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I will keep post a lot of ebooks here... Keep visiting this thread here But you have to give me time also.. It is taking time to upload ebooks... ...
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Q1 Let the roots of f(x)=x be α and β where f(x) is a quadratic polynomial. It is true that α,β also satisfies f(f(x))=x. Let the other roots of the eqn. f(f(x))=x be γ and δ. Now Correct statements are: a) If α β are ...
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A heavy, flexible, inelastic chain of length L is placed almost symmetrically onto a light pulley which can rotate about a fixed axle, as shown in the figure. *Image* What will the speed of the chain be when it leaves the pul ...
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A point-like electric dipole (dipole moment = p) is kept at the origin, pointing along the +z direction. A point charge q having mass m is released at rest from a point on the xy plane at a distance R from the origin. Assumin ...
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Q 1) \int\frac{x-1}{(x+1)\sqrt{x^{3}+x^{2}+x}}dx Q 2) \int{\left({\tan^{-1}\sqrt{(\sqrt x-1)}}\right)}dx Q 3) \int{(x^{1/3}+(\tan x)^{1/3})}dx Q 4) \int_{1}^{e}\frac{Inx}{x(\sqrt{1-Inx}+\sqrt{Inx+1})}dx Q 5) \int_{\frac{\pi } ...
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*Image* This is an infinite grid... Find the resistance between two consecutive nodes... PS: This is a very old question which has appeared in a lot of places including IE Irodov..(If I remember correctly) This problem uses a ...
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Let C1 and C2 be the graphs of the function y = x2 and y = 2x, 0<x<1 respectively. Let C3 be the graph of a function y = f (x), 0<x<1, f(0) = 0. For a point P on C1, let the lines through P, parallel to the axes, ...
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1. \int_{e^-^1}^{e^2}{|lnx / x | } dx = ? 2. \int_{sinx}^{1}{t^2 f(t)dt }= ( 1 - sinx ) , then find f (1 / √3) = ? 3. \lim_{x \rightarrow infinity}1/\pi \sum_{r=1}^{n}{tan^-^1(1/2r ^2)} = ? ...
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this thread is mainly intended to give some insight into congruences and how to solve various jee related problems using that concept.. definition of congruent: A number `a` is said to be congruent to `b` modulo `m` if `m` di ...
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A continuation of what b555 started, I'm posting here another theorem namely the Totient theorem or the famous "EULER'S-PHI-FUNCTION-FORMULA" to ease the mod-bashings....beleive me this is another tool to ease rem calculation ...
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I C or Instantaneous Centre of Rotation It is a simple theory to make problems of specific type easier......... if wisely used..... It states When a body is moving on horizontal floor with pure rolling, then it is as good as ...
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\int \frac{t(1-t^{2})^{-7/4}}{\sqrt{t+2\sqrt{1-t^{2}}+\sqrt{t+3\sqrt{1-t^{2}}}}}dt ...
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Evaluate the following integral: \int_{-100}^{-10}\left(\dfrac{x^2-x}{x^3-3x+1}\right)^2\mathrm dx+\int_{\frac{1}{101}}^{\frac{1}{11}}\left(\dfrac{x^2-x}{x^3-3x+1}\right)^2\mathrm dx + \int_{\frac{101}{100}}^{\frac{11}{10}}\l ...
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Consider the polynomials f(x) =a_1 +a_2x+a_3x^2+a_4x^4 and g(x) =b_1 +b_2x+b_3x^2+b_4x^4 where all coefficients are real It is known that \forall \ x \in \mathbb{R} \ \ [f(x)] = [g(x)] Is it necessary that f(x) = g(x)? ...
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\int \frac{ dx}{ (a^2 sin^2x + b^2 cos^2x ) ^2} ...
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(1) \int_{0}^{\pi }{|\sqrt{2}sinx+2cosx|dx}= (2) If \int_{0}^{1}(ax+b)/(x^{2}+3x+2)^{2}dx = 5/2 then find value of a and b ...
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*Image* I need ans to Q2,3 only ...
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\int_{0}^{\frac{\pi }{2}}{\frac{sec^{2}x}{(secx+tanx)^{n}}}dx,n>1 ...
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*Image* *Image* *Image* ...
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Value of k for which kx2 - 2kx + 3x - 6 is positive for exactly two integral values of x is.................. ...
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I WANT TO KNOW WHAT IS ANTI- AROMATIC. NEVER LEANT ANY THEORY ON IT. NEED HELP GUYS.....PLEASE HELP ME KNOW IT !!!! ...
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*Image* *Image* *Image* circled questions are doubts ticked answers are my answers circles options are fiitjee answers ...
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Find: \lim_{x\to\infty} \left(\dfrac{ex}{2}+x^2\left\{\left(1+\dfrac{1}{x}\right)^x-e\right\}\right) Note that {.} is NOT the fractional part. ...
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1) \\\textit{Find the values of }\left | a \right |+\left | b \right |\textit{such that the identity }\\ \left | ax+by \right |+\left | bx+ay \right |=\left | x \right |+\left | y \right |\emph{holds } \forall x ,y\epsilon R ...
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Q1 min value of f(x)= a2cos2x+b2sin2x + a2sin2x+b2cos2x Q2 What is condition so that f(x)=ax3+bx2+cx+dsinx is one one fn ...
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Q. A radioactive nuclide A_{1} with decay constant \lambda _{1} transform into a radioactive nuclide A_{2} with decay constant \lambda _{2} . Assuming that at the initial moment the preparation contained only the radio nuclid ...
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1) cos (x+y) dy = dx 2) x+y dy/dx /y-x dy/dx = (1 + x2/y2 ) ( ln ( x2+y2 )) 3) dy/dx = (4x + y + 1)2 4) 2x3y3 + x4y2 dy/dx = -b2/a2 y - b2/a2 x dy/dx [ GUYS POST THE SOLN. FULL AS I CANNOT CONFIRM UR ANS. SINCE I DON'T HAVE T ...
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DETERMINING OPTICAL NATURE OF PRODUCTS IS A BIT TROUBLESOME TO ME SO HERE IS A THREAD WHERE WE COULD POST IN ALL THE LOGICS THAT CAN BE USED TO SOLVE SUCH QS ...
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Identify the major product (3) formed in the following sequence of reactions. *Image* (a) *Image* (b) *Image* (c) *Image* (d) Both b and c ...
