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If one root of the equation ax2+bx+c=0 is the square of the other, then a(c-b)3=cX, where X is (a) a3+b3 (b) (a-b)3 (c) a3-b3 (d) N.O.T Please show the method .. ...
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If the equation ax3+3bx2+3cx+d=0 has two equal roots,show that it must be equal to bc-ad/2(ac-b2) . ...
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If a,b,c are in AP ;b,c,a In GP then prove that 1/c , 1/a , 1/b are in ap ...
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\text{1)Evaluate:} a)\lim_{n\rightarrow \infty}\frac{1}{2n}\log\binom{2n}{n} b)\lim_{n\rightarrow \infty}\left[\frac{1}{a+n}+\frac{1}{2a+n}+\cdots +\frac{1}{na+n}\right] \text{2)Let } a_{1}=1 \text{ and }a_{n}=n(a_{n-1}+1)\ \ ...
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\text{1)Evaluate:} a)\lim_{n\rightarrow \infty}\frac{1}{2n}\log\binom{2n}{n} b)\lim_{n\rightarrow \infty}\left[\frac{1}{a+n}+\frac{1}{2a+n}+\cdots +\frac{1}{na+n}\right] \text{2)Let } a_{1}=1 \text{ and }a_{n}=n(a_{n-1}+1)\ \ ...
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\text{1)Evaluate:} a)\lim_{n\rightarrow \infty}\frac{1}{2n}\log\binom{2n}{n} b)\lim_{n\rightarrow \infty}\left[\frac{1}{a+n}+\frac{1}{2a+n}+\cdots +\frac{1}{na+n}\right] \text{2)Let } a_{1}=1 \text{ and }a_{n}=n(a_{n-1}+1)\ \ ...
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\text{1)Evaluate:} a)\lim_{n\rightarrow \infty}\frac{1}{2n}\log\binom{2n}{n} b)\lim_{n\rightarrow \infty}\left[\frac{1}{a+n}+\frac{1}{2a+n}+\cdots +\frac{1}{na+n}\right] \text{2)Let } a_{1}=1 \text{ and }a_{n}=n(a_{n-1}+1)\ \ ...
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\text{1)Evaluate:} a)\lim_{n\rightarrow \infty}\frac{1}{2n}\log\binom{2n}{n} b)\lim_{n\rightarrow \infty}\left[\frac{1}{a+n}+\frac{1}{2a+n}+\cdots +\frac{1}{na+n}\right] \text{2)Let } a_{1}=1 \text{ and }a_{n}=n(a_{n-1}+1)\ \ ...
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\text{1)Evaluate:} a)\lim_{n\rightarrow \infty}\frac{1}{2n}\log\binom{2n}{n} b)\lim_{n\rightarrow \infty}\left[\frac{1}{a+n}+\frac{1}{2a+n}+\cdots +\frac{1}{na+n}\right] \text{2)Let } a_{1}=1 \text{ and }a_{n}=n(a_{n-1}+1)\ \ ...
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\text{1)Evaluate:} a)\lim_{n\rightarrow \infty}\frac{1}{2n}\log\binom{2n}{n} b)\lim_{n\rightarrow \infty}\left[\frac{1}{a+n}+\frac{1}{2a+n}+\cdots +\frac{1}{na+n}\right] \text{2)Let } a_{1}=1 \text{ and }a_{n}=n(a_{n-1}+1)\ \ ...
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\text{1)Evaluate:} a)\lim_{n\rightarrow \infty}\frac{1}{2n}\log\binom{2n}{n} b)\lim_{n\rightarrow \infty}\left[\frac{1}{a+n}+\frac{1}{2a+n}+\cdots +\frac{1}{na+n}\right] \text{2)Let } a_{1}=1 \text{ and }a_{n}=n(a_{n-1}+1)\ \ ...
