Ayush Agarwal Maths

Trigonometry solutions

My Grandmother's Aim - Become a Teacher  Introduction- Teacher is the biggest reformer in the student's life.Teaching is the best profession in the world. Many women has reached to great heights with the help of teaching by earning and dignity. Teaching is a favourable job for many of us because of it's timming. School and Colleges is the only place where mothers has to go along with the child.  Status - In our society a teacher is compared equal to God as GURU. A teacher gets much respect and high values.  Appearance- A teacher should be strict enough to guide the child and should also be little friendly to know the inner skills of the child. A teacher should be polite in nature to handle the students.  Me as a teacher - I will help many of the students to go on the right path. I will become a maths teacher as I like maths very much.  Thank you 

                            3D Printing      The concept of 3D printing is an advanced form of the traditional 2D printing done on a surface. 3D printing creates tangible objects and those that can occupy space. This is done by the use of computer aided designs and by applying different types of the design software.         3D Designs helps to give a preview to the customers and also helps many companies to work accordingly.   Examples of 3D Printing 3D printing encompasses many forms of technologies and materials as 3D printing is being used in almost all industries you could think of. A few examples:–  consumer products (eyewear, footwear, design, furniture) – industrial products (manufacturing tools, prototypes, functional end-use parts) – dental products – prosthetics – architectural scale models & maquettes – reconstructing fossils – replicating ancient artefacts – reconstructing evidence in forensic pathology – movie props I will suggest this profession to my bes

               Circle Theorem  Theorem 1 - The perpendicular bisectors of two chords of a circle intersect at its centre.  Theorem 2- The perpendicular from the centre of a circle to a chord bisects the chord. Theorem 3- If two arcs of a circle are congruent then the corresponding chords are equal.  Theorem 4 - The line joining the centre to the mid point of a chord is perpendicular to the chord.  Theorem 5 - Equal chords of a circle are equidistant from the corresponding centre.  Theorem 6 -chords which are equidistant from the corresponding centres are equal.  Theorem 7 - The angle in a semi circle is a right angle.  Theorem 8 - There is one and only one circle passing through three non collinear points.  Theorem 9 - An infinite number of circles can be drawn to pass through a single point.  Theorem 10 - An infinite number of circles can be drawn to pass through two given points.  Theorem 11 - A unique circle can be drawn to pass through three given non collinear points.  Theorem 12

                                                DOCTOR  GOD on Earth - Doctor  People who practise medicine are called doctors. A doctor is a medical practitioner who conducts health checkups and removes problems related to a person’s mental or physical health issues. Doctors are an integral part of society The medical profession is considered one of the best professions.  Thus doctors are considered life-saving. He spends many years of his life studying medical science.  Doctor's Status Doctors are often considered equal to God as they can save lives. Doctors are highly respected and honoured by everyone in society. A doctor should never differentiate between his patients based on their caste, religion, or financial crisis. A doctor must be serious and responsible about their job as other people’s lives depend on them. Many Indian doctors are making India proud all over the world. A doctor has a very hectic and busy life, and they hardly have any holidays.

                         Divisibility Rules   Divisibility by 1  Every number is divisible by 1. It does not have any condition. Any number divided by 1 will give the number itself.  For example, 8 is divisible by 1 than answer will be 8 and 6789  is also divisible by 1 than answer will be 6789.  Divisibility by 2   If a number is even or a number whose last digit is an even number i.e.  2,4,6,8 including 0, it is always completely divisible by 2. For example -   Let's take 216  it is an even number so it will be divisible by 2 completely. If we take 765 it is not an even number so it will not be divisible by 2.  Divisibilty by 3  Condition of Divisibility rule for 3 is a number is completely divisible by 3 if the sum of its digits is divisible by 3. For example-  let's take a number 723 add the digits  7+2+3 = 12 , after adding the digits we will get 12 it is a multiple of 3 so the number 723 is divisible by 3 .  Let's take another number 562 add the digits 5+6

     Science Test for practice    Thanks for visiting 

Maths Test / Revision For Different Exams  Thank you for Visiting😊 Keep sharing 

💯👩‍🏫      💯👩‍🏫            💯👩‍🏫         💯👩‍🏫      💯👩‍🏫  Hello friends welcome to ayushagarwal_maths page. Are you preparing for board exams or competitive exams than you are at the right place to enhance your knowledge.                             REAL NUMBERS  Real numbers - Real numbers are the numbers which can be obtained on the number line. Real numbers are denoted by 'R'. They includes Natural numbers, Whole numbers, Integers, Rational numbers, Irrational numbers.  Natural numbers - Natural numbers are the counting and ordering numbers (excluding 0) i.e. N = { 1, 2, 3, 4, 5, .......... } Whole numbers- Whole numbere are collection of natural numbers including zero (0) i.e. W = {0, 1, 2, 3, 4, 5, ........ }  Integers - Integers consist of natural numbers, their negatives and zero i.e. Z = { ....... -3, -2, -1, 0, 1, 2, 3, 4, 5, ........... }  Prime numbers - A prime number is defined as a number that has no factor other than 1 and its

