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If a and b are +ve integers.......find the probabilty that \frac{1}{2}(a^{2}+b^{2}) is a +ve integer ...
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if sinα ,sinβ,sinγ are in AP and cosα,cosβ,cosγ are in gp then find the value of \frac{cos^{2}\alpha +cos^{2}\gamma -4cos(\alpha)cos(\gamma ) }{1-sin(\alpha )sin(\gamma) } ...
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\lim_{n\rightarrow \infty }\prod_{r=2}^{r=n}{\frac{r^{3}-1}{r^{3}+1}} ...
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let x and y be two numbers chosen at random from set {1,2,3......n}with replacement.let Qn(p) denote probability that (xp-1 -yp-1) is divisible by p then find Qn(p) in terms of p and n and find Q25(3) ...
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how to do this q using congruences find the remainder wen 32n+2-8n-9 is divided by 64? i know the procedure by binomial ...
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let f(x)=x^{3}+x^{2}+100x+7sinx then the eq \frac{1}{y-f(1)}+ \frac{2}{y-f(2)}+ \frac{3}{y-f(3)}=0 has 1)exactly one root lying in (f(1),f(2)) 2)booth roots lying in (f(2),f(3)) 3)exactly one root lying in (-∞,f(1)) 4)exact ...
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if the squares of a 8x8 chess board are painted either red or black at random 1)the probability taht not all squares in any column are allternating in color 3)the probability that all the squares in any column are of same col ...
