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*Image* ...
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Normal at 3 points P,Q,R of parabola y^2=4x meet at A and SP\cdot SQ\cdot SR=\alpha SA^2 . If S is the focus of the parabola find the value of \alpha . ...
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In a \Delta ABC , let x=\tan\left(\frac{B-C}{2}\right)\tan\left(\frac{A}{2}\right) y =\tan\left(\frac{C-A}{2}\right)\tan\left(\frac{B}{2}\right) z =\tan\left(\frac{A-B}{2}\right)\tan\left(\frac{C}{2}\right) Prove that x+y+z+x ...
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The exponential function ex is strolling along the road insulting the functions he sees walking by. He scoffs at a wandering polynomial for the shortness of its Taylor series. He snickers at a passing smooth function of compa ...
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My friend gave me this question.. For n\ge2 Prove that 1 - \frac{1}{2}+\frac{1}{3} - ... \pm \frac{1}{n} is not an integer. ...
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Let I_n=\int \frac{dx}{(a+\sin{x})^n} Find the relations between I_n,I_{n+1}\ \text{and}\ I_{n+2} ...
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Prove that x9999+x8888+x7777+.....+x1111+1 is divisible by x+1 ...
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Prove that for all n\ge1 , 1+5^n+5^{2n}+5^{3n}+5^{4n} is composite ...
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Prove that there are infinitely many primes congruent to 9 mod 10. ...
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Let A be the sum of the digits of the number 4444^{4444} , and B the sum of the digits of A. Compute the sum of the digits of B. ...
