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Topic : TOTAL AIEEE SYLLABUS........
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SYLLABUS MATHEMATICSUNIT 1 : SETS, RELATIONS AND FUNCTIONS: Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Types of relations, equivalence relations, functions;. oneone, into and onto functions, composition of functions.UNIT 2 : COMPLEX NUMBERS AND QUADRATIC EQUATIONS: Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex num
Topic : ROORKEE EXAMINATION QUESTIONS:
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ROORKEE UNIVERSITY (NOW IITROORKEE)EXAMINATION WAS CONSIDERED ONE OF THE TOUGHEST EXAMINATION IN IT'S TIME.THE QUESTIONS WERE NOT ONLY TO TEST CONCEPTS BUT ALSO THERE WERE LOT OF CALCULATIONS IN THOSE QUESTIONS.ALTHOUGH MANY OF YOU MAY HAVE THESE QUESTIONS AND U MAY THINK THESE ARE SUBJECTIVES AND NOT UP THE PRESENT PATTERN BUT I M PUTTING THESE UP FOR THEM WHO DON'T HAVE ,AS THESE CAN BE BENEFICIAL FOR JEE ADVANCE.ALTHOUGH THESE ARE TIME CONSUMING (I REALISED WHEN I DID QUES 4 AN EASY ONE FROM SEQUENCE SERIES SECTION BUT SLIGHTLY CALCULATIVE):1)A ball moving around the circle x2+y22x4y20=0 in anticlockwise sense direction leaves it tangentially
Topic : Application of differential equations to optics and the brachistochrone problem
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mm, the link is nt visible..:(
Topic : complex no unleashed
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Complex no SOLVED EXAMPLES 8 ? 1+i ? ? 1 – i ?Example 1. Prove that ?? +?? =2? 2 ? ? 2 ?Solution. We change (1 + i) and (1 – i) into polar formππ??We have1 + i = = 2 ? cos + i sin ?44?? Then 8 ππ?ππ?(1 + i)8 = ? cos + i sin ? = cos8. + i sin 8.44?44?= cos 2π + i sin 2πππ??1 – i = 2 ? cos − i sin ?44?? 8 8 Also 8 ππ??1− i ? ?and ?? = ? cos − i sin ? = cos 2π − i sin 2π then = 144?? 2? ?Adding (1) and (2), 8 ?1+ i ? ?1− i ??? +??? 2? ? 2? 8 = 2 Example 2. If the roots of the equation x2 – 2x + 4 = 0
Topic : IIT JEE EBOOKS
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Tons of ebooks here..See and Belive nd download.All Ebooks as comments
Topic : Very tough Comprehension question(must try to do this)..Acc to new pattern
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Here is the value of pi and answer the following question given below in the comments3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502 8410270193852110555964462294895493038196442881097566593344612847564823 3786783165271201909145648566923460348610454326648213393607260249141273 7245870066063155881748815209209628292540917153643678925903600113305305 4882046652138414695194151160943305727036575959195309218611738193261179 3105118548074462379962749567351885752724891227938183011949129833673362 44065664308602139494639522473719070217986094370277053921717629317
Topic : FROM RICHES TO RAGS..........KOTA THE EDUCATION CITY FINALLY MEETS ITS NADIR......
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KOTA ...........................FINALLY DEVOID OF STUDENTS BECAUSE OF CHANGE IN JEE PATTERN..... AFTER THE ANNOUNCEMENT THAT THE BOARD EXAMS WOULD BE HAVING A 40 PERCENT WEIGHTAGE IN THE SELECTION FOR THE PRESTIGIOUS IITS,THE PLACE WHICH WAS ONCE MECCA OF EDUCATION HAS BEEN REDUCED TO A SECLUDED PLACE......HAVING SPENT 3 YEARS OF MY LIFE THERE.....IN THE CROWD OF STUDENTS MANY OF WHOM ARE THERE BECAUSE OF SHEER PEER PRESSURE AND FOR ENJOYING A LUXURIOUS LIFE..{AT PUBS AND CYBER CAFES}....EVEN YESTERDAY WHILE STROLLING IN THE MARKET HERE I FOUND GLOOM ON THE FACES OF THE LOCAL PEOPLE I
Topic : The magic of Usubstitution in integral calculus.
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This is one of the most valuable shortcuts that we use. It is advanced, but once you master this, integrals can become much, much faster. Nearly every integral that you come across after Calculus II requires USubstitution, and that is why this trick is very useful.Before we get to the good stuff, let’s do an example with regular USubstitution.Let’s try this again, but completely avoid USubstitution. It’s a very similar concept, but it is much faster and will help you make less mistakes. With USubstitution, you must remove yourself from the problem, go off to the side, figure out what u and du are, and then finally come
Topic : A bouncing ball..
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Application: A Bouncing Ball Suppose you drop a basketball from a height of 10 feet. After it hits the floor, it reaches a height of 7.5 = 10 . feet; after it his the floor for the second time, it reaches a height of 5.625 = 7.5 . = 10 . feet, and so on and so on.Does the ball ever come to rest, and if so, what total vertical distance will it have traveled? This will lead to summing a geometric series, but let us first investigate, what happens to a ball being dropped from a height h.Since the ball is subject to free fall, at time t&nbs
Topic : A bouncing ball..
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Application: A Bouncing Ball Suppose you drop a basketball from a height of 10 feet. After it hits the floor, it reaches a height of 7.5 = 10 . feet; after it his the floor for the second time, it reaches a height of 5.625 = 7.5 . = 10 . feet, and so on and so on.Does the ball ever come to rest, and if so, what total vertical distance will it have traveled? This will lead to summing a geometric series, but let us first investigate, what happens to a ball being dropped from a height h.Since the ball is subject to free fall, at time t&nbs
Topic : Beauty of mathsMUST SEE!!
