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Question Number 52421    Answers: 0   Comments: 2

Question Number 52418    Answers: 0   Comments: 1

find the value of ∫_0 ^∞ ((arctan(x))/(1+x^4 )) dx

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{4}} }\:{dx} \\ $$

Question Number 52412    Answers: 0   Comments: 3

Question Number 52409    Answers: 1   Comments: 1

Question Number 52406    Answers: 2   Comments: 0

Find the cube root of 26 + 5(√3)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{root}\:\mathrm{of}\:\:\:\:\:\mathrm{26}\:+\:\mathrm{5}\sqrt{\mathrm{3}} \\ $$

Question Number 52397    Answers: 0   Comments: 1

Question Number 52392    Answers: 0   Comments: 0

Question Number 52391    Answers: 1   Comments: 1

2299/(7x+20)=11 sir could you help me?

$$\mathrm{2299}/\left(\mathrm{7x}+\mathrm{20}\right)=\mathrm{11}\:\:\:\: \\ $$$$\mathrm{sir}\:\mathrm{could}\:\mathrm{you}\:\mathrm{help}\:\mathrm{me}? \\ $$

Question Number 52381    Answers: 2   Comments: 0

If all the words with or without meaning are written using the letters of the word QUEEN and are arranged as in English dictionary.What is the position of the word QUEEN? a)44th b)45th c)46th d)47th

$${If}\:{all}\:{the}\:{words}\:{with}\:{or}\:{without} \\ $$$${meaning}\:{are}\:{written}\:{using}\:{the} \\ $$$${letters}\:{of}\:{the}\:{word}\:{QUEEN}\:{and} \\ $$$${are}\:{arranged}\:{as}\:{in}\:{English} \\ $$$${dictionary}.{What}\:{is}\:{the}\:{position} \\ $$$${of}\:{the}\:{word}\:{QUEEN}? \\ $$$$\left.{a}\left.\right)\left.\mathrm{4}\left.\mathrm{4}{th}\:{b}\right)\mathrm{45}{th}\:{c}\right)\mathrm{46}{th}\:{d}\right)\mathrm{47}{th} \\ $$

Question Number 52379    Answers: 1   Comments: 0

The sum of the digits in the unit place of all four digit numbers formed using the numbers 3 4 5 andL 6 without repetition is a)432 b)108 c)36 d)18

$${The}\:{sum}\:{of}\:{the}\:{digits}\:{in}\:{the}\:{unit} \\ $$$${place}\:{of}\:{all}\:{four}\:{digit}\:{numbers} \\ $$$${formed}\:{using}\:{the}\:{numbers}\:\mathrm{3}\:\mathrm{4}\:\mathrm{5}\:{and}\mathscr{L} \\ $$$$\mathrm{6}\:{without}\:{repetition}\:{is} \\ $$$$\left.{a}\left.\right)\left.\mathrm{4}\left.\mathrm{32}\:{b}\right)\mathrm{108}\:{c}\right)\mathrm{36}\:{d}\right)\mathrm{18} \\ $$

Question Number 52377    Answers: 0   Comments: 3

An iceberg is floating in sea water. The density of ice is 0.92g/cm^3 and that of sea water is 1.02g/cm^3 . What % of ice will be below the water?

$${An}\:{iceberg}\:{is}\:{floating}\:{in}\:{sea}\:{water}. \\ $$$${The}\:{density}\:{of}\:{ice}\:{is}\:\mathrm{0}.\mathrm{92}{g}/{cm}^{\mathrm{3}} \\ $$$${and}\:{that}\:{of}\:{sea}\:{water}\:{is}\:\mathrm{1}.\mathrm{02}{g}/{cm}^{\mathrm{3}} . \\ $$$${What}\:\%\:{of}\:{ice}\:{will}\:\:{be}\:{below}\:{the} \\ $$$${water}? \\ $$

