Question and Answers Forum

AllQuestion and Answers: Page 1606

Question Number 40857 Answers: 1 Comments: 2

Question Number 40847 Answers: 1 Comments: 0

If the coordinate of the points A and B be (3,3) and (7,6) then the length of the portion of the line AB intercepted between the axes is (a) (5/4) (b) ((√(10))/4) (c) ((√(13))/3) (d) none

$${If}\:{the}\:{coordinate}\:{of}\:{the}\:{points}\:{A}\: \\ $$$${and}\:{B}\:{be}\:\left(\mathrm{3},\mathrm{3}\right)\:{and}\:\left(\mathrm{7},\mathrm{6}\right)\:{then}\:{the} \\ $$$${length}\:{of}\:{the}\:{portion}\:{of}\:{the}\:{line}\: \\ $$$${AB}\:{intercepted}\:{between}\:{the}\:{axes}\:{is} \\ $$$$\left({a}\right)\:\:\frac{\mathrm{5}}{\mathrm{4}}\:\:\:\left({b}\right)\:\:\:\frac{\sqrt{\mathrm{10}}}{\mathrm{4}}\:\:\:\:\left({c}\right)\:\:\frac{\sqrt{\mathrm{13}}}{\mathrm{3}}\:\:\:\:\left({d}\right)\:{none} \\ $$

Question Number 40830 Answers: 0 Comments: 1

find ∫ (√(2+tan^2 t))dt

$${find}\:\int\:\sqrt{\mathrm{2}+{tan}^{\mathrm{2}} {t}}{dt} \\ $$

Question Number 40829 Answers: 1 Comments: 0

let f(t) = ∫_0 ^∞ ((arctan(tx))/(x^3 +8))dx 1)find a simple form of f(t) 2)calculate ∫_0 ^∞ ((arctan(x))/(x^3 +8))dx .

$${let}\:{f}\left({t}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({tx}\right)}{{x}^{\mathrm{3}} +\mathrm{8}}{dx} \\ $$$$\left.\mathrm{1}\right){find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({t}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left({x}\right)}{{x}^{\mathrm{3}} \:+\mathrm{8}}{dx}\:. \\ $$

Question Number 40826 Answers: 1 Comments: 0

Question Number 40823 Answers: 0 Comments: 1

calculate ∫_0 ^(π/2) (√(cos^2 x +3sin^2 x))dx

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \sqrt{{cos}^{\mathrm{2}} {x}\:+\mathrm{3}{sin}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 40822 Answers: 2 Comments: 0

Question Number 40818 Answers: 1 Comments: 0

Two large parallel metal plates carrying opposite charges are seperated by a distance of 0.2m,and the potential difference between them is 0.5KV. (a)Calculate the magnitude of the uniform electric field between them. (b)Also calculate the workdone by this field on a charge of 4.0×10^(−9) C when it moves from the plate of higher potential to that of lower potential.

$${Two}\:{large}\:{parallel}\:{metal}\:{plates}\:{carrying} \\ $$$${opposite}\:{charges}\:{are}\:{seperated}\:{by}\:{a} \\ $$$${distance}\:{of}\:\mathrm{0}.\mathrm{2}{m},{and}\:{the}\:{potential} \\ $$$${difference}\:{between}\:{them}\:{is}\:\mathrm{0}.\mathrm{5}{KV}. \\ $$$$\left({a}\right){Calculate}\:{the}\:{magnitude}\:{of}\:{the} \\ $$$${uniform}\:{electric}\:{field}\:{between}\:{them}. \\ $$$$\left({b}\right){Also}\:{calculate}\:{the}\:{workdone}\:{by} \\ $$$${this}\:{field}\:{on}\:{a}\:{charge}\:{of}\:\mathrm{4}.\mathrm{0}×\mathrm{10}^{−\mathrm{9}} {C} \\ $$$${when}\:{it}\:{moves}\:{from}\:{the}\:{plate}\:{of} \\ $$$${higher}\:{potential}\:{to}\:{that}\:{of}\:{lower} \\ $$$${potential}. \\ $$

Question Number 40817 Answers: 1 Comments: 0

An electric field of 2.66KV/m,and a magnetic field of 1.20T,act on a moving electron.Calculate the speed of the electron if the resultant force due to both fields is zero.

$${An}\:{electric}\:{field}\:{of}\:\mathrm{2}.\mathrm{66}{KV}/{m},{and} \\ $$$${a}\:{magnetic}\:{field}\:{of}\:\mathrm{1}.\mathrm{20}{T},{act}\:{on}\:{a} \\ $$$${moving}\:{electron}.{Calculate}\:{the}\:{speed} \\ $$$${of}\:{the}\:{electron}\:{if}\:{the}\:{resultant}\:{force} \\ $$$${due}\:{to}\:{both}\:{fields}\:{is}\:{zero}. \\ $$$$ \\ $$

Question Number 40816 Answers: 0 Comments: 0

An electric field of 2.66KV/m,and a magnetic field of 1.20T,act on a moving electron.Calculate the speed of the electron if the resultant force due to both fields is zero.