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\text{1)Evaluate:} a)\lim_{n\rightarrow \infty}\frac{1}{2n}\log\binom{2n}{n} b)\lim_{n\rightarrow \infty}\left[\frac{1}{a+n}+\frac{1}{2a+n}+\cdots +\frac{1}{na+n}\right] \text{2)Let } a_{1}=1 \text{ and }a_{n}=n(a_{n-1}+1)\ \ ...
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\text{1)Evaluate:} a)\lim_{n\rightarrow \infty}\frac{1}{2n}\log\binom{2n}{n} b)\lim_{n\rightarrow \infty}\left[\frac{1}{a+n}+\frac{1}{2a+n}+\cdots +\frac{1}{na+n}\right] \text{2)Let } a_{1}=1 \text{ and }a_{n}=n(a_{n-1}+1)\ \ ...
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If each pair of the following three equations x2+ax+b=0, x2+cx+d=0, x2+ex+f=0 has exactly one root in common,then show that (a+c+e)2=4(ac+ce+ea-b-d-f). ...
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If 'a' is a complex number such that |a|=1.Find the values of a,so that equation az2+z+1=0 has one purely imaginary root. ...
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\hspace{-18}$All positive Integer ordered pairs $\bf{(x,y)}$ for which $\bf{\binom{x}{y} = 120}$ ...
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\hspace{-18}$All positive Integer ordered pairs $\bf{(x,y)}$ for which $\bf{\binom{x}{y} = 120}$ ...
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\hspace{-18}$Integer values of $\bf{x}$ for which $\bf{x^4+x^3+x^2+x+1}$ is a perfect square. ...
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What is the remainder 709! is divided by 719? ...
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Limn→ ∞ [ n2 . ∫ ( tan-1 nx)/( sin-1 nx) dx Integration upper limit:- ( 1/n ) Integration lower limit:- { (1+ n ) / n } ...
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\hspace{-16}$Determine all pairs $\bf{(a, b)}$ of natural numbers, for which the number\\\\ of $ \bf{a ^ 3 + 6ab + 1} $ and $ \bf{b ^ 3 + 6ab + 1}$ are cubes of natural numbers. ...
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if f(xy)=f(x)f(y) for all x and y and f(x)is continuous at x=1 ,prove that f(x)is continuous at all non zero x. ...
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Given a polynomial of n degree such that f(x)+f(1/x)=f(x)*f(1/x) Find the polynomial ...
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Given a polynomial of n degree such that f(x)+f(1/x)=f(x)*f(1/x) Find the polynomial ...
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Find remainder when 2013C101 is divided by 101 ...
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Show that infinete series Σ sin( 1/k ) is div? ...
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\hspace{-16}$Prove that for all Natural no. $\bf{k}$\\\\ $\bf{(k^3)!}$ is Divisible by $\bf{(k!)^{1+k+k^2}}$ any method other then Induction ...
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\hspace{-16}$If $\bf{\mathbb{A}=\frac{1}{2\sqrt{1}}+\frac{1}{3\sqrt{2}}+\frac{1}{4\sqrt{3}}+.........+\frac{1}{100\sqrt{99}}}$\\\\\\ Then $\bf{\lfloor \mathbb{A}\rfloor =}$ ...
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\hspace{-16}$If $\bf{x=\frac{\sqrt{10+\sqrt{1}}+\sqrt{10+\sqrt{2}}+\sqrt{10+\sqrt{3}}+.......+\sqrt{10+\sqrt{99}}}{\sqrt{10-\sqrt{1}}+\sqrt{10-\sqrt{2}}+\sqrt{10-\sqrt{3}}+.......+\sqrt{10-\sqrt{99}}}}$\\\\\\ Then value of $\ ...
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\hspace{-16}$If $\bf{a,b,c\in\mathbb{R}}$ and $\bf{f(x)}$ is a Quadratic Polynomial such that\\\\ $\bf{\begin{Bmatrix} \bf{f(a)=bc} \\\\ \bf{f(b)=ca} \\\\ \bf{f(c)=ab} \end{Bmatrix}}$\\\\\\ Then $\bf{f(a+b+c)=}$ I am Getting ...
