 decimal places (the sixteenth spot is inaccurate).

The numbers we manage each day are of the decimal (base 10) number framework. Be that as it may, software engineers (for the most part inserted developers) need to work with binary (base 2), hexadecimal (base 16) and octal (base 8) number frameworks.

In Python, we can address these numbers by suitably placing a prefix before that number. The following table records these prefixes.

Number System Prefix

Binary '0b' or '0B'

Octal '0o' or '0O'

Hexadecimal '0x' or '0X'

Here are a few models

# Output: 107

print(0b1101011)

# Output: 253 (251 + 2)

print(0xFB + 0b10)

# Output: 13

print(0o15)

At the point when you run the program, the yield will be:

107

253

13

Type Conversion

We can change over one type of number into another. This is otherwise called compulsion.

Activities like expansion, deduction pressure integer to coast verifiably (consequently), in the event that one of the operands is glide.

>>> 1 + 2.0

3.0

We can see over that 1 (integer) is forced into 1.0 (glide) for expansion and the outcome is additionally a floating point number.

We can likewise utilize worked in capacities like int(), buoy() and complex() to change over between types expressly. These capacities can even change over from strings.

>>> int(2.3)

2

>>> int(- 2.8)

- 2

>>> float(5)

5.0

>>> complex('3+5j')

(3+5j)

While converting from buoy to integer, the number gets shortened (decimal parts are eliminated).

Python Decimal

Python worked in class skim plays out certain estimations that may astonish us. We as a whole realize that the amount of 1.1 and 2.2 is 3.3, however Python appears to conflict.

>>> (1.1 + 2.2) == 3.3

What is happening?

Incidentally, floating-point numbers are carried out in PC equipment as binary divisions as the PC just understands binary (0 and 1). Because of this explanation, the majority of the decimal divisions we know, can't be precisely put away in our PC.

We should take a model. We can't address the division 1/3 as a decimal number. This will give 0.33333333... which is infinitely long, and we can just surmised it.

Incidentally, the decimal division 0.1 will bring about an infinitely long binary part of 0.000110011001100110011... and our PC just stores a finite number of it.

This will just rough 0.1 however never be equivalent. Thus, it is the impediment of our PC equipment and not a blunder in Python.

>>> 1.1 + 2.2

3.3000000000000003

To defeat this issue, we can utilize the decimal module that accompanies Python. While floating-point numbers have accuracy up to 15 decimal places, the decimal module has client settable exactness.

We should see the distinction:

import decimal

print(0.1)

print(decimal.Decimal(0.1))

Yield

0.1

0.1000000000000000055511151231257827021181583404541015625

This module is utilized when we need to do decimal computations as we learned in school.

It additionally saves importance. We realize 25.50 kg is more exact than 25.5 kg as it has two huge decimal spots contrasted with one.

from decimal import Decimal as D

print(D('1.1') + D('2.2'))

print(D('1.2') * D('2.50'))

Yield

3.3

3.000

Notice the trailing zeroes in the above model.

We may ask, why not carry out Decimal without fail, instead of buoy? The main explanation is effectiveness. Floating point activities are done should quicker than Decimal tasks.

When to utilize Decimal instead of buoy?

We for the most part utilize Decimal in the following cases.

At the point when we are making financial applications that need definite decimal portrayal.

At the point when we need to control the degree of accuracy required.

At the point when we need to carry out the thought of critical decimal spots.

Read our Latest Blog: Tuples in Python

Python Fractions

Python gives tasks involving partial numbers through its portions module.

A portion has a numerator and a denominator, the two of which are integers. This module has support for levelheaded number math.

We can make Fraction objects in different manners. How about we view them.

import portions

print(fractions.Fraction(1.5))

print(fractions.Fraction(5))

print(fractions.Fraction(1,3))

Yield

3/2

5

1/3

While creating Fraction from drift, we may get some surprising outcomes. This is because of the defective binary floating point number portrayal as examined in the past area.

