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\hspace{-16}$ Let $\bf{\omega}$ be a cube root of unity which is not equal to $1$.\\\\ Then the number of distinct elements in the set $\bf{{(1+\omega+\omega^2+\omega^3+...+\omega^n)^m}$\\\\ Where $\bf{m,n=\left\{1,2,3,...\ri ...
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*Image* ...
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\hspace{-16}\mathbf{\int_{0}^{\pi}\ln(3+\cos x)dx} ...
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\hspace{-16}\mathbf{\int_{\frac{1}{2}}^{2}\frac{\tan^{-1}(x)}{x^2-x+1}dx} ...
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\hspace{-16}$Prove that the equation $\mathbf{2x^{n+2}+1=3x}$ has one real root in $\mathbf{(0,1)}$ ...
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Here are the problems of RMO 2011 *Image* Source: Mathlinks. ro ...
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\hspace{-16}$If $\mathbf{f:\mathbb{N}\rightarrow \mathbb{R}}$ be a function such that $\mathbf{f(1)=\frac{2007}{6}}$ and \\\\\\ $\mathbf{\frac{f(1)}{1}+\frac{f(2)}{2}+\frac{f(3)}{3}+.........+\frac{f(n)}{n}=\frac{n+1}{2}.f(n) ...
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\hspace{-16}$If $\mathbf{f:\mathbb{N}\rightarrow \mathbb{R}}$ be a function such that $\mathbf{f(1)=\frac{2007}{6}}$ and \\\\\\ $\mathbf{\frac{f(1)}{1}+\frac{f(2)}{2}+\frac{f(3)}{3}+.........+\frac{f(n)}{n}=\frac{n+1}{2}.f(n) ...
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\hspace{-16}$If $\mathbf{f:\mathbb{N}\rightarrow \mathbb{R}}$ be a function such that $\mathbf{f(1)=\frac{2007}{6}}$ and \\\\\\ $\mathbf{\frac{f(1)}{1}+\frac{f(2)}{2}+\frac{f(3)}{3}+.........+\frac{f(n)}{n}=\frac{n+1}{2}.f(n) ...
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how many ways can the word VENUS be arranged so that the vowels do not change thein orders?? ...
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x2+x3≤x+f(x)≤x5-x3 , for value of x near 0, f(x) is: A) -1 B) 0 C) 1 D) none of these ...
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*Image* *Image* From 360 mathematical contests ...
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have faith in urself,u have done enough to do well in JEE,feel the confidence in urself,it's ur day tomorrow,stay positive and focussed,all the very best ...
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Q. Why do capacitors block D.C Current and allow A.C Current ? Ans: *Image* :-B........lol........ ...
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*Image* ...
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A Long pliablle carpet is laid on ground. One end of the carpet is bent back and pulled backwards with a constant velocity of 16 m/s. If mass/length of the carpet is 1 Kg/m , the minimum force required to pull the carpet is : ...
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*Image* ...
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At the center or a neutral hollow metallic shell, a point charge is placed Is it a point of equilibrium? if yes what kind of equilibrium? ...
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1.A point charge is placed at the origin.Calculate electric flux through the open hemispherical surface:...... {x-a}2+y2+z2=a2;x≥a Ans.q/2ε0*{1-1/ 2 ) 2.A point charge is located on the axis of a disc of radius R at a dist ...
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prove \int_{0}^{\infty}{\frac{x^3}{e^x-1}\mathrm{dx}}=\frac{\pi^4}{15} ...
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prove \int_{0}^{\infty}{\frac{x^3}{e^x-1}\mathrm{dx}}=\frac{\pi^4}{15} ...
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*Image* which formulae to use?? ...
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*Image* which formulae to use?? ...
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evaluate 1) \sum_{n=1}^{\infty }\frac{1}{n^3(n+1)^3} 2) \sum_{n=1}^{\infty }\frac{1}{n^2(n+1)^2} ...
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A smooth sphere of mass m impinges on another of mass M at rest, the direction of motion making angle 45° with the line of centers at the moment of impact. If the coeffcient of restitution e = 1/2, show that direction of m i ...
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Does n! = the integral from 0 to infinity of (x^n)(e^-x)dx hold true for all real numbers? If so, can we find the derivative of n!? ...
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find *Image* ...
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find *Image* ...
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find all the numbered pairs (x,y) that satisfy the equation tan^4x+tan^4y+2cot^2x.cot^2y=3+sin^2(x+y) ...
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find all the numbered pairs (x,y) that satisfy the equation tan^4x+tan^4y+2cot^2x.cot^2y=3+sin^2(x+y) ...
