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this is a gud one... find the last two digits of 32012 or find 32012 mod 100? ...
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1)Find tan-1 1/x2+x+1 + tan-1 1/x2+3x+3 + tan-1 1/x2+5x+7 + tan-1 1/x2+7x+13 ..... upto n terms.... 2)If sin(cot-1(x+1))=cos(tan-1x),then x= ? 3) If \sum_{n=1}^{10}{}\sum_{m=1}^{10}{}tan^{-1}(\frac{m}{n})=k\pi\, then \: find ...
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1)Find tan-1 1/x2+x+1 + tan-1 1/x2+3x+3 + tan-1 1/x2+5x+7 + tan-1 1/x2+7x+13 ..... upto n terms.... 2)If sin(cot-1(x+1))=cos(tan-1x),then x= ? 3) If \sum_{n=1}^{10}{}\sum_{m=1}^{10}{}tan^{-1}(\frac{m}{n})=k\pi\, then \: find ...
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In an examination hall there are four rows of chairs. Each row has 8 chairs one behind the other.There are two classes sitting for the examination with 16 students in each class.It is desired that in each row,all students bel ...
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consider a function f on non-negative integers such that f(0)=1 , f(1)=0 and f(n) + f(n-1) = nf(n-1) + (n-1)f(n-2) for n≥2 . Show that , \frac{f(n)}{n!} = \sum_{k=0}^{n}{\frac{(-1)^{k}}{k!}} ...
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suppose a,b,n are positive integers , all greater than 1. if an+bn is Prime then what can be said about n ? A) n must be 2 B) n need not be 2 but must be a power of 2 C) n need not be a power of 2 but must be even D) none of ...
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suppose a,b,n are positive integers , all greater than 1. if an+bn is Prime then what can be said about n ? A) n must be 2 B) n need not be 2 but must be a power of 2 C) n need not be a power of 2 but must be even D) none of ...
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suppose a,b,n are positive integers , all greater than 1. if an+bn is Prime then what can be said about n ? A) n must be 2 B) n need not be 2 but must be a power of 2 C) n need not be a power of 2 but must be even D) none of ...
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\hspace{-16}\bf{(1)\;\; \int_{0}^{\infty}\frac{\ln (x)}{x^2+4}dx}$\\\\\\ $\bf{(2)}\;\;$ Find Max. value of $\bf{\int_{0}^{1}f^3(x)dx}$\\\\\\ Given $\bf{\mid f(x)\mid \leq 1}$ and $\bf{\int_{0}^{1}f(x)dx=0}$\\\\\\ $\bf{(3)\;\; ...
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\hspace{-16}\mathbf{\lim_{n\rightarrow \infty}\sum_{r=0}^{n}\frac{1}{\binom{n}{r}}=} ...
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\hspace{-16}\bf{(1)\;\; \int_{0}^{\infty}\frac{\ln (x)}{x^2+4}dx}$\\\\\\ $\bf{(2)}\;\;$ Find Max. value of $\bf{\int_{0}^{1}f^3(x)dx}$\\\\\\ Given $\bf{\mid f(x)\mid \leq 1}$ and $\bf{\int_{0}^{1}f(x)dx=0}$\\\\\\ $\bf{(3)\;\; ...
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\hspace{-16}\bf{(1)\;\; \int_{0}^{\infty}\frac{\ln (x)}{x^2+4}dx}$\\\\\\ $\bf{(2)}\;\;$ Find Max. value of $\bf{\int_{0}^{1}f^3(x)dx}$\\\\\\ Given $\bf{\mid f(x)\mid \leq 1}$ and $\bf{\int_{0}^{1}f(x)dx=0}$\\\\\\ $\bf{(3)\;\; ...
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\hspace{-16}\bf{\int_{-\pi}^{\pi}\frac{\sin (0.5+n)x}{2\sin (0.5)x}dx=}$\\\\\\ Where $\mathbf{n\in\mathbb{N}}$ and $\bf{0.5=\frac{1}{2}}$ ...