Luckily, Fraction permits us to instantiate with string too. This is the favored choice when using decimal numbers.

import parts

# As buoy

# Output: 2476979795053773/2251799813685248

print(fractions.Fraction(1.1))

# As string

# Output: 11/10

print(fractions.Fraction('1.1'))

Yield

2476979795053773/2251799813685248

11/10

This data type upholds every fundamental activity. Here are a couple of models.

from parts import Fraction as F

print(F(1, 3) + F(1, 3))

print(1/F(5, 6))

print(F(- 3, 10) > 0)

print(F(- 3, 10) < 0)

Yield

2/3

6/5

Bogus

Valid

Python Mathematics

Python offers modules like math and random to do diverse mathematics like geometry, logarithms, likelihood and measurements, and so on

import math

print(math.pi)

print(math.cos(math.pi))

print(math.exp(10))

print(math.log10(1000))

print(math.sinh(1))

print(math.factorial(6))

Yield

3.141592653589793

- 1.0

22026.465794806718

3.0

1.1752011936438014

720

Here is the full rundown of capacities and properties accessible in the Python math module.

import random

print(random.randrange(10, 20))

x = ['a', 'b', 'c', 'd', 'e']

# Get random decision

print(random.choice(x))

# Shuffle x

random.shuffle(x)

# Print the rearranged x

print(x)

# Print random component

print(random.random())

At the point when we run the above program we get the yield as follows.(Values might be diverse because of the random conduct)

18

e

['c', 'e', 'd', 'b', 'a']

0.5682821194654443

Read Full Article: Python Numbers

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Free education is the right of every student. Ashish Kumar – Let’s Learn is providing deep and detailed explanations of full syllabus, all important questions, all important examples and all NCERT solutions for Class 11 Maths through videos on YouTube Channel as well as Blogs and PDFs on website.

Students can learn through videos and blogs and can ask their doubts on Website’s Discussion panel or on YouTube’s Comments Page. Students will also be provided notes, assignments, books and various other educational resources in electronic forms like PDFs, Docs, mp4 etc., which will help them to prepare for CBSE Class 12 Board Exams but more importantly for their upcoming life’s adventures.

You can easily access all chapters with NCERT Solutions for class 11 maths on this page:  https://www.ashishkumarletslearn.com/cbse/class-11/maths/

Following are summaries of chapter wise syllabus recommended by CBSE for Class 11 mathematics students with their YouTube as well as Website links.

Unit-I: Sets and Functions

1. Sets: 

Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of a set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and Intersection of sets. Difference of sets. Complement of a set. Properties of Complement.

2. Relations & Functions:

Ordered pairs. Cartesian product of sets. Number of elements in the Cartesian product of two finite sets. Cartesian product of the set of reals with itself (upto R x R x R). Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special type of relation. Pictorial representation of a function, domain, co-domain and range of a function. Real valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product and quotients of functions.

3. Trigonometric Functions:

Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin2x+cos2x=1, for all x. Signs of trigonometric functions. Domain and range of trigonometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple applications. Deducing identities. Identities related to sin2x, cos2x, tan2x, sin3x, cos3x and tan3x. General solution of trigonometric equations of the type siny = sina, cosy = cosa and tany = tana.

Unit-II: Algebra

4. Principle of Mathematical Induction:

Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications.

5. Complex Numbers and Quadratic Equations:

Need for complex numbers, especially √ , to be motivated by inability to solve some of the quadratic equations. Algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with real coefficients) in the complex number system. Square root of a complex number.

6. Linear Inequalities:

Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Graphical method of finding a solution of system of linear inequalities in two variables.

7. Permutations and Combinations:

Fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of formulae for and and their connections, simple applications.

8. Binomial Theorem:

History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, General and middle term in binomial expansion, simple applications.

9. Sequence and Series:

Sequence and Series. Arithmetic Progression (A. P.). Arithmetic Mean (A.M.) Geometric Progression (G.P.), general term of a G.P., sum of n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), relation between A.M. and G.M. Formulae for the following special sums.

Unit-III: Coordinate Geometry

10. Straight Lines:

Brief recall of two dimensional geometry from earlier classes. Shifting of origin. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, point -slope form, slope intercept form, two-point form, intercept form and normal form. General equation of a line. Equation of family of lines passing through the point of intersection of two lines. Distance of a point from a line.

