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Question Number 90223 Answers: 0 Comments: 0

The number of ways in which 12 books can be put in 3 shelves, 4 on each, is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which}\:\mathrm{12}\:\mathrm{books} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{put}\:\mathrm{in}\:\mathrm{3}\:\mathrm{shelves},\:\mathrm{4}\:\mathrm{on}\:\mathrm{each},\:\mathrm{is} \\ $$

Question Number 90222 Answers: 0 Comments: 1

Question Number 90220 Answers: 0 Comments: 0

The number of ways in which 8 distinct toys can be distributed among 5 children is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which}\:\mathrm{8}\:\mathrm{distinct} \\ $$$$\mathrm{toys}\:\mathrm{can}\:\mathrm{be}\:\mathrm{distributed}\:\mathrm{among}\:\mathrm{5}\: \\ $$$$\mathrm{children}\:\mathrm{is} \\ $$

Question Number 90221 Answers: 0 Comments: 0

There are 3 copies each of 4 different books. The number of ways in which in which they can be arranged in a shelf is

$$\mathrm{There}\:\mathrm{are}\:\mathrm{3}\:\mathrm{copies}\:\mathrm{each}\:\mathrm{of}\:\mathrm{4}\:\mathrm{different} \\ $$$$\mathrm{books}.\:\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which} \\ $$$$\mathrm{in}\:\mathrm{which}\:\mathrm{they}\:\mathrm{can}\:\mathrm{be}\:\mathrm{arranged}\:\mathrm{in}\:\mathrm{a}\: \\ $$$$\mathrm{shelf}\:\mathrm{is} \\ $$

Question Number 90217 Answers: 0 Comments: 2

let x_(n ) be a sequence with x_0 =2 and x_1 =7 and x_(n+1) =7x_n −12x_(n−1) . Find the general term of x_n .

$${let}\:{x}_{{n}\:} \:{be}\:{a}\:{sequence}\:{with}\:{x}_{\mathrm{0}} =\mathrm{2}\:{and}\:{x}_{\mathrm{1}} =\mathrm{7} \\ $$$${and}\:{x}_{{n}+\mathrm{1}} =\mathrm{7}{x}_{{n}} −\mathrm{12}{x}_{{n}−\mathrm{1}} . \\ $$$${Find}\:{the}\:{general}\:{term}\:{of}\:{x}_{{n}} . \\ $$

Question Number 90212 Answers: 0 Comments: 4

if x^2 = 5x+1 find E = (((x^3 −140) (x^(11) )^(1/(3 )) )/((x^4 +1))^(1/(3 )) )

$${if}\:{x}^{\mathrm{2}} \:=\:\mathrm{5}{x}+\mathrm{1}\: \\ $$$${find}\:{E}\:=\:\frac{\left({x}^{\mathrm{3}} −\mathrm{140}\right)\:\sqrt[{\mathrm{3}\:\:}]{{x}^{\mathrm{11}} }}{\sqrt[{\mathrm{3}\:\:}]{{x}^{\mathrm{4}} +\mathrm{1}}} \\ $$

Question Number 90210 Answers: 1 Comments: 1

lim_(x→(π/3)) (((1−2cos (x))/(π−3x)))=?

$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{3}}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}−\mathrm{2cos}\:\left({x}\right)}{\pi−\mathrm{3}{x}}\right)=? \\ $$

Question Number 90208 Answers: 0 Comments: 0

Question Number 90200 Answers: 0 Comments: 7

26≡R_1 [37] 1 ≡R_2 [3] 2≡R_3 [5] Find R_1 , R_2 and R_3

$$\mathrm{26}\equiv\mathrm{R}_{\mathrm{1}} \left[\mathrm{37}\right] \\ $$$$\mathrm{1}\:\:\equiv\mathrm{R}_{\mathrm{2}} \left[\mathrm{3}\right] \\ $$$$\mathrm{2}\equiv\mathrm{R}_{\mathrm{3}} \left[\mathrm{5}\right] \\ $$$$\mathrm{Find}\:\mathrm{R}_{\mathrm{1}} ,\:\mathrm{R}_{\mathrm{2}} \mathrm{and}\:\mathrm{R}_{\mathrm{3}} \\ $$

Question Number 90198 Answers: 3 Comments: 3

∫sin(dx)

$$\int{sin}\left({dx}\right)\: \\ $$

Question Number 90195 Answers: 0 Comments: 0

Question Number 90194 Answers: 1 Comments: 0

(x^2 /(x+a))+(√x)=a (a∈R) solve for: x .

$$\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{a}}}+\sqrt{\boldsymbol{\mathrm{x}}}=\boldsymbol{\mathrm{a}}\:\:\:\:\:\left(\boldsymbol{\mathrm{a}}\in\boldsymbol{\mathrm{R}}\right) \\ $$$$\mathrm{solve}\:\mathrm{for}:\:\:\mathrm{x}\:\:. \\ $$

Question Number 90196 Answers: 0 Comments: 0

A bag contains 5 balls, 2 green and 3red They are selected without replacement till the remaining balls in the bag are of same colours. Let the random variable X be the number of selections possible 1) Determine the set of values of X 2)Determine the it′s expectation, its variance and its standard deviation.