                        Key Points and Useful Formulas for Exams       Important Formulas For Board Exams                                                            Number system  Prime numbers - A prime number is defined as a number that has no factor other than 1 and itself. Co-prime numbers - co-primes are considered in pairs and two numbers are co-prime if they have no common factors other than 1. Twin prime numbers - Twin prime numbers are the prime numbers whose difference is always equal to 2. For example, the difference between 5 and 7 is 2, and hence 5 and 7 are twin prime numbers. Composite numbers -  All the natural numbers which are not prime numbers are composite numbers as they can be divided by more than two numbers.  HCF and LCM  About Fraction  ° HCF =       HCF of Numerators /LCM of Denominators  ° LCM =  LCM of Numerators / HCF of Denominators • Product of two Numbers = L.C.M. × H.C.F  Keys/ Formulas  (a + b) 2  = a 2  + 2ab + b 2 (a – b) 2   = a 2  – 2ab + b 2 (a

Monomial  - Polynomial having one term.  Binomial  - Polynomial having two terms.  Trinomial  - Polynomial having three terms.  Zero Polynomial  - Polynomial having all its coefficient zero.  Constant Polynomial  - A polynomial having only a single term ( of real number).  Acute angle -  An angle whose measure is less than 90° is called a acute angle.  Adjacent angles  - Two angles are called adjacent angles if :-  i) they have the same vertex.  ii) they have a common arm, and  iii) Uncommon arms and an either side of the common arm.  Arithmatic Mean -  The arithmatic mean of a set of Observations is equal to their sum divided by the total number of ovservations.  Axioms -  The basic facts which are taken for granted, without proof are called axioms.  Bi -  Quadratic polynomial -  A fourth degree polynomial is called a bi-quadratic polynomial.  Chord-  A line segment joining any two points on a circle is called a chord of the circle. Circle-  A circle is a collection of tho

                       Quadrilaterals ° What is quadrilateral?      A plane, closed figure bounded by four line segments is called quadrilateral. There are different types of quadrilaterals, they are trapezium, parallelogram, rhombus, rectangle, square.  • What is the sum of all the interior angles of a quadrilateral?  The sum of all the interior angles of a quadrilateral is 360 degree.              Important Formulae                      Special quadrilaterals Parallelogram - A parallelogram is a quadrilateral with both pairs of opposite sides parallel.  Important points - Opposite sides of a parallelogram are equal Opposite angles of a parallelogram are equal The diagonals of a parallelogram bisect one another.  Each diagonal divides it into two congruent triangles.  The opposite sides and angles of a parallelogram are equal. The diagonals of a parallelogram bisect each other.  Rectangle - a parallelogram in which all four angles are right angles is a rectangle.  Important points - 

      NTSE EXAM   -----  SCHOLARSHIP  NTSE or  National Talent Search Examination  conducted by the National Council of Educational Research and Training (NCERT) for granting the scholarships to the exemplary students studying in class 10th .  The exam is conducted in two different stages: Stage I – at the State level and Stage II – at the National level. The first stage exam which is at a state-level exam and is conducted by all the Indian states and UTs. On the other hand, NTSE stage II is conducted for those students who qualifies the first stage.                          NTSE Terminology  NTSE scholarship will be awarded on the basis of the overall performance of students in both stages of the examination. NTSE Scholarship Awardee can pursue there career in two streams science or social studies. They also get many benefits in their higher studies.  . NCERT Conducts NTSE Exam once in a year in a offline mode while applications are to be submitted online only.  .NTSE exam

              POLYNOMIALS Monomial - Polynomial having one term.  Binomial - Polynomial having two terms.  Trinomial - Polynomial having three terms Zero Polynomial - Polynomial having all its coefficient zero.  Constant Polynomial - A polynomial having only a single term ( of real number).  Standard form - Powers of x are either in increasing or decreasing order.  1. A parallelogram whose all sides are equal is called a rhombus.  2. A quadrilateral is called a square if all of its sides are equal and all of its angles are equal.  3. A quadrilateral which has one pair of opposite sides parallel is called a trapezium.  4. A square is a rectangle.  5. A square is a rhombus.  6. A parallelogram is a trapezium but converse is not true.  7. A rectangle ( Or rhombus) is not a square.                   Thanks for visiting 

