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Topic : MATHEMATICS - FEW FORMULAE IN LIMITS
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6
4914
Engineering Entrance
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JEE Main
COURTESY: MTG MATHEMATICS TODAY..........HERE ARE SOME TRICKS WHICH ARE VERY USEFUL IN EVALUATION OF LIMITS FOR COMPETETIVE EXAMS...1. X0 (Sin mx)/(Sin nx) = m/n (also applicable when tan is present in place of sin) 2. x0 (sin ax sin bx)/(sin cx sin dx ) = (ab)/(cd) {also applicable in tan case also) 3. xa (xp- ap)/(xq-aq) = (p/q)ap-q 4. x0 { p(a+xn)- p(a-xn) } / (xn) = 2a1/p -1/p 5. x0 p (a+xn) - pa / xn = a1/p - 1 / p 6.[ x] (xn+yn)1/n =y , where o<x<y
Topic : PERMUTATION AND COMBINATION SHORTCUTS ------PART 1
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3041
Engineering Entrance
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JEE Main
1)THE NO. OF PERMUTATIONS OF N THINGS TAKEN TOGETHER WHEN P ARE ALIKE OF ONE KIND, Q OF OTHER TYPE, R OF OTHER KIND AND REST OF ALL DIFFERENT IS . WE MAY CONTINUE IT FOR ANY NUMBER OF ITEMS.2)THE NO. OF PERMUTATIONS OF N DISSIMILAR THINGS, TAKEN ALL AT A TIME IS (N-1)!3)THE NUMBER OF WAYS OF ARRANGING N DISTINCT OBJECTS ALONG A CIRCLE, WHEN CLOCKWISE AND ANTICLOCKWISE ARRANGEMENTS ARE CONSIDERED SAME IS 4)THE NUMBER OF NECKLACES FORMED WITH N BEADS OF
Topic : Permutations & Combinations - Made Easy
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1698
Engineering Entrance
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JEE Main
Permutations and combinationsWhen we talk of permutations and combinations in everyday talk we often use the two terms interchangeably. In mathematics, however, the two each have very specific meanings, and this distinction often causes problems. In brief, the permutation of a number of objects is the number of different ways they can be ordered; i.e. which is first, second, third, etc. If you wish to choose some objects from a larger number of objects, the way you position the chosen objects is also important. With combinations, on the other hand, one does not consider the order in which objects were chosen or placed, just which objects were chosen. We could summar
Topic : PLZ SOLVE
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312
Engineering Entrance
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JEE Main
PLZ REPLY WITH THE ANSWER AND SOLUTION..........WHAT IS THE PERIOD OF THE FUNCTION f(x)+f(x+2) = *f(x+1) ?????
Topic : Short cut for finding orthocentre when three vertices are given
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1282
Engineering Entrance
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JEE Main
can tell u a short cut for this."Elessar sir plz tell ur opinions on this.i will try to xplain the procedure wid an exampleGiven the vertices are(1,-3),(6,1), and (4,-1)) shift the origin to (1,-3) by transformation of axes then the vertices are (0,0) (5,4) (3,2). First we hav to find QQ = x1x2+y1y2/x1y2-x2y1 = 15+8/10-12 = -23/2.Now before calculating ortho do this [Q(y2-y1), -Q(x2-x1)] = [-23/2(-2), 23/2(-2)] = (23, -23)therefore Ortho centre = [23+1, 23+(-3)] = (24, -26)........the last step is becoz we had transformed the origin if the vertices are lik (0,0) (x1,y1) (x2,y2) the last step can be omitted.
Topic : HOW TO SOLVE MATH PROBLEMS.
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763
Engineering Entrance
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Mathematics
Mathematics is one of the most important subjects for school students. Broadly speaking, the process of learning and mastering any topic in mathematics involves three steps or stages:1. Learning the conceptual foundations of that topic2. Understanding the applications of these concepts to problem solving3. Solving “new” problems. **Article edited by Moderation team
Topic : Ramanujam !
