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Question Number 12305    Answers: 1   Comments: 0

If c>0 and 4a+c<2b,then ax^2 −bx+c=0 has a root in which intervals? (a) (0,2) (b) (2,3) (c) (3,4) (d) (−2,0)

$${If}\:{c}>\mathrm{0}\:{and}\:\mathrm{4}{a}+{c}<\mathrm{2}{b},{then} \\ $$$${ax}^{\mathrm{2}} −{bx}+{c}=\mathrm{0}\:{has}\:{a}\:{root}\:{in}\:{which} \\ $$$${intervals}? \\ $$$$\left({a}\right)\:\:\left(\mathrm{0},\mathrm{2}\right) \\ $$$$\left({b}\right)\:\:\left(\mathrm{2},\mathrm{3}\right) \\ $$$$\left({c}\right)\:\:\left(\mathrm{3},\mathrm{4}\right) \\ $$$$\left({d}\right)\:\:\left(−\mathrm{2},\mathrm{0}\right) \\ $$

Question Number 12304    Answers: 1   Comments: 0

How many geometric progressions is/are possible contauning 27,8 and 12 as three of its/their terms? (a) 1 (b) 2 (c) 4 (d) infinitely many

$${How}\:{many}\:{geometric}\:{progressions} \\ $$$${is}/{are}\:{possible}\:{contauning}\:\mathrm{27},\mathrm{8} \\ $$$${and}\:\mathrm{12}\:{as}\:{three}\:{of}\:{its}/{their}\:{terms}? \\ $$$$\left({a}\right)\:\:\mathrm{1} \\ $$$$\left({b}\right)\:\:\mathrm{2} \\ $$$$\left({c}\right)\:\:\mathrm{4} \\ $$$$\left({d}\right)\:\:{infinitely}\:{many} \\ $$$$ \\ $$

Question Number 12207    Answers: 0   Comments: 0

Multi−point ∮(x)=x^3 well be equal to the values of the function ant its harvest.

$$\boldsymbol{\mathrm{Multi}}−\boldsymbol{\mathrm{point}}\:\:\:\oint\left(\boldsymbol{\mathrm{x}}\right)=\boldsymbol{\mathrm{x}}^{\mathrm{3}} \:\:\boldsymbol{\mathrm{well}}\:\boldsymbol{\mathrm{be}} \\ $$$$\boldsymbol{\mathrm{equal}}\:\:\boldsymbol{\mathrm{to}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{values}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{function}} \\ $$$$\boldsymbol{\mathrm{ant}}\:\:\boldsymbol{\mathrm{its}}\:\:\boldsymbol{\mathrm{harvest}}. \\ $$

Question Number 12077    Answers: 1   Comments: 0

A man travels 29 km on an open road at a certain speed. In the city, he reduce his speed by 420 km/hr, and he find that he take him the same time to cover 15 km, Find his average speed. (a) On the open road (b) In the city

$$\mathrm{A}\:\mathrm{man}\:\mathrm{travels}\:\mathrm{29}\:\mathrm{km}\:\mathrm{on}\:\mathrm{an}\:\mathrm{open}\:\mathrm{road}\:\mathrm{at}\:\mathrm{a}\:\mathrm{certain}\:\mathrm{speed}.\:\mathrm{In}\:\mathrm{the}\:\mathrm{city},\:\mathrm{he}\: \\ $$$$\mathrm{reduce}\:\mathrm{his}\:\mathrm{speed}\:\mathrm{by}\:\mathrm{420}\:\mathrm{km}/\mathrm{hr},\:\mathrm{and}\:\mathrm{he}\:\mathrm{find}\:\mathrm{that}\:\mathrm{he}\:\mathrm{take}\:\mathrm{him}\:\mathrm{the}\:\mathrm{same}\:\mathrm{time} \\ $$$$\mathrm{to}\:\mathrm{cover}\:\mathrm{15}\:\mathrm{km},\:\mathrm{Find}\:\mathrm{his}\:\mathrm{average}\:\mathrm{speed}.\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{On}\:\mathrm{the}\:\mathrm{open}\:\mathrm{road} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{In}\:\mathrm{the}\:\mathrm{city} \\ $$

Question Number 12064    Answers: 0   Comments: 0

A heat pump gas C.P = 3, while the indoor temperature is 27°C and the outdoor temperature is 8°C. How much work per hour is required to pump 3.07 J of heat per hour into the individual unit of 10^5 J.

