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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

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

Question Number 52273 Answers: 1 Comments: 0

A cuboid block is floating in a liquid with half of its volume immersed in the liquid.When the whole system accelerates upwards with an acceleration of g/3 . The fraction of volume immersed in the liquid will be a)1/2 b)3/8 c)2/3 d)3/4 please help

$${A}\:{cuboid}\:{block}\:{is}\:{floating}\:{in}\:{a} \\ $$$${liquid}\:{with}\:{half}\:{of}\:{its}\:{volume} \\ $$$${immersed}\:{in}\:{the}\:{liquid}.{When}\:{the} \\ $$$${whole}\:{system}\:{accelerates}\:{upwards} \\ $$$${with}\:{an}\:{acceleration}\:{of}\:{g}/\mathrm{3}\:.\:{The} \\ $$$${fraction}\:{of}\:{volume}\:{immersed}\:{in} \\ $$$${the}\:{liquid}\:{will}\:{be} \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left./\mathrm{2}\:{b}\right)\mathrm{3}/\mathrm{8}\:{c}\right)\mathrm{2}/\mathrm{3}\:{d}\right)\mathrm{3}/\mathrm{4} \\ $$$$ \\ $$$${please}\:{help} \\ $$

Question Number 52268 Answers: 0 Comments: 3