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969
Engineering Entrance
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JEE Main
Ramanujam: By age 11, he had exhausted the mathematical knowledge of two college students who were lod
Topic : Integration shortcuts
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2125
Engineering Entrance
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JEE Main
1) [ o][ n] {x} dx = n/2 where {x} means fractional part of x (n belongs to integers) 2) [ o][n ] [x] dx = n (n-1)/2 ( n belongs to integers) 3) [ a][ b] [x] dx = 1/2( [b] - [a] ) ( [b] +[a] - 1) + [b]{b} - [a]{a} ( a , b are not integers) 4)[a ][b ] modulus (x)/x dx = modulus(b) - modulus (a) 5)[ 0][ ] dx / (x+[ 2]x2 +1)n = n/n2 - 1 6)[o ][ /2] sinnx / sinnx + cosnx dx = /4 the above formula is valid for( tan and cot), (sec and
Topic : shortcut to find the rank of a given word
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2185
Engineering Entrance
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JEE Main
Shortcut for finding the Rank having words repeated:Rank of AGAIN1 2 1 3 4A G A I N1st numbers r given to the letters in dictionary orderthen under each letter, write down the number of letters assigned with lesser number occuring towards the right of the letter under which v r writing. 1 2 1 3 4A G A I &n
Topic : Tanzalin Method for easier integration by parts
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505
Engineering Entrance
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Mathematics
Lets understand this with the help of exampleHow to integrate Integration by Parts MethodFirst, let’s see normal Integration by Parts for comparison.We identify u, v, du and dv as follows: u = 2x dv = (3x − 2)6dx du = 2dx Integration by Parts then gives us:Now, we find the unknown integral:Putting it together, we have:We can then factor and simplify this to give: Now, lets do it using Tanzalin's Method of integrationIn the Tanzalin Method, we set up a table as f
Topic : PROOF OF TAYLOR'S THEOREM
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6328
Engineering Entrance
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JEE Main
Proof: Taylor's theorem in one variable[edit] Integral versionWe first prove Taylor's theorem with the integral remainder term.[4]The fundamental theorem of calculus states thatwhich can be rearranged to:Now we can see that an application of Integration by parts yields:The first equation is arrived at by letting and dv = dt; the second equation by noting that ; the third just factors out some common terms.Another application yields:By repeating this process, we may derive Taylor's theorem for higher values of n.This can be formalized by applying the technique of induction. So, suppose that Taylor's theorem holds for a particular n, that
Topic : HOW TO FIND ROOTS(IMAGINARY AND REAL )OF A CUBIC EQUATION?????
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246
Engineering Entrance
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JEE Main
HOW TO FIND ROOTS(IMAGINARY AND REAL )OF A CUBIC EQUATION?????
Topic : SET THEORY
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2032
Engineering Entrance
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JEE Main
SET THEORYMULTIPLE CHOICE QUESTIONS1. If A = {1, 2, 5} and B = {3, 4, 5, 9}, then A ? B is equal to (a) {1, 2, 5, 9} (b) {1, 2, 3, 4, 9} (c) {1, 2, 3, 4, 5, 9} (d) none of these2. If A = {x: x = 3n, n ? 6, n ? N} and B = {x: x = 9n, n ? 4, n ? N}, then which of the following is false?(a) A U B = {3, 9, 27, 81,243, 729, 6561} (b) A ? B = {9, 81, 729, 6561} (c) A-B = {3, 27,243} (d) A ? D = {3, 27, 243, 6561}3. If Y is the smallest set such that Y U {1, 2} = {1, 2, 3, 5, 9}, then Y is equal to (a) {1,2,3,5,9} (b) {3,5,9} (c) {1,2} (d) none of these4. If n (A) = 115, n (B) = 326, n (A-B) = 47, then n (A U B) is equal to(a) 373 (b) 165 (c) 370 (d) none
Topic : Mathematical Reasoning
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1412
Engineering Entrance
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JEE Main
Of late many of us have been asking for books or sources to read theory regarding mathematical reasoning. Many of you may have googled it but didn't pay heed to this link :http://www.regentsprep.org/regents/math/math-a.cfmSo compiling it from there . Read it here else the link has been provided . Types of Sentences One of the goals of studying mathematics is to develop the ability to think critically. The study of critical thinking, or reasoning, is called logic. All reasoning is based on the ways we put sentences together. Let's start our examination of l