Question Number 40815 Answers: 1 Comments: 0

Calculate the magnetic force,F_b on an electron with velocity,v=20j^ m/s which enters a magnetic field of flux density,B=0.6k^ T

$${Calculate}\:{the}\:{magnetic}\:{force},{F}_{{b}} \:{on} \\ $$$${an}\:{electron}\:{with}\:{velocity},{v}=\mathrm{20}\hat {{j}m}/{s} \\ $$$${which}\:{enters}\:{a}\:{magnetic}\:{field}\:{of} \\ $$$${flux}\:{density},{B}=\mathrm{0}.\mathrm{6}\hat {{k}T} \\ $$

Question Number 40814 Answers: 0 Comments: 3

Question Number 40813 Answers: 0 Comments: 4

Question Number 40804 Answers: 0 Comments: 6

Question Number 40787 Answers: 1 Comments: 4

Let I_1 = ∫_(π/6) ^(π/3) ((sin x)/x) dx , I_2 = ∫_(π/6) ^(π/3) ((sin (sin x))/(sin x))dx , I_3 = ∫_(π/6) ^(π/3) ((sin (tan x))/(tan x))dx. Prove that I_2 > I_1 > I_3 .

$$\mathrm{Let}\:\mathrm{I}_{\mathrm{1}} =\:\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{3}}} \frac{\mathrm{sin}\:{x}}{{x}}\:{dx}\:\:,\:\:\mathrm{I}_{\mathrm{2}} =\:\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{3}}} \frac{\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right)}{\mathrm{sin}\:{x}}{dx} \\ $$$$,\:\mathrm{I}_{\mathrm{3}} =\:\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{3}}} \frac{\mathrm{sin}\:\left(\mathrm{tan}\:{x}\right)}{\mathrm{tan}\:{x}}{dx}.\: \\ $$$${P}\mathrm{rove}\:\mathrm{that}\:\mathrm{I}_{\mathrm{2}} \:>\:\mathrm{I}_{\mathrm{1}} \:>\:\mathrm{I}_{\mathrm{3}} \:. \\ $$

Question Number 40786 Answers: 1 Comments: 0

A parallel plate capacitor of plate spacing, 1mm is charged to a potential of 50V.Find the energy density in the capacitor

$${A}\:{parallel}\:{plate}\:{capacitor}\:{of}\:{plate} \\ $$$${spacing},\:\mathrm{1}{mm}\:{is}\:{charged}\:{to}\:{a}\:{potential} \\ $$$${of}\:\mathrm{50}{V}.{Find}\:{the}\:{energy}\:{density}\:{in} \\ $$$${the}\:{capacitor} \\ $$

Question Number 40782 Answers: 0 Comments: 0

let f(x)=ln(1+arctanx) 1) calculate f^((n)) (x) then f^((n)) (0) 2) developp f at integr serie .

$${let}\:{f}\left({x}\right)={ln}\left(\mathrm{1}+{arctanx}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{then}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$

Question Number 40773 Answers: 1 Comments: 0

A pair of oppositely charged plane parallel plates each of area,100cm^2 has the electric field of the value 5.0×10^4 N/C.Calculate the charge on each plate.

$${A}\:{pair}\:{of}\:{oppositely}\:{charged}\:{plane} \\ $$$${parallel}\:{plates}\:{each}\:{of}\:{area},\mathrm{100}{cm}^{\mathrm{2}} \\ $$$${has}\:{the}\:{electric}\:{field}\:{of}\:{the}\:{value} \\ $$$$\mathrm{5}.\mathrm{0}×\mathrm{10}^{\mathrm{4}} {N}/{C}.{Calculate}\:{the}\:{charge} \\ $$$${on}\:{each}\:{plate}. \\ $$

Question Number 40771 Answers: 2 Comments: 1

Question Number 40770 Answers: 1 Comments: 0

An electric dipole is placed at rest in a uniform external electric field,and released.Discuss its motion mathematically.

$${An}\:{electric}\:{dipole}\:{is}\:{placed}\:{at}\:{rest} \\ $$$${in}\:{a}\:{uniform}\:{external}\:{electric} \\ $$$${field},{and}\:{released}.{Discuss}\:{its} \\ $$$${motion}\:{mathematically}. \\ $$

Question Number 40764 Answers: 1 Comments: 0

a piece of wire 40cm long is cut into two parts and each part is then bent into a square.if the sum of these squares is 68cm^2 find the lengths of the two pieces of wire.

Question Number 40763 Answers: 2 Comments: 0

Question Number 40760 Answers: 0 Comments: 0

find ∫ ((√(1+x^2 ))/(√(1−x^3 ))) dx

$${find}\:\:\int\:\:\:\frac{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{\sqrt{\mathrm{1}−{x}^{\mathrm{3}} }}\:{dx} \\ $$

Question Number 40759 Answers: 1 Comments: 2

calculate lim_(n→+∞) ((1−e^(−nx^2 ) )/(x^2 sin((π/n))))

$${calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\:\:\frac{\mathrm{1}−{e}^{−{nx}^{\mathrm{2}} } }{{x}^{\mathrm{2}} {sin}\left(\frac{\pi}{{n}}\right)} \\ $$

Question Number 40745 Answers: 3 Comments: 0

Question Number 40743 Answers: 2 Comments: 0

Pg 1601 Pg 1602 Pg 1603 Pg 1604 Pg 1605 Pg 1606 Pg 1607 Pg 1608 Pg 1609 Pg 1610

Contact: info@tinkutara.com