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Question Number 179906 Answers: 2 Comments: 0

2 boxes, 1st contains 4 white & 6 black balls 2nd box contains 8 white & 8 black balls We randomly draw a ball, got a black one What′s probability that it was drawn from Box_2 ?

$$\mathrm{2}\:{boxes},\:\mathrm{1}{st}\:{contains}\:\mathrm{4}\:{white}\:\&\:\mathrm{6}\:{black}\:{balls} \\ $$$$\:\mathrm{2}{nd}\:{box}\:{contains}\:\mathrm{8}\:{white}\:\&\:\mathrm{8}\:{black}\:{balls} \\ $$$$\:{We}\:{randomly}\:{draw}\:{a}\:{ball},\:{got}\:{a}\:{black}\:{one} \\ $$$$\:{What}'{s}\:{probability}\:{that}\:{it}\:{was}\:{drawn}\:{from}\:{Box}_{\mathrm{2}} ? \\ $$

Question Number 179900 Answers: 1 Comments: 0

Prove that: f = 5x^4 + 35x^3 + 28x^2 + 14x + 7 is irreducible in Q[x]

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{f}\:=\:\mathrm{5x}^{\mathrm{4}} \:+\:\mathrm{35x}^{\mathrm{3}} \:+\:\mathrm{28x}^{\mathrm{2}} \:+\:\mathrm{14x}\:+\:\mathrm{7}\:\:\mathrm{is}\:\mathrm{irreducible}\:\mathrm{in}\:\:\mathrm{Q}\left[\mathrm{x}\right] \\ $$

Question Number 179890 Answers: 3 Comments: 1

p(x)=(1−x)(1+2x)(1−3x)....(1−15x) find the coefficient of the x^3 term in the expansion.

$${p}\left({x}\right)=\left(\mathrm{1}−{x}\right)\left(\mathrm{1}+\mathrm{2}{x}\right)\left(\mathrm{1}−\mathrm{3}{x}\right)....\left(\mathrm{1}−\mathrm{15}{x}\right) \\ $$$$ \\ $$$${find}\:{the}\:{coefficient}\:{of}\:{the}\:{x}^{\mathrm{3}} \:{term} \\ $$$${in}\:{the}\:{expansion}. \\ $$

Question Number 179886 Answers: 0 Comments: 5

Question Number 179879 Answers: 0 Comments: 0

Question Number 179862 Answers: 2 Comments: 2

Question Number 179857 Answers: 0 Comments: 1

Question Number 179853 Answers: 1 Comments: 2

∫((xdx)/((x−1)(x−2)))

$$\int\frac{\boldsymbol{{xdx}}}{\left(\boldsymbol{{x}}−\mathrm{1}\right)\left(\boldsymbol{{x}}−\mathrm{2}\right)} \\ $$

Question Number 179852 Answers: 0 Comments: 4

prove ∫_0 ^(𝛑/2) log(sinx)dx=(π/2)log(1/2)

$$\boldsymbol{{prove}}\:\:\:\:\:\int_{\mathrm{0}} ^{\frac{\boldsymbol{\pi}}{\mathrm{2}}} \boldsymbol{{log}}\left(\boldsymbol{{sinx}}\right)\boldsymbol{{dx}}=\frac{\pi}{\mathrm{2}}\boldsymbol{{log}}\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 179848 Answers: 0 Comments: 1

In how many years ,Rs 50000 amounts to Rs672720 at compounded annually if the interest rate is 1 paisa per rupee per month?

$$ \\ $$$$\:\:\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{years}\:,\mathrm{Rs}\:\mathrm{50000}\:\mathrm{amounts}\:\mathrm{to}\:\mathrm{Rs672720} \\ $$$$\mathrm{at}\:\mathrm{compounded}\:\mathrm{annually}\:\mathrm{if}\:\mathrm{the}\:\mathrm{interest}\:\mathrm{rate}\:\mathrm{is}\:\mathrm{1}\:\mathrm{paisa}\:\mathrm{per} \\ $$$$\mathrm{rupee}\:\mathrm{per}\:\mathrm{month}? \\ $$

Question Number 179844 Answers: 1 Comments: 0

∫^1 _0 ((x−1)/((x+1)lnx))dx=?

$$\underset{\mathrm{0}} {\int}^{\mathrm{1}} \:\frac{{x}−\mathrm{1}}{\left({x}+\mathrm{1}\right){lnx}}{dx}=? \\ $$

