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\hspace{-16}$Let $f(x)=x+x^2+x^4+x^8+x^{16}+x^{32}+...........................$\\\\ Then find Coeff. of $x^{10}$ in $f(f(x))$ ...

Q4 Let f(x) = ln(2x-x2) + sin Î x/2, then a) Graph of f is symmetrical about the line x=1 b) graph of f is symetrical about the line x=2 c) maximum value of f is 1 d) minimum value of f does not exist ...

Q1 If f(x) and g(x) be periodic and non periodic functions respectively, then f(g(x)) is a) always periodic b) never periodic c) periodic when g(x) is a linear function of x d) can't say Answer is c. Please tell why it is not ...

\hspace{-16}\mathbf{\int\frac{\sqrt{1-x^2}-x}{x^3-x^2-x+1-\sqrt{1-x^2}+x\sqrt{1-x^2}}dx} ...

Find all positive integers x and y satisfying the equation 3^x-2^y=7 ...

1. Please tell me the difference between subset and a proper-subset. 2. And that between the powerset and proper-power set 3. What does P(A) denote? 4. Prove that, (A U B)' = (A' ∩ B') Thanks in advance !! ...

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\hspace{-16}$If $\mathbf{x,y>0}$ and $\mathbf{f(x,y)=\sin^{-1}\left(\frac{x}{1+x^2}\right)+\sin^{-1}\left(\frac{y^2+y+1}{y^4+1}\right)}$\\\\\\ Then Find $\mathbf{\mathbb{R}}$ange of The Following $\mathbf{\mathbb{E}}$xpres ...

\hspace{-16}(1)\;\; \int\frac{x^3}{(1+x^3)^2}dx\\\\\\ (2)\;\; \int\frac{2012x-1}{e^{2012x}-2011x}dx ...

Show that the locus formed by z in the equation z^3+iz=1 never crosses the coordinate axes in the argand`s plane.Further show that |z|=√((-Im(z))/(2Re(z)Im(z)+1)) ...

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\text{The equation} (1+k)\cdot\frac{\cos x\cdot\cos(2x-\alpha)}{\cos(x-\alpha )} =1+k\cos 2x \; has no repeated root in it's domain of definition, if : a) |k| ≤ |csc α| , k ≠± 1 a) |k| ≤ |csc α| , k ≠- 1 a) |k| ≥ ...

1)In any discrete series when all the values are not the same, Mean deviation___standard deviation (=,≤,≥,<,greater than) 2)A measure of dispersion is an indicator of the reliability of __________ (an average/variabili ...

Nuclear density of iodine-125 atom is approx a)2 x 1015 g/cc b)2 x 1014 g/cc c)2 x 1015 kg/cc d)4 x 10-14 g/cc e)2 x 10-14 g/cc ...

\bg_green \hspace{-16}$Solve System of equations for real $\mathbf{x\;,y\;,z}$\\\\\\ \begin{Bmatrix} \bold{x^2+y^2=2.(\lfloor z^2 \rfloor +1).(\left\{z^2\right\}+1)} & \\\\ \bold{y^2+z^2=2.(\lfloor x^2 \rfloor +1).(\left\{x^2 ...

\hspace{-16}$(1)\;\; Find all Triplet $x,y,z$ such that \\\\ $\lfloor x \rfloor -y=2\lfloor y \rfloor -z=3\lfloor z \rfloor -x=\frac{2004}{2005}$\\\\\\ (2)\;\; Find all Real no. $x$ such that\\\\ $\frac{x}{x+4}=\frac{5\lfloor ...

How to find the centre of mass of an L shaped lamina formed by 3 squares of different masses? ...

\hspace{-16}$Find Max. and Min. value of $\mathbf{f(x)=\frac{2\cos x+2}{\sin x+\cos x+2}}$ ...

\hspace{-16}(1)\;\; \int\frac{\sin^{3n-1}.\cos^{n-1}}{\sin^{4n}x+\cos^{4n}x}dx$\\\\\\ Where $n\in\mathbb{N}$ ...

Wen we r given to find the equation of a circle thru three given points, we go by the family approach..we tend to form the equation of the circle taking the first two points as the end point of the diameter nd den form a stra ...

domain of √(x12-x9+x4-x+1) is __________ ...

\hspace{-16}\mathbf{\int \sin (101\;x).\sin^{99}\;xdx} ...

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Two uniform solid spheres of equal radii R, but mass M and 4M have a centre to centre seperation 6R.The two spheres are held fixed.A projectile of mass m is projected from the surface of the sphere of mass M directly towards ...

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\hspace{-16}$If each side of Square $\mathbf{OABC}$ is $\mathbf{4}\;$unit\\\\ and There are $\mathbf{4}$ Quarter Circle Center at Corrosponding Vertex\\\\ Then Find Area of Region denoted by $\mathbf{\bold{\alpha}}$ and $\mat ...

1)f(x) and g(x) are linear functions for all x such that f(g(x)) and g(f(x)) are Identity functions.If f(0)=4 and g(5)=17 find f(2006)? 2)let f(x)=(x+1)(x+2)(x+3)(x+4)+5 where x belongs to [-6,6].If range of f(x) is [a,b] whe ...

\hspace{-16}\mathbf{\int\frac{x.\sin^2 x}{\cos (2x).\cos^2 x}dx} ...

Show that out of {[x,2x,..,(n-1)x]} there must be one which differ from an integer by at most 1/n . Where x is a given real number and n is a given positive integer. ...

\hspace{-16}\mathbf{(1)\;\; \int\frac{1}{x+\sqrt{x^2+x+1}}dx}$\\\\\\ $\mathbf{(2)\;\; \int\frac{\sqrt{\sqrt{x^4+1}-x^2}}{x^4+1}dx}$ ...