$$\mathrm{A}\:\mathrm{heat}\:\mathrm{pump}\:\mathrm{gas}\:\mathrm{C}.\mathrm{P}\:=\:\mathrm{3},\:\mathrm{while}\:\mathrm{the}\:\mathrm{indoor}\:\mathrm{temperature}\:\mathrm{is}\:\mathrm{27}°\mathrm{C}\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{outdoor}\:\mathrm{temperature}\:\mathrm{is}\:\mathrm{8}°\mathrm{C}.\:\mathrm{How}\:\mathrm{much}\:\mathrm{work}\:\mathrm{per}\:\mathrm{hour}\:\mathrm{is}\:\mathrm{required}\:\mathrm{to}\:\mathrm{pump} \\ $$$$\mathrm{3}.\mathrm{07}\:\mathrm{J}\:\mathrm{of}\:\mathrm{heat}\:\mathrm{per}\:\mathrm{hour}\:\mathrm{into}\:\mathrm{the}\:\mathrm{individual}\:\mathrm{unit}\:\mathrm{of}\:\mathrm{10}^{\mathrm{5}} \:\mathrm{J}.\: \\ $$

Question Number 12018    Answers: 0   Comments: 0

Question Number 11988    Answers: 2   Comments: 3

Question Number 11987    Answers: 1   Comments: 0

The radius of the moon is (1/4), and its mass is (1/(81)) that of the earth. If the acceleration due to gravity on the surface of the earth is 9.8m/s^2 . What is its value on the moon′s surface.

$$\mathrm{The}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{moon}\:\mathrm{is}\:\frac{\mathrm{1}}{\mathrm{4}},\:\mathrm{and}\:\mathrm{its}\:\mathrm{mass}\:\mathrm{is}\:\:\frac{\mathrm{1}}{\mathrm{81}}\:\:\mathrm{that}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth}.\:\mathrm{If}\:\mathrm{the} \\ $$$$\mathrm{acceleration}\:\mathrm{due}\:\mathrm{to}\:\mathrm{gravity}\:\mathrm{on}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth}\:\mathrm{is}\:\mathrm{9}.\mathrm{8m}/\mathrm{s}^{\mathrm{2}} .\:\mathrm{What} \\ $$$$\mathrm{is}\:\mathrm{its}\:\mathrm{value}\:\mathrm{on}\:\mathrm{the}\:\mathrm{moon}'\mathrm{s}\:\mathrm{surface}. \\ $$

Question Number 11968    Answers: 0   Comments: 0

A motorcyclist, passing a road junction , moves due east for 8 seconds at a uniform speed of 5 m/s. He then moves due north for another 6 seconds with the same speed. At the end of 6 seconds his displacement from the road junction is 50 m in the diretion of A) 53°E (B) 37°E (C) 53°W (D) 37°W

$$\mathrm{A}\:\mathrm{motorcyclist},\:\mathrm{passing}\:\mathrm{a}\:\mathrm{road}\:\mathrm{junction}\:,\:\mathrm{moves}\:\mathrm{due}\:\mathrm{east}\:\mathrm{for}\:\mathrm{8}\:\mathrm{seconds}\:\mathrm{at} \\ $$$$\mathrm{a}\:\mathrm{uniform}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{5}\:\mathrm{m}/\mathrm{s}.\:\mathrm{He}\:\mathrm{then}\:\mathrm{moves}\:\mathrm{due}\:\mathrm{north}\:\mathrm{for}\:\mathrm{another}\:\mathrm{6}\:\mathrm{seconds} \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{same}\:\mathrm{speed}.\:\mathrm{At}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{6}\:\mathrm{seconds}\:\mathrm{his}\:\mathrm{displacement}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{road}\:\mathrm{junction}\:\mathrm{is}\:\mathrm{50}\:\mathrm{m}\:\mathrm{in}\:\mathrm{the}\:\mathrm{diretion}\:\mathrm{of} \\ $$$$\left.\mathrm{A}\right)\:\mathrm{53}°\mathrm{E}\:\:\left(\mathrm{B}\right)\:\:\mathrm{37}°\mathrm{E}\:\:\left(\mathrm{C}\right)\:\:\mathrm{53}°\mathrm{W}\:\:\left(\mathrm{D}\right)\:\:\mathrm{37}°\mathrm{W} \\ $$

Question Number 11966    Answers: 0   Comments: 0

If a force of 200N is used to pull a block of mass 30 kg up a plane inclined at 60° to the horizontal at a steady speed . Calculate the percentage efficiency of the incline plane.

$$\mathrm{If}\:\mathrm{a}\:\mathrm{force}\:\mathrm{of}\:\mathrm{200N}\:\mathrm{is}\:\mathrm{used}\:\mathrm{to}\:\mathrm{pull}\:\mathrm{a}\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{30}\:\mathrm{kg}\:\mathrm{up}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{inclined} \\ $$$$\mathrm{at}\:\mathrm{60}°\:\mathrm{to}\:\mathrm{the}\:\mathrm{horizontal}\:\mathrm{at}\:\mathrm{a}\:\mathrm{steady}\:\mathrm{speed}\:.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{percentage}\:\mathrm{efficiency} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{incline}\:\mathrm{plane}. \\ $$