Tables from 1 to 25 Tables from 26 to 50

Q. 1. If a : b = 7 : 9 and b : c =15 : 7, then what is a : c A) 5 : 3 B) 3 : 5 C) 7 : 21 D) 7 : 15 Q. 2. ₹ 6200 is divided into three parts proportional to 1/2 : 1/3 : 1/5 are respectively A) ₹3000, ₹2000, ₹1200 B) ₹3500, ₹1500, ₹1200 C) ₹2500, ₹2000, ₹1700 D) ₹2200,  ₹3000,  ₹1000   Q. 3. The ratio of A to B is 4 : 5 and that of B to C is 2 : 3.If A equals 800,C equals A) 1000 B) 1200 C) 1500 D) 2000 Q. 4. If A = 4/5 of B and B = 5/2 of C, then the ratio of A : C is  A) 1 : 2 B) 2 : 1 C) 2 : 3 D) 1 : 3 Q. 5. If 2A=3B=4C, then A:B:C is A) 2 : 3 : 4 B) 4 : 3 : 2 C) 6 : 4 : 3 D) 3 : 4 : 6 Q. 6. If (3x + 5)/(5x - 2) = 2/3, then the  value of x is  A) 11 B) 19 C) 23 D) 7 Q. 7. What must be added to each term of the ratio 2 : 5 so that it may equal to 5 : 6 ? A) 65 B) 78 C) 13 D) 12 Q. 8. If x/y = 3/4, the ratio of (2x +3y) and (3y - 2x) is A) 2 : 1 B) 3 : 2 C) 1 : 1 D) 3 : 1 Q. 9. Two numbers are in the ratio 4 : 5 and their L.C.M. is 180. The smaller number is  A) 9 B) 15 C) 36 D) 45 Q. 1

SSC CGL....  Q. 1. L.C.M. of 2/3, 4/9, 5/6 is  A) 8/27 B) 20/3 C) 10/3 D) 20/27 Q. 2. H.C.F. of 2/3, 4/5 and 6/7 is  A) 48/105 B) 2/105 C) 1/105 D) 24/105 Q.3. The HCF of two numbers is 16 and their LCM is 160. If one of the number is 32, then the other number is  A) 48 B) 80 C) 96 D) 112 Q. 4. The least number which when divided by 4, 6, 8, 12 and 16 leaves a remainder of 2 in each case is:  A) 46 B) 48 C) 50 D) 56 Q. 5. Four bells ring at the intervals of 5, 6, 8 and 9 seconds. All the bells ring simultaneously at same time. They will again ring simultaneously after A) 6 minutes B) 12 minutes C) 18 minutes D) 24 minutes Q. 6.The LCM of two numbers is 48. The numbers are in the ratio 2:3. The sum of the numbers is  A) 28 B) 32 C) 40 D) 64 Q. 7. The H.C.F. and L.C.M. of two numbers are 21 and 84 respectively. If the ratio of two numbers is 1:4, then the larger of the two numbers is  A) 12 B) 108 C) 48 D) 84 Q. 8. The sum of two numbers is 36 and their H.C.F. is

                      Number System Natural Numbers - Counting numbers are called natural numbers.  •  The least natural number is 1.  • There are infinitely many natural numbers.  Whole Numbers - All natural numbers together with 0 form the collection of all whole numbers.  • The least whole number is 0.  • There are infinitely many whole numbers.  • Every natural number is a whole number.  • All whole numbers are not natural numbers, as 0 is a whole number which is not a natural number.  Integers -   All natural numbers, 0 and negatives of natural numbers form the collection of all integers.  • 0 is neither negative nor positive.  • There are infinitely many integers.  • Every natural number is an integer.  • Every whole number is an integer.  SSC previous year questions (Important)  Q. 1. Which of the following fraction is the greatest? 2/3 , 5/6 , 11/15 , and 7/8 A). 7/8 B). 11/15 C).  5/6 D). 2/3 Q. 2. If a number is as much greater than 31 as it is less than 75, then

Magic maths puzzles  Increase your IQ level  Comment your answer

Q.1. लुप्त संख्या ज्ञात कीजिए?             8,  10, 23,?,  297 A) 83     B) 82      C) 22        D)73 Q. 2.लुप्त संख्या ज्ञात कीजिए?               20, 28, 37, ?, 58, 70 A) 47       B) 46           C) 45             D) 48 Q. 3.लुप्त संख्या ज्ञात कीजिए?                 150, 135, 120, ?, 90, 75 A) 100       B) 110           C) 105         D) 95 Q. 4.लुप्त संख्या ज्ञात कीजिए?                 520, 510, 490, 460, ? , 360, 280 A) 420        B) 480            C) 470        D) 450 Q. 5. लुप्त संख्या ज्ञात कीजिए?                  20,  40,  63,  90,   122, ?  A) 130          B) 138            C) 150          D)160 Q. 6. लुप्त संख्या ज्ञात कीजिए?              9,  16,  25,   36,  49,  64,  ?  A) 61              B) 81               C) 68             D) 52 Q. 7. लुप्त संख्या ज्ञात कीजिए?                 8, 27, 64,  ?,  216, 343, 512 A) 225            B) 125              C) 115           D) 215 Q. 8. लुप्त संख्या ज्ञात कीजिए?              4, 7, 12, 19, 28, ?  A) 39            B) 42           C) 71     