Question Number 179829 Answers: 1 Comments: 1

Question Number 179819 Answers: 1 Comments: 0

x+y+z=2 x+2y−z=4 2x+y−2z=2

$${x}+{y}+{z}=\mathrm{2} \\ $$$${x}+\mathrm{2}{y}−{z}=\mathrm{4} \\ $$$$\mathrm{2}{x}+{y}−\mathrm{2}{z}=\mathrm{2} \\ $$$$ \\ $$

Question Number 179818 Answers: 4 Comments: 0

in how many ways can you distribute 20 different books to 5 students such that each student gets at least 2 books?

$${in}\:{how}\:{many}\:{ways}\:{can}\:{you}\:{distribute} \\ $$$$\mathrm{20}\:{different}\:{books}\:{to}\:\mathrm{5}\:{students}\:{such} \\ $$$${that}\:{each}\:{student}\:{gets}\:{at}\:{least}\:\mathrm{2}\:{books}? \\ $$

Question Number 179811 Answers: 1 Comments: 4

Question Number 179869 Answers: 0 Comments: 5

Question Number 179799 Answers: 2 Comments: 0

Question Number 179781 Answers: 2 Comments: 8

Question Number 179777 Answers: 1 Comments: 0

p(x)=(1−x)(1+2x)(1−3x)....(1+14x)(1−15x) the absolute value of the coefficient of the x^2 in the expression?

$${p}\left({x}\right)=\left(\mathrm{1}−{x}\right)\left(\mathrm{1}+\mathrm{2}{x}\right)\left(\mathrm{1}−\mathrm{3}{x}\right)....\left(\mathrm{1}+\mathrm{14}{x}\right)\left(\mathrm{1}−\mathrm{15}{x}\right) \\ $$$$ \\ $$$${the}\:{absolute}\:{value}\:{of}\:{the}\:{coefficient}\:{of}\:{the}\:{x}^{\mathrm{2}} \:{in}\:{the}\:{expression}? \\ $$

Question Number 179775 Answers: 4 Comments: 0

(122−a)^2 = (123−a)^2

$$\:\left(\mathrm{122}−{a}\right)^{\mathrm{2}} =\:\left(\mathrm{123}−{a}\right)^{\mathrm{2}} \\ $$

Question Number 179773 Answers: 1 Comments: 1

What′s the sum of the odd numbers between 2313 and 4718

$${What}'{s}\:{the}\:{sum}\:{of}\:{the}\:{odd}\:{numbers} \\ $$$$\:{between}\:\mathrm{2313}\:{and}\:\mathrm{4718} \\ $$

Question Number 179948 Answers: 2 Comments: 3

20 students should stand in 5 different rows. each row should have at least 2 students. in how many ways can you arrange them? (an unsolved old question)

$$\mathrm{20}\:{students}\:{should}\:{stand}\:{in}\:\mathrm{5} \\ $$$${different}\:{rows}.\:{each}\:{row}\:{should}\:{have} \\ $$$${at}\:{least}\:\mathrm{2}\:{students}.\:{in}\:{how}\:{many}\:{ways} \\ $$$${can}\:{you}\:{arrange}\:{them}? \\ $$$$\left({an}\:{unsolved}\:{old}\:{question}\right) \\ $$

Question Number 179752 Answers: 2 Comments: 2

Question Number 179749 Answers: 0 Comments: 0

Question Number 179741 Answers: 0 Comments: 0

prove that ∫_0 ^( ∞ ) (( (√x))/(1 +7x^( 2) + x^( 4) )) dx = (π/( (√( 90))))

$$ \\ $$$$\:\:\:\:\:{prove}\:\:{that} \\ $$$$ \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\infty\:} \frac{\:\sqrt{{x}}}{\mathrm{1}\:+\mathrm{7}{x}^{\:\mathrm{2}} \:+\:{x}^{\:\mathrm{4}} }\:{dx}\:=\:\frac{\pi}{\:\sqrt{\:\mathrm{90}}}\:\: \\ $$$$ \\ $$

Question Number 179738 Answers: 2 Comments: 0

Number of distributions of 12 different things be taken to 3different boxes so as 1)5 things in 1st box exactly 2)5 things in any one box?

$${Number}\:{of}\:{distributions}\:{of} \\ $$$$\mathrm{12}\:{different}\:{things}\:{be}\:{taken}\:{to} \\ $$$$\mathrm{3}{different}\:{boxes}\:{so}\:{as} \\ $$$$\left.\mathrm{1}\right)\mathrm{5}\:{things}\:{in}\:\mathrm{1}{st}\:{box}\:{exactly} \\ $$$$\left.\mathrm{2}\right)\mathrm{5}\:{things}\:{in}\:{any}\:{one}\:{box}? \\ $$

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