Question Number 11964    Answers: 0   Comments: 0

A load of 60 kg is pushed up a 400 m incline side of a platform 3 m high. what is the velocity ratio of the plane ?

$$\:\mathrm{A}\:\mathrm{load}\:\mathrm{of}\:\mathrm{60}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{pushed}\:\mathrm{up}\:\mathrm{a}\:\mathrm{400}\:\mathrm{m}\:\mathrm{incline}\:\mathrm{side}\:\mathrm{of}\:\mathrm{a}\:\mathrm{platform}\:\mathrm{3}\:\mathrm{m}\:\mathrm{high}.\: \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{plane}\:? \\ $$

Question Number 11930    Answers: 1   Comments: 0

Let a and b be two numbers, x be the single arithmetic mean of a and b. Show that the sum of n arithmetic means between a and b is nx.

$$\mathrm{Let}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{be}\:\mathrm{two}\:\mathrm{numbers},\:\mathrm{x}\:\mathrm{be}\:\mathrm{the}\:\mathrm{single}\:\mathrm{arithmetic}\:\mathrm{mean}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}. \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{n}\:\mathrm{arithmetic}\:\mathrm{means}\:\mathrm{between}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{is}\:\mathrm{nx}. \\ $$

Question Number 11898    Answers: 1   Comments: 0

(a) You are listening to your favourite song on a CD. You note that the sound wave has a pleasant frequency of 12 Hertz. (i) What is the velovity of the sound wave (ii) What wavelenght are the wave moving at (iii) What is the period (b) 60 complete waves pass a particular point in 4 secs, if the distance between 3 successive troughs of the water is 15m. Calculate the speed of the wave.

$$\left(\mathrm{a}\right) \\ $$$$\mathrm{You}\:\mathrm{are}\:\mathrm{listening}\:\mathrm{to}\:\mathrm{your}\:\mathrm{favourite}\:\mathrm{song}\:\mathrm{on}\:\mathrm{a}\:\mathrm{CD}.\:\mathrm{You}\:\mathrm{note}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sound} \\ $$$$\mathrm{wave}\:\mathrm{has}\:\mathrm{a}\:\mathrm{pleasant}\:\mathrm{frequency}\:\mathrm{of}\:\mathrm{12}\:\mathrm{Hertz}. \\ $$$$\left(\mathrm{i}\right)\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{velovity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sound}\:\mathrm{wave} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{What}\:\mathrm{wavelenght}\:\mathrm{are}\:\mathrm{the}\:\mathrm{wave}\:\mathrm{moving}\:\mathrm{at} \\ $$$$\left(\mathrm{iii}\right)\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{period} \\ $$$$\left(\mathrm{b}\right) \\ $$$$\mathrm{60}\:\mathrm{complete}\:\mathrm{waves}\:\mathrm{pass}\:\mathrm{a}\:\mathrm{particular}\:\mathrm{point}\:\mathrm{in}\:\mathrm{4}\:\mathrm{secs},\:\mathrm{if}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{between} \\ $$$$\mathrm{3}\:\mathrm{successive}\:\mathrm{troughs}\:\mathrm{of}\:\mathrm{the}\:\mathrm{water}\:\mathrm{is}\:\mathrm{15m}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{wave}. \\ $$

Question Number 11883    Answers: 1   Comments: 0

Draw the structural formula of the compound 2,2,7 - trimethyl - 4 - (1 - methylpropyl) nonane

$$\mathrm{Draw}\:\mathrm{the}\:\mathrm{structural}\:\mathrm{formula}\:\mathrm{of}\:\mathrm{the}\:\mathrm{compound} \\ $$$$\mathrm{2},\mathrm{2},\mathrm{7}\:-\:\mathrm{trimethyl}\:-\:\mathrm{4}\:-\:\left(\mathrm{1}\:-\:\mathrm{methylpropyl}\right)\:\mathrm{nonane} \\ $$

Question Number 11828    Answers: 0   Comments: 0

A sample of steam at 140 bar is states to have enthalpy of 3009.1 kJ/kg, Calculate the internal energy and entropy.

$$\mathrm{A}\:\:\mathrm{sample}\:\mathrm{of}\:\mathrm{steam}\:\mathrm{at}\:\mathrm{140}\:\mathrm{bar}\:\mathrm{is}\:\mathrm{states}\:\mathrm{to}\:\mathrm{have}\:\mathrm{enthalpy}\:\mathrm{of}\:\:\mathrm{3009}.\mathrm{1}\:\mathrm{kJ}/\mathrm{kg}, \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{internal}\:\mathrm{energy}\:\mathrm{and}\:\mathrm{entropy}. \\ $$

