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Question Number 50330 Answers: 1 Comments: 1

Question Number 50299 Answers: 1 Comments: 7

please help me solve these two questions 1. A magician cuts a rope into two parts at a point selected at random. what is the probability that the length of the longer rope is at least 8 times the length of the shorter rope. 2. find the sum of co−efficient of thebinomial expansion of (4x−1)^(16)

$${please}\:{help}\:{me}\:{solve}\:{these}\:{two} \\ $$$${questions}\: \\ $$$$\mathrm{1}.\:{A}\:{magician}\:{cuts}\:{a}\:{rope}\:{into}\:{two}\: \\ $$$$\:\:{parts}\:{at}\:{a}\:{point}\:{selected}\:{at}\: \\ $$$${random}.\:{what}\:{is}\:{the}\:{probability}\:{that} \\ $$$${the}\:{length}\:{of}\:\:{the}\:{longer}\:\:{rope}\:{is}\:{at}\:{least}\: \\ $$$$\mathrm{8}\:{times}\:{the}\:{length}\:{of}\:{the}\:{shorter}\: \\ $$$${rope}. \\ $$$$\mathrm{2}.\:{find}\:{the}\:{sum}\:{of}\:{co}−{efficient}\:{of}\: \\ $$$${thebinomial}\:\:{expansion}\:\:{of}\:\: \\ $$$$\left(\mathrm{4}{x}−\mathrm{1}\right)^{\mathrm{16}} \\ $$$$ \\ $$

Question Number 50293 Answers: 2 Comments: 4

lim_(x→0) Σ_(r=1) ^(2n) ((1/(r+n)))=? please help

$${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\:\underset{{r}=\mathrm{1}} {\overset{\mathrm{2}{n}} {\sum}}\left(\frac{\mathrm{1}}{{r}+{n}}\right)=? \\ $$$${please}\:{help} \\ $$

Question Number 50279 Answers: 2 Comments: 0

{ ((x+y=6)),((y+z=10)) :} (x,y,z>0)

$$\begin{cases}{\mathrm{x}+\mathrm{y}=\mathrm{6}}\\{\mathrm{y}+\mathrm{z}=\mathrm{10}}\end{cases}\:\:\left(\mathrm{x},\mathrm{y},\mathrm{z}>\mathrm{0}\right) \\ $$

Question Number 50278 Answers: 1 Comments: 6

(√(a+(√(a−x)))) + (√(a−(√(a+x)))) = 2x please i beg u guys please solve this question

$$\sqrt{\mathrm{a}+\sqrt{\mathrm{a}−\mathrm{x}}}\:+\:\sqrt{\mathrm{a}−\sqrt{\mathrm{a}+\mathrm{x}}}\:=\:\mathrm{2x} \\ $$$$\mathrm{please}\:\mathrm{i}\:\mathrm{beg}\:\mathrm{u}\:\mathrm{guys}\: \\ $$$$\mathrm{please}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{question} \\ $$

Question Number 50275 Answers: 1 Comments: 0

Question Number 50274 Answers: 2 Comments: 0

Question Number 50258 Answers: 1 Comments: 0

A delegation of 4 students is to be selected from a total of 12 students. In how many ways can the delegation be selected if: 1) 2 particular students wish to be included together only in the delegation? 2) 2 particular students refuse to be together and 2 other particular students wish to be together only in the delegation?

$${A}\:{delegation}\:{of}\:\mathrm{4}\:{students}\:{is}\:{to}\:{be} \\ $$$${selected}\:{from}\:{a}\:{total}\:{of}\:\mathrm{12}\:{students}. \\ $$$${In}\:{how}\:{many}\:{ways}\:{can}\:{the}\:{delegation} \\ $$$${be}\:{selected}\:{if}: \\ $$$$\left.\mathrm{1}\right)\:\mathrm{2}\:{particular}\:{students}\:{wish}\:{to}\:{be}\: \\ $$$${included}\:{together}\:{only}\:{in}\:{the}\:{delegation}? \\ $$$$\left.\mathrm{2}\right)\:\mathrm{2}\:{particular}\:{students}\:{refuse}\:{to}\:{be}\: \\ $$$${together}\:{and}\:\mathrm{2}\:{other}\:{particular}\:{students} \\ $$$${wish}\:{to}\:{be}\:{together}\:{only}\:{in}\:{the}\:{delegation}? \\ $$

Question Number 50257 Answers: 1 Comments: 0

Question Number 50248 Answers: 1 Comments: 0

Question Number 50228 Answers: 0 Comments: 3

Question Number 50226 Answers: 0 Comments: 1

Three prizes are awarded each for getting more than 80%marks, 98% attendance and good behaviour in the college.In how many ways the prozes can be awarded if 15 student of the college are eligible for the three prizes?

$$\mathrm{Three}\:\mathrm{prizes}\:\mathrm{are}\:\mathrm{awarded}\:\mathrm{each}\:\mathrm{for} \\ $$$$\mathrm{getting}\:\mathrm{more}\:\mathrm{than}\:\mathrm{80\%marks}, \\ $$$$\mathrm{98\%}\:\mathrm{attendance}\:\mathrm{and}\:\mathrm{good} \\ $$$$\mathrm{behaviour}\:\mathrm{in}\:\mathrm{the}\:\mathrm{college}.\mathrm{In}\:\mathrm{how} \\ $$$$\mathrm{many}\:\mathrm{ways}\:\mathrm{the}\:\mathrm{prozes}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{awarded}\:\mathrm{if}\:\mathrm{15}\:\mathrm{student}\:\mathrm{of}\:\mathrm{the}\:\mathrm{college} \\ $$$$\mathrm{are}\:\mathrm{eligible}\:\mathrm{for}\:\mathrm{the}\:\mathrm{three}\:\mathrm{prizes}? \\ $$

Question Number 50220 Answers: 0 Comments: 4