Topic : cube root onemore-only for perfect cubes
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3
980
Engineering Entrance
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JEE Main
write the list of cubes of 1-10 as follows1 12 83 274 645 1256 2167 3438 5129 729revise the last numbersknow pick a perfect cube to check:474552group it by 3 digits, 474 552 see the last digit, &nb
Topic : find the cube root easy technique
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741
Engineering Entrance
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JEE Main
General MethodThe divisor should not be too small. The smallness will giverise to big quotients with several digits. This will lead tocomplications.Another method is to multiply the given number by anothersmall number cubed and find the cube root. Final answer iscalculated by dividing the result by small numberExample 4: Find the cube root of 2We multiply 2 by 53The new Number becomes 2 x 125 = 250Find the cube root of 250 and divide the answer by 5 [since we multiplied the original number by 5Step 1250 : 0 0 0By inspection write down 6 and 34 as the first Q and R .Since 216 is the perfect cube close to 250 and thereminder from 250 is 34.Step 2250 : 0 0 0108 : : 34:
Topic : Trick to find squares of numbers which have 5 as their last digit
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1192
Engineering Entrance
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JEE Main
Here is an Easy way to find Squares of numbers which contain 5 as their last digit..Consider the digits written before 5 as a single number and multiply it be its succcessor and then write it and put 25 as the last two digits of it...For example:to find square of 15:: (1*2)=2 and then write 25 at the end ,ie. 225similarly to find square of 25:: (2*3)=6 and then write 25 at the end i.e, 625for finding square of 105:: (10*11)=110 and then write 25 at the end ,i.e, 11025PLS RATE IT IF YOU LIKE IT !!Some of The Related Articles:What is PSEUDO FORCE ?Image formation in Plane Mirror @ Infinity DistanceKaprekar Transformation for 3-Digit Numbers
Topic : Quick Maths Trick #1
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806
Engineering Entrance
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JEE Main
Shortcut to Squaring Any 2-Digit NumberWhat do you do when your calculator has been confiscated and the world is depending on you to square a two-digit number within a minute? Don’t panic – just follow three simple steps that require basic addition and multiplication, and you’ll be able to solve the problem in no time. If you practice enough, you’ll even be able to complete each step mentally, rendering scratch paper unnecessary. This will save you time on drills and strengthen your skills so you can tackle other challenges. Eventually, you’ll be able to solve multi-step squaring problems without ever breaking a sweat – or a penci
Topic : PLAY WITH GRAPHS
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1544
Engineering Entrance
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GATE
PLAY WITH GRAPHS Please click like and comment the graph which you like.Try to find some relationship between graphs i.e y=x^2 and sin x and (sin x)^2 .Let your mind and brain blossomTell me the graphs that you want to display Graph for sin(x) -32-30-28-26-24-22-20-18-16-14-12-10-8-6-4-22468101214161820222426283032 -3.5-3-2.5-2-1.5-1-0.50.511.522.533.5 x: 10.5139131y: -0.88622658 Graph for cos(?x)
Topic : Maths Trick #2
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550
Engineering Entrance
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JEE Main
Mentally Multiply by 5, 25, 50, 250This is a simple quicker math trick but it can be very useful for young students to solve seemingly difficult calculations. I will be glad to get your feedback on this.Mental multiplication by 5, 25, 50, 250, 500 and so on. Any number can be expressed in different ways. For example, 5 can be expressed as 10x(1/2).Trick: Multiplication by 5Step 1: Multiply the number by 10, i.e. simply place a zero after the number.Step 2: Halve the resultant number.Example 1: 5 × 136 = ten times of 136 i.e. 1360 should be divided by 2 = 1360/2 = 680Example 2:5 × 343, half of 3430 is 1715Also check out, how to mentally mu
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