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Hey everyone, google this: (sqrt(cos(x))*cos(200*x)+sqrt(abs(x))0.7)*(4x*x)^0.01, sqrt(9x^2), sqrt(9x^2) Must see!!!
Topic : Integral 0 to infinity e^(x2)dx ? Here's a nice trick..
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Why?Well, there isn't a closedform expression for the antiderivative of the integrand, so the Fundamental Theorem of Calculus won't help.But the expression is meaningful, since the it represents the area under the curve from 0 to infinity.Furthermore, there is a nice trick to find the answer!Call the integral I. Multiply the integral by itself: this gives I2 =then view as an integral over the first quadrant in the plane: I2 then change to polar coordinates (!): Now this is quite easy to evaluate: you find that .This means that I, the original value of the integral you were looking for, is . Wow! Source:http
Topic : read the peigonhol proble an inmo regular
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Pigeonhole Principle Here's a challenging problem with a surprisingly easy answer: can you show that for any 5 points placed on a sphere, some hemisphere must contain 4 of the points? How about an easier question: can you show that if you place 5 points in a square of sidelength 1, some pair of them must be within distance 3/4 of each other? If you play with this problem for a while, you'll realize quickly that the extreme case occurs when 4 points are at the corners of the square with a 5th point at the center. In this case adjacent points
Topic : The Square Root of any numner: A trick worth knowing !!!
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It is the quickest way, and it works for all non perfect squares ..Find two perfect squares that your square falls between. For example if I am trying to find the square root of 12, then I know my number is going to fall between the square root of 9 (3^2=9) and the square root of 16 (4^2=16).Divide your square by one of these two square roots. Therefore, I am going to divide my square, 12, by one of the square roots 3 or 4. I will choose 3. So, 12/3 = 4.I will average the result from Step 2 with the root I divided by. So, I take my answer from Step 2 (4), and will average this with the root I chose to divide my square by in Step 2 (3). Therefore, (4+3)/2 = 3.5. The
Topic : ISAT Syllabus
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1.) SYLLABUS For ISAT:PHYSICS Syllabus:MECHANICSUnits & Measurements: The international system of units, measurement oflength, mass and time, accuracy, precision of instruments and errors inmeasurement, Significant figures, dimension of physical quantities, dimensionalformulae and equations, dimensional analysis and its applications.Motion in a straight line: position, path length and displacement, average velocityand speed, instantaneous velocity and speed, acceleration, kinematic equations foruniformly accelerated motion, relative velocity. Motion in a plane: scalars and vectors, multiplication of vectors by real numbers,addition and aubtraction of vector
Topic : Cube Root of Unity
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THE CUBE ROOTS OF UNITY:Let the cube root of 1 be x i.e., 3√ 1 = x. Then by definition, x3 = 1 or x3 – 1 = 0 or (x – 1) (x2 + x + 1) = 0 Either x – 1 = 0 i.e., x = 1 or (x2 + x + 1) = 0 Hence Hence, there are three cube roots of unity which are which the first one is real and the other two are conjugate complex numbers. These complex cube roots of unity are also called imaginary cube roots of unity. PROPERTIES OF THE CUBE ROOTS OF UNITY: 1.) One imaginary cube root of unity is the square of the other. Hence it is clear that one cube root of uni
Topic : Best Way To Remember Trigo Ratios
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Method1:Some People Have Curly Brown Hair Through Proper BrushingSome= People/Have > Sine=Perpendicular/HypotenuseCurly=Brown/Hair > Cosine=Base/HypotenuseThrough=Proper/Brushing > Tangent=Perpendicular/BaseMethod 2:Pandit Bhadri Prasad Har Har BoleNow Seperating themsin cos tanP B PH H BPlzzzzzzzz Plzzzzzzzzzzzzzzzzzzzzz rate me.Parth Chhaparwal
Topic : an introductory tutorial to complex numbers.
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/* Style Definitions */table.MsoNormalTable{msostylename:"Table Normal";msotstylerowbandsize:0;msotstylecolbandsize:0;msostylenoshow:yes;msostylepriority:99;msostyleqformat:yes;msostyleparent:"";msopaddingalt:0in 5.4pt 0in 5.4pt;msoparamargin:0in;msoparamarginbottom:.0001pt;msopagination:widoworphan;fontsize:10.0pt;fontfamily:"Times New Roman","serif";}Hi there!!! I am gonna write here a full fledged tutorial on introduction to complex numbers (at the moment only for the people in 11th ).Those who are new to it are welcome to read it. Before starting off we must know the first and foremost thing. That is iota.Iota is the square
Topic : North India Tourism, North India Tour Packages, North India Tour Operator, Budget Tour Pac
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India being one of the long haul destinations is the perfect holiday destination for budget tourists. The multiplicity of tourist places in India is simply mind boggling. Be it people, places, customs, dresses or food, the sheer diversity you get to see is an eye opener for tourists. Nowhere in the world one gets to see such a diverse congregation of cultures in one landmass. India with its diverse landscape provides the perfect destination for any type of tour that you would like to undertake. Whether you want to undertake a Yoga tour, Ayurveda tour or a pilgrimage that you and your family would like to undertake. North India tour packages typically cover the stat
Topic : Trigonometry : Truly difficult Practice Questions. . .
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these are too good question. remember to rate me if you like these. :) Q) If and are positive integers such that,compute the ordered pair . Q) Find y : Q) Find the value of Q) Prove that Q) Prove that if , then .Q) Calculate Q) evaluate : Q) evaluate : Q) Solve the equation Q) Evaluate: Q) solve for x where . Q) Find the value of:Q)Prove that : Q) find Q)Prove that . here Q stands for the set of rational numbers. source : www.artofproblemsolving.com
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