Question Number 52363    Answers: 2   Comments: 0

integrate ((sin^2 xcos^2 x )/(sin^3 x+cos^3 x))dx

$${integrate}\:\frac{\mathrm{sin}^{\mathrm{2}} {x}\mathrm{cos}^{\mathrm{2}} {x}\:}{{sin}^{\mathrm{3}} {x}+{cos}^{\mathrm{3}} {x}}{dx} \\ $$

Question Number 52360    Answers: 1   Comments: 1

Question Number 52356    Answers: 1   Comments: 8

Question Number 52349    Answers: 2   Comments: 3

Determine if the series converges or diverges. (i) Σ_(n = 2) ^∞ (1/(n^2 − 1)) (ii) Σ_(n = 1) ^∞ (1/3^(n − 1) )

$$\mathrm{Determine}\:\mathrm{if}\:\mathrm{the}\:\mathrm{series}\:\mathrm{converges}\:\mathrm{or}\:\mathrm{diverges}. \\ $$$$\:\:\:\left(\mathrm{i}\right)\:\:\:\:\underset{\mathrm{n}\:=\:\mathrm{2}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} \:−\:\mathrm{1}} \\ $$$$ \\ $$$$\:\:\:\left(\mathrm{ii}\right)\:\:\:\:\underset{\mathrm{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{n}\:−\:\mathrm{1}} } \\ $$$$\:\:\: \\ $$

Question Number 52341    Answers: 0   Comments: 0

A sound wave of velocity 350m/s is directed towards the surface of the water. If the ratio of the wavelength of sound in air to that in water 150 ratio 475.Calculate the velocity of the wave in water.

$${A}\:{sound}\:{wave}\:{of}\:{velocity}\:\mathrm{350}{m}/{s} \\ $$$${is}\:{directed}\:{towards}\:{the}\:{surface}\:{of} \\ $$$${the}\:{water}.\:{If}\:{the}\:{ratio}\:{of}\:{the} \\ $$$${wavelength}\:{of}\:{sound}\:{in}\:{air}\:{to}\:{that} \\ $$$${in}\:{water}\:\mathrm{150}\:{ratio}\:\mathrm{475}.{Calculate} \\ $$$${the}\:{velocity}\:{of}\:{the}\:{wave}\:{in}\:{water}. \\ $$

Question Number 52340    Answers: 1   Comments: 0

A 90cm uniform lever has a load of 30N suspended at 15cm from one of its ends.If the fulcrum is at the centre of gravity what is the force that must be applied to its other end to keep it in horizontal equilibrium?

$${A}\:\mathrm{90}{cm}\:{uniform}\:{lever}\:{has}\:{a}\:{load} \\ $$$${of}\:\mathrm{30}{N}\:{suspended}\:{at}\:\mathrm{15}{cm}\:{from} \\ $$$${one}\:{of}\:{its}\:{ends}.{If}\:{the}\:{fulcrum}\:{is}\:{at} \\ $$$${the}\:{centre}\:{of}\:{gravity}\:{what}\:{is}\:{the} \\ $$$${force}\:{that}\:{must}\:{be}\:{applied}\:{to}\:{its} \\ $$$${other}\:{end}\:{to}\:{keep}\:{it}\:{in}\:{horizontal} \\ $$$${equilibrium}? \\ $$

Question Number 52324    Answers: 1   Comments: 2

Two carnot emgines A and B are operated in series. engine A receiepved heat?from a reservoir at 600 K and rejects it to a reservoir at temp T. B receives heat rejected by A and in turn rejects it to reservoir at 100K. Find (η_B /η_A ) η efficiency