$$\mathrm{A}\:\mathrm{bag}\:\mathrm{contains}\:\mathrm{5}\:\mathrm{balls},\:\mathrm{2}\:\mathrm{green}\:\mathrm{and}\:\mathrm{3red} \\ $$$$\mathrm{They}\:\mathrm{are}\:\mathrm{selected}\:\mathrm{without}\:\mathrm{replacement}\:\mathrm{till} \\ $$$$\mathrm{the}\:\mathrm{remaining}\:\mathrm{balls}\:\mathrm{in}\:\mathrm{the}\:\mathrm{bag}\:\mathrm{are}\:\mathrm{of}\:\mathrm{same}\:\mathrm{colours}. \\ $$$$\mathrm{Let}\:\mathrm{the}\:\mathrm{random}\:\mathrm{variable}\:\mathrm{X}\:\mathrm{be}\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{selections}\:\mathrm{possible} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:\mathrm{X} \\ $$$$\left.\mathrm{2}\right)\mathrm{Determine}\:\mathrm{the}\:\mathrm{it}'\mathrm{s}\:\mathrm{expectation},\:\mathrm{its}\:\mathrm{variance} \\ $$$$\mathrm{and}\:\mathrm{its}\:\mathrm{standard}\:\mathrm{deviation}. \\ $$

Question Number 90192 Answers: 1 Comments: 1

∫_0 ^(infinity) (((1−e^(−x) )cosx dx)/x)

$$\int_{\mathrm{0}} ^{\mathrm{infinity}} \frac{\left(\mathrm{1}−\mathrm{e}^{−\mathrm{x}} \right)\mathrm{cosx}\:\mathrm{dx}}{\mathrm{x}} \\ $$

Question Number 90178 Answers: 1 Comments: 1

Question Number 90171 Answers: 2 Comments: 0

find ∫_0 ^2 (⌊x^2 ⌋+⌊x⌋^2 )dx

$${find}\:\int_{\mathrm{0}} ^{\mathrm{2}} \left(\lfloor{x}^{\mathrm{2}} \rfloor+\lfloor{x}\rfloor^{\mathrm{2}} \right){dx} \\ $$

Question Number 90168 Answers: 1 Comments: 4

Question Number 90158 Answers: 1 Comments: 2

Question Number 90157 Answers: 0 Comments: 0

Question Number 90151 Answers: 1 Comments: 1

find the limit of lim (1/(t((√(1+t))))−(1/t) t→0

$${find}\:{the}\:{limit}\:{of}\: \\ $$$${lim}\:\:\frac{\mathrm{1}}{{t}\left(\sqrt{\mathrm{1}+{t}}\right.}−\frac{\mathrm{1}}{{t}} \\ $$$${t}\rightarrow\mathrm{0} \\ $$

Question Number 90148 Answers: 0 Comments: 1

Question Number 90139 Answers: 0 Comments: 3

x = 2021^3 −2019^3 (√((x−2)/6)) = ?

$$\mathrm{x}\:=\:\mathrm{2021}^{\mathrm{3}} −\mathrm{2019}^{\mathrm{3}} \\ $$$$\sqrt{\frac{\mathrm{x}−\mathrm{2}}{\mathrm{6}}}\:=\:? \\ $$

Question Number 90138 Answers: 0 Comments: 2

∫x(√(3x^3 +7)) dx

$$\int{x}\sqrt{\mathrm{3}{x}^{\mathrm{3}} +\mathrm{7}}\:{dx} \\ $$

Question Number 90135 Answers: 1 Comments: 0

I_n =∫_(t=0) ^(+∞) (dt/((t+1)(t+2)...(t+n)))

$$\mathrm{I}_{\mathrm{n}} =\int_{\mathrm{t}=\mathrm{0}} ^{+\infty} \frac{\mathrm{dt}}{\left(\mathrm{t}+\mathrm{1}\right)\left(\mathrm{t}+\mathrm{2}\right)...\left(\mathrm{t}+\mathrm{n}\right)} \\ $$

Question Number 90134 Answers: 0 Comments: 0

Question Number 90122 Answers: 0 Comments: 1

each vertex of a cube is to be labeled with an integer 1 through 8 , with each integer being used once,in such a way that the sum of the four numbers on the vertices of a face is the same for each face.Arrangements that can be obtained from each other through rotations of the cube are considered to be the same. Find all the arrangements

$${each}\:{vertex}\:{of}\:{a}\:{cube}\:{is}\:{to}\:{be}\:{labeled} \\ $$$${with}\:{an}\:{integer}\:\mathrm{1}\:{through}\:\mathrm{8}\:,\:{with} \\ $$$${each}\:{integer}\:{being}\:{used}\:{once},{in}\:{such} \\ $$$${a}\:{way}\:{that}\:{the}\:{sum}\:{of}\:{the}\:{four}\:{numbers} \\ $$$${on}\:{the}\:{vertices}\:{of}\:{a}\:{face}\:{is}\:{the}\:{same}\: \\ $$$${for}\:{each}\:{face}.{Arrangements}\:{that}\:{can} \\ $$$${be}\:{obtained}\:{from}\:{each}\:{other}\:{through} \\ $$$${rotations}\:{of}\:{the}\:{cube}\:{are}\:{considered} \\ $$$${to}\:{be}\:{the}\:{same}.\: \\ $$$${Find}\:{all}\:{the}\:{arrangements} \\ $$$$ \\ $$$$ \\ $$

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