Unit-IV: Calculus

13. Limits and Derivatives:

Derivative introduced as rate of change both as that of distance function and geometrically. Intuitive idea of limit. Limits of polynomials and rational functions trigonometric, exponential and logarithmic functions. Definition of derivative relate it to scope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

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GEOMETRY AND RENAISSANCE

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Renaissance is one of the recorded ages that genuinely affected the cutting edge human advancement as far as improvement in training, outline and numerous different fields and furthermore it didn't disregard displaying out the most essential figures amid this age which had a similar effect on present day progress. This time of age began from the fourteenth century and finished on the seventeenth century beginning in "Florence" in Italy and completion of whatever is left of Europe. Filippo Brunelleschi was one of its most imperative figures, in the blink of an eye, the Renaissance style began to spread crosswise over Italian urban areas and some different nations like France, Germany, England, Russia and different parts of Europe at various dates and with fluctuating degrees of effect. This paper will talk about the effect of Renaissance on the advancement of science and geometry in the cutting edge age, its connection and the essential assumes that really affected this period. It will likewise examine the imperative illustrations and structures that got influenced by such developments in this timeframe.

Renaissance is one of the periods that affected mathematic and geometry because of the splendid assumes that have been in this timeframe which will be examined in this passage. Above all else, Geometry is basically a branch of science that is worried about shapes, estimate, position of figure, and properties of a space like for instance, a square have a property of the level equivalent separation lines from all sides that gives it, its shape and the same goes for alternate shapes like rectangle, hexagon, hover etc…Mathematics all in all is the investigation of any sorts of structure, a space like a house, any outlines and so on., changes in speed of a protest, when all is said in done, anything that needs to do with conditions and counts is classified under arithmetic. The most vital assumes that showed up in this time of age and truely affected Geometric and arithmetic are" "Filippo Brunelleschi" dating from 1377 - 1446 he is the designer of the science of point of view in painting. "Paolo dal Pozzo Toscanelli" dating from 1397-1482 making an enormous sundial and making cosmic estimations and furthermore giving a higher precision in figuring scope at the ocean and "luca pacioli" who composed various hypotheses and built up the geometrical extents." (Fletcher, 2000-11)

Renaissance structures intensely depended on the utilization of geometry and the arithmetic in their plan which vigorously affected other present day outlines till now. Renaissance kind of structures depended on bends, curves, triangle, circles and squares, which are the principle components of geometry, additionally should be characterizes as structures like places of worship, strongholds and significantly more depended on those fundamental components and formed it into curves, vaults, rectangular portions inside and outside the structures the same number of floor designs could depict it.

Renaissance building development and how it was influenced by such fundamental components of geometry. The Renaissance extraordinary masterminds took the individual as a model for the universe being the ideal being made by god and utilized it in geometry and science. This thought was created by essentially drawing this impeccable figure which is the "Vitruvian man" remaining in a square figure extending his arms and legs shaping an ideal hover around him. In view of these thoughts, Leonardo made his own particular illustrations in view of the utilization of human extents and the Vitruvius' hypothesis. In the renaissance age, it was their expect to try such thoughts created in genuine structures .What was done is that he mixed the utilization of circles and squares much in his general format of his arrangement and in the arrangement itself he separated it promote into spaces using sections in addition to having the upside of supporting the rooftop and with respect to the round part, he utilized it to go about as an arches which was a standout amongst the most critical figures in this timeframe which gives the building its surface and special style.

In this illustration, Leonardo made a few changes in accordance with the Vitruvius estimation of the human figure which was enlivened by his own examinations and perception. At long last after changes and his own particular investigations, he made the ideal picture of the human figure with the best extents. Leonardo had the conviction that god was the ideal geometer and the person who made the universe in view of extents and numbers, he trusted that the human body was one of his ideal creation, in light of Leonardo's idea, he drawn the Vitruvian man extending his own legs and arms to shape an immaculate spinning circle around him and a square. In any case, keeping in mind the end goal to make this work, he needed to put the circle fixated however the middle on the square is a bit lower. Through modifications and examines of his own estimations in view of investigations of life models, the Vitruvian figure isn't perceived as a perfect picture and extent of the human body. "Extent isn't just to be found in numbers and measures, yet additionally in sounds, weights, interims of time, and in each dynamic power in presence." expressed by "Leonardo da Vinci" (University of the Arts).