$$\mathrm{Two}\:\mathrm{carnot}\:\mathrm{emgines}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{operated}\:\mathrm{in} \\ $$$$\mathrm{series}.\:\mathrm{engine}\:\mathrm{A}\:\mathrm{receiepved}\:\mathrm{heat}?\mathrm{from} \\ $$$$\mathrm{a}\:\mathrm{reservoir}\:\mathrm{at}\:\mathrm{600}\:\mathrm{K}\:\mathrm{and}\:\mathrm{rejects}\:\mathrm{it}\:\mathrm{to} \\ $$$$\mathrm{a}\:\mathrm{reservoir}\:\mathrm{at}\:\mathrm{temp}\:\mathrm{T}.\:\mathrm{B}\:\mathrm{receives} \\ $$$$\mathrm{heat}\:\mathrm{rejected}\:\mathrm{by}\:\mathrm{A}\:\mathrm{and}\:\mathrm{in}\:\mathrm{turn}\:\mathrm{rejects} \\ $$$$\mathrm{it}\:\mathrm{to}\:\mathrm{reservoir}\:\mathrm{at}\:\mathrm{100K}. \\ $$$$\mathrm{Find}\:\frac{\eta_{{B}} }{\eta_{{A}} } \\ $$$$\eta\:\mathrm{efficiency} \\ $$

Question Number 52321    Answers: 0   Comments: 0

Question Number 52305    Answers: 1   Comments: 1

calculate Σ_(n=1) ^∞ (((−1)^n )/(n(4n^2 −1)))

$${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}\left(\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}\right)} \\ $$

Question Number 52299    Answers: 0   Comments: 0

Question Number 52312    Answers: 1   Comments: 3

Question Number 52282    Answers: 1   Comments: 7

Find the range of values of x ∣((x − 1)/(2x))∣ ≥ x^2 + 1

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:\:\mathrm{x} \\ $$$$\:\:\:\mid\frac{\mathrm{x}\:−\:\mathrm{1}}{\mathrm{2x}}\mid\:\geqslant\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1} \\ $$

Question Number 52278    Answers: 2   Comments: 0

8 digit numbers are formed using 1 1 2 2 2 3 4 4. The number of such numbers in which the odd digits do not occupy odd places is a)160 b)120 c)60 d)48

$$\mathrm{8}\:{digit}\:{numbers}\:{are}\:{formed}\:{using} \\ $$$$\mathrm{1}\:\mathrm{1}\:\mathrm{2}\:\mathrm{2}\:\mathrm{2}\:\mathrm{3}\:\mathrm{4}\:\mathrm{4}.\:{The}\:{number}\:{of}\:{such} \\ $$$${numbers}\:{in}\:{which}\:{the}\:{odd}\:{digits} \\ $$$${do}\:{not}\:{occupy}\:{odd}\:{places}\:{is} \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left.\mathrm{60}\:{b}\right)\mathrm{120}\:{c}\right)\mathrm{60}\:{d}\right)\mathrm{48} \\ $$

Question Number 52275    Answers: 0   Comments: 0

Question Number 52276    Answers: 1   Comments: 0

An 8 digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is? a)72(7i) b)18(7i) c)40(7i) d)36(7i) please I mean factorial by i.The part of my screen where the factorial symbol is isnt functioning.Thanks

$${An}\:\mathrm{8}\:{digit}\:{number}\:{divisible}\:{by}\:\mathrm{9}\:{is} \\ $$$${to}\:{be}\:{formed}\:{using}\:{digits}\:{from} \\ $$$$\mathrm{0}\:{to}\:\mathrm{9}\:{without}\:{repeating}\:{the}\:{digits}. \\ $$$${The}\:{number}\:{of}\:{ways}\:{in}\:{which}\:{this} \\ $$$${can}\:{be}\:{done}\:{is}? \\ $$$$\left.{a}\left.\right)\left.\mathrm{7}\left.\mathrm{2}\left(\mathrm{7}{i}\right)\:{b}\right)\mathrm{18}\left(\mathrm{7}{i}\right)\:{c}\right)\mathrm{40}\left(\mathrm{7}{i}\right)\:{d}\right)\mathrm{36}\left(\mathrm{7}{i}\right) \\ $$$$ \\ $$$${please}\:{I}\:{mean}\:\boldsymbol{{factorial}}\:{by}\:{i}.{The} \\ $$$${part}\:{of}\:{my}\:{screen}\:{where}\:{the}\:{factorial} \\ $$$${symbol}\:{is}\:{isnt}\:{functioning}.{Thanks} \\ $$

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