Question Number 11791    Answers: 1   Comments: 0

What is the velocity of sound at 100°C if the velocity of sound at 0°C is 340 m/s

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{sound}\:\mathrm{at}\:\mathrm{100}°\mathrm{C}\:\:\mathrm{if}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{sound}\:\mathrm{at}\:\mathrm{0}°\mathrm{C}\:\mathrm{is}\:\mathrm{340}\:\mathrm{m}/\mathrm{s} \\ $$

Question Number 11540    Answers: 1   Comments: 0

Question Number 11536    Answers: 2   Comments: 0

Question Number 11433    Answers: 1   Comments: 5

for r=(1/θ), show that the arc length between θ=3π^(−1) and θ=nπ^(−1) (where n>3) is aproxiately equal to the length of the line y=3π^(−1) between the same bounds. Or show otherwise.

$$\mathrm{for}\:{r}=\frac{\mathrm{1}}{\theta},\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{arc}\:\mathrm{length}\:\mathrm{between} \\ $$$$\theta=\mathrm{3}\pi^{−\mathrm{1}} \:\:\mathrm{and}\:\theta={n}\pi^{−\mathrm{1}} \:\:\:\left(\mathrm{where}\:\:{n}>\mathrm{3}\right)\:\:\mathrm{is}\:\mathrm{aproxiately} \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:{y}=\mathrm{3}\pi^{−\mathrm{1}} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{same}\:\mathrm{bounds}.\:\mathrm{Or}\:\mathrm{show}\:\mathrm{otherwise}. \\ $$$$ \\ $$

Question Number 11413    Answers: 1   Comments: 0

Find the length of the arc of the hyperbolic spiral rθ=a lying between r=a and r=2a.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{arc}\:\mathrm{of}\:\mathrm{the}\:\mathrm{hyperbolic} \\ $$$$\mathrm{spiral}\:\:\mathrm{r}\theta=\mathrm{a}\:\:\mathrm{lying}\:\mathrm{between}\:\:\mathrm{r}=\mathrm{a}\:\:\mathrm{and}\: \\ $$$$\mathrm{r}=\mathrm{2a}. \\ $$

Question Number 11393    Answers: 0   Comments: 0

Question Number 11389    Answers: 1   Comments: 0

Given that the mean relative atomic mass of chlorine contain two isotopes of mass numbe 35 and 37. What is the percentage of composition of the isotope of mass number 37

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{mean}\:\mathrm{relative}\:\mathrm{atomic}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{chlorine}\:\mathrm{contain}\:\mathrm{two}\:\mathrm{isotopes} \\ $$$$\mathrm{of}\:\mathrm{mass}\:\mathrm{numbe}\:\mathrm{35}\:\mathrm{and}\:\mathrm{37}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{percentage}\:\mathrm{of}\:\mathrm{composition}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{isotope}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{number}\:\mathrm{37}\: \\ $$

Question Number 11373    Answers: 1   Comments: 0

Question Number 11372    Answers: 0   Comments: 0

If G_1 and G_2 are groups , and f : G_1 →G_2 is a group homomorphism , then prove that o(G_1 ) = o(G_2 ) .

$$\mathrm{If}\:\mathrm{G}_{\mathrm{1}} \:\mathrm{and}\:\mathrm{G}_{\mathrm{2}} \:\mathrm{are}\:\mathrm{groups}\:,\:\mathrm{and}\:\mathrm{f}\::\:\mathrm{G}_{\mathrm{1}} \:\rightarrow\mathrm{G}_{\mathrm{2}} \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{group}\:\mathrm{homomorphism}\:,\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:\mathrm{o}\left(\mathrm{G}_{\mathrm{1}} \right)\:=\:\mathrm{o}\left(\mathrm{G}_{\mathrm{2}} \right)\:. \\ $$

Question Number 11388    Answers: 0   Comments: 0

A cell supplies a current of 6 ameter through a 2 coil and a current of 0.2 ameter through 7 coil. Calculate the limits and the internal resistance of the cell

$$\mathrm{A}\:\mathrm{cell}\:\mathrm{supplies}\:\mathrm{a}\:\mathrm{current}\:\mathrm{of}\:\mathrm{6}\:\mathrm{ameter}\:\mathrm{through}\:\mathrm{a}\:\mathrm{2}\:\mathrm{coil}\:\mathrm{and}\:\mathrm{a}\:\mathrm{current}\:\mathrm{of}\:\mathrm{0}.\mathrm{2}\: \\ $$$$\mathrm{ameter}\:\mathrm{through}\:\mathrm{7}\:\mathrm{coil}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{limits}\:\mathrm{and}\:\mathrm{the}\:\mathrm{internal}\:\mathrm{resistance} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{cell} \\ $$

Question Number 11332    Answers: 0   Comments: 0

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