The improvement of science and figurings in the renaissance time frame is for certain a standout amongst the most essential issues in this age. Amid the Renaissance, mathematicians and specialists wrapped their arms around the inquiries of point of view, unendingness, emblematic variable based math and quartic conditions, delivering treatises regarding these matters and offering new experiences into the field of arithmetic. The fifteenth through seventeenth hundreds of years saw numerical advancements in European nations like France and Italy, the effect of which stretches out right up 'til the present time. These figurings were partitioned into various classes, for example, Analysis versus amalgamation where the Renaissance saw the progression of representative polynomial math. In his "Artem Analyticem Isogoge" of 1591, François Viéte took the thoughts of Ancient Greeks Euclid, Diophantus and Pappus and looked to clarify and clear up them through deliberate logarithmic documentation. In doing as such he could clarify the ideas of investigation and amalgamation. Investigation, or a suspicion of something that is searched for and the landing at something confessed to be valid through its results, was to be recognized from union, which is a supposition of something that is conceded (surrendered) and the touching base at something confessed to be valid through its outcomes. In addition, he connected guidelines for computing species "Viéte" additionally settled standards for "species," instead of numerical estimations. His first control stipulates to "add a greatness to an extent," or to include just homogeneous sizes, for example, one type to it's logical counterpart; his third and fourth guidelines train to increase and gap sizes, separately, which will bring about heterogeneous sorts. For instance, a side increased by a side is a plane, not another side. Communicated through species, administrators and units, conditions could now be taken care of all the more effectively. Additionally, in the advancement of conditions, cubic and quartic was principle fixings Two achievements amid the Renaissance in arithmetic included the explaining of both cubic and quartic conditions, which had overwhelmed mathematicians previously and amid the Renaissance. Despite the fact that the work was not his own, Girolamo Cardano is attributed with giving general answers for the two sorts of conditions as radicals. Already, conditions of the second degree were tackled in this way, however not cubic or higher conditions. He distributed these discoveries in his work, "Artis Magnae," in 1545. At long last, the fanciful and complex numbers, another progress for arithmetic amid the Renaissance time frame was the affirmation of the legitimacy of nonexistent or complex numbers. Cardano, in settling cubic conditions, happened upon the presence of negative numbers under the radical sign. Ancestors either dismissed these or were not ready to fathom such numbers. Cardano, despite the fact that he fused these numbers in his figurings, conceded that he didn't completely comprehend them. Regardless, his work with these new numbers conveyed science to a more elevated amount of deliberation.

Subsequent to knowing the effect of arithmetic and geometry in this timeframe, renaissance did likewise affect present day age building configuration despite the fact that this time of age is so old however till these days regardless it affect us not in the plan of the façade but rather in specific outlines. We can perceive how did the Renaissance impacted engineering and its outline surrounding us. The Use of symmetry, segments, and adjust of windows in present day engineering, regardless of whether at a bank or courthouse, or even in a costly home, all point to the impacts of Renaissance design on current structures. Thus to successfully contemplate the impact of Renaissance engineering on more present day design one should start by more intently analyzing the components and effect of Renaissance engineering and how those components have been fused into design today. Renaissance engineering took after the Gothic time of engineering, which gave us the house of prayer at Notre Dame, and was prevailing by the Baroque time frame, which is set apart by very lavish compositional outlines and furniture, and is regularly connected with the King Louis of France.

The Renaissance time frame emphatically underlined the accompanying components: Geometry which depended on having structures, windows, and entryways in square and rectangular shapes. Extent, adjust was basic in the Renaissance, and components of the structure should have been planned in extent to different components of the building. Symmetry depended on the utilization of geometric figures came an accentuation on symmetry and clean lines. Normality which implies that there is a little about the Renaissance style that is irregular or indiscreet. A building must have repeating topics and components. To achieve these plan objectives, the Renaissance style utilizes numerous repeating components, including: Columns, Pilasters, Lintels, Arches and arcades, Domes, Symmetrical windows and entryways lastly Niches with figures. Every one of these components is utilized as a part of prop