                          Number Series Reasoning previous year questions  Q.1. Find the missing number?  10, 15, 20, 25, ?, 35, 40 A) 33         B) 31       C) 30          D)38 Q. 2. Find the missing number?  20, 28, 37, ?, 58, 70 A) 47      B) 46          C) 45            D) 48 Q. 3. Find the missing number?  150, 135, 120, ?, 90, 75 A) 100       B) 110          C) 105        D) 95 Q. 4.Find the missing number?  520, 510, 490, 460, ? , 360, 280 A) 420       B) 480           C) 470       D) 450 Q. 5. Find the missing number?  20, 40, 63, 90, 122, ?  A) 130         B) 138           C) 150         D)160 Q. 6. Find the missing number?  9, 16, 25, 36, 49, 64, ?  A) 61             B) 81              C) 68            D) 52 Q. 7. Find the missing number?  8, 27, 64,  ?,  216, 343, 512 A) 225           B) 125             C) 115          D) 215 Q. 8. Find the missing number?  4, 7, 12, 19, 28, ?  A) 39           B) 42          C) 71         D) 36 Q. 9.Find the missing n

“Kishore Vaigyanik Protsahan Yojana”  ( KVPY) - is a scholarship program started by the Department of Science and Technology (DST) of the Government of India to encourage the students to take up research careers in the areas of basic sciences without facing financial problems. Students who are in 11th standard must apply for this scheme if they are from science side or aimed to become a scientist. From 11th you may come across the experience of different govt exams which helps you a lot in future. Secure your future by taking a right decision at right time. Eligibility  - Students enrolled in XI Standard (Science Subjects) during the academic year 2020-21 and having secured a minimum of 75% (65% for SC/ST/PWD) marks in aggregate in MATHEMATICS and SCIENCE subjects in the X Standard Board examination immediately in the preceding academic year are eligible to appear for Aptitude test. Likely fellowships are provided up to the pre-Ph.D. level to the selected KVPY Fellows. For more details

              Matrix In class 12th matrix plays an important role in board exams.Learn deeply with simple method and gain full marks in maths.  Matrix Definition - A matrix is an array of real numbers (or other suitable entities), arranged in rows and columns. Types of matrices Rectangular matrix-  Any m×n matrix, where m≠n, is called a rectangular matrix. Row matrix - A matrix having only one row is called a row matrix. Column matrix - A matrix which has only one column is called a column matrix. Square matrix-  A matrix in which the number of rows is equal to the number of columns is called a square matrix. Diagonal matrix-  It is a square matrix all of whose elements except those in the leading diagonal, are zero. Scalar matrix -  A square matrix in which the diagonal elements are all equal, all other elements being zeros, is called a scalar matrix. Unit matrix or Identity matrix- A square matrix in which each diagonal element is unity, all other elements being zeros,

                              Statistics  Meaning-  Statistics means numerical presentation of facts. Statistics is the science of collecting, classifying or organising, interpreting numerical facts(data) from the logical analysis.  Use of Statistics in Education 1. It helps the teacher to provide the accurate description of the child.  2. It enables the teacher to extract general conclusions.  3. Statistics forms the basis of scientific approach to problems of Educational Psychology. 4. It proves useful in number of fields viz. railways, Banks, Army etc.   Collection  - Data collection is a process of gathering information from all the relevant sources to find a solution of the problem.  Sources of collecting of data :- 1. Primary data - Directly from field or experiment. 2. Secondary data -Obtained from pre saved data or review.      Methods of Collection of data 1. Direct personal investigation 2. Observation method 3. Interview method 4. Information through Questionnai

                               EXPONENTS Exponents - An exponent refers to a number that how many times to use the number in a mathematical operation like multiplication, division etc.  Exponents is also termed as power.  Power - An expression that represents repeated multiplication of the same number is called a power. Special cases when the exponent is 0 or 1 :- Case 1.  When the power is 0 a^0 = 1 67^0 = 1 Case 2. When the power is 1  a^1 = a 9^1 = 9                     Laws of Exponents The following identities hold for all integer exponents :- Practice Questions:- 1.Find out the value of (2/5) 3  ?   2.What is the power of a number when squared? 3. Simplify: (3/2) 2  + (2/3) 2  + (5/4) 2 4.  If 4 x  = 64, then 3 2x  = ? 5. Divide x 5  by x 2     Thank you for visiting  Keep sharing  Join us now :-  Instagram