Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1758

Question Number 24152    Answers: 0   Comments: 1

Let matrice A = ((a,b),(c,d) ), and A^T = A^(−1) Find d − bc

$$\mathrm{Let}\:\mathrm{matrice}\:{A}\:=\:\begin{pmatrix}{{a}}&{{b}}\\{{c}}&{{d}}\end{pmatrix},\:\mathrm{and}\:{A}^{{T}} \:=\:{A}^{−\mathrm{1}} \\ $$$$\mathrm{Find}\:{d}\:−\:{bc} \\ $$

Question Number 24151    Answers: 0   Comments: 1

y=f(t) and y′′=ksiny y=?

$${y}={f}\left({t}\right)\:{and}\:{y}''={ksiny}\:{y}=? \\ $$

Question Number 24211    Answers: 1   Comments: 13

Question Number 24142    Answers: 0   Comments: 2

Prove that Σ_(r=1) ^(2n−1) (−1)^(r−1) (∫_0 ^1 x^r (1−x)^(2n−r) dx) =∫_0 ^1 [(1−x)^(2n) +x^(2n) −(1−x)^(2n+1) −x^(2n+1) ]dx

$${Prove}\:{that} \\ $$$$\underset{{r}=\mathrm{1}} {\overset{\mathrm{2}{n}−\mathrm{1}} {\sum}}\left(−\mathrm{1}\right)^{{r}−\mathrm{1}} \left(\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}^{{r}} \left(\mathrm{1}−{x}\right)^{\mathrm{2}{n}−{r}} {dx}\right) \\ $$$$=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\left[\left(\mathrm{1}−{x}\right)^{\mathrm{2}{n}} +{x}^{\mathrm{2}{n}} −\left(\mathrm{1}−{x}\right)^{\mathrm{2}{n}+\mathrm{1}} −{x}^{\mathrm{2}{n}+\mathrm{1}} \right]{dx} \\ $$

Question Number 24127    Answers: 1   Comments: 1

Question Number 24125    Answers: 1   Comments: 1

Question Number 24150    Answers: 0   Comments: 0

if y is a function of t then solve this y′′=ksiny diff.equ

$${if}\:{y}\:{is}\:{a}\:{function}\:{of}\:{t}\:{then}\:{solve}\:{this}\:{y}''={ksiny}\:{diff}.{equ} \\ $$

Question Number 24149    Answers: 1   Comments: 0

Question Number 24111    Answers: 1   Comments: 1

Question Number 24100    Answers: 1   Comments: 1

The distance between point P(lat 65°S, long 25°E) and Q(lat 65°S, long X) on the earth surface along the parallel of latitute is 2502.5 km. If π = ((22)/2) and earth radius is 6370 km, find the two possible values of x.

$$\mathrm{The}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{point}\:\:\mathrm{P}\left(\mathrm{lat}\:\mathrm{65}°\mathrm{S},\:\:\mathrm{long}\:\mathrm{25}°\mathrm{E}\right)\:\mathrm{and}\:\mathrm{Q}\left(\mathrm{lat}\:\mathrm{65}°\mathrm{S},\:\mathrm{long}\:\mathrm{X}\right) \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{earth}\:\mathrm{surface}\:\mathrm{along}\:\mathrm{the}\:\mathrm{parallel}\:\mathrm{of}\:\mathrm{latitute}\:\mathrm{is}\:\:\mathrm{2502}.\mathrm{5}\:\mathrm{km}.\:\mathrm{If}\:\:\pi\:=\:\frac{\mathrm{22}}{\mathrm{2}} \\ $$$$\mathrm{and}\:\mathrm{earth}\:\mathrm{radius}\:\mathrm{is}\:\:\mathrm{6370}\:\mathrm{km},\:\mathrm{find}\:\mathrm{the}\:\mathrm{two}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}. \\ $$

Question Number 24098    Answers: 1   Comments: 0

sin^(−1) ((ax)/c)+sin^(−1) ((bx)/c)=sin^(−1) x [When a^2 +b^2 =c^2 ]

$$\mathrm{sin}^{−\mathrm{1}} \frac{{ax}}{{c}}+\mathrm{sin}^{−\mathrm{1}} \frac{{bx}}{{c}}=\mathrm{sin}^{−\mathrm{1}} {x}\:\:\:\:\:\left[{When}\:\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={c}^{\mathrm{2}} \:\right] \\ $$

Question Number 24175    Answers: 1   Comments: 6

A cyclist goes round a circular track of radius 70m.The total mass of bicycle and rider is 70kg.Calculate the frictional force which will ensure that the rider successfully negotiates the track with a speed of 25m/s.What happens to the rider if μ=0.3?

$${A}\:{cyclist}\:{goes}\:{round}\:{a}\:{circular} \\ $$$${track}\:{of}\:{radius}\:\mathrm{70}{m}.{The}\:{total}\:{mass} \\ $$$${of}\:{bicycle}\:{and}\:{rider}\:{is}\:\mathrm{70}{kg}.{Calculate} \\ $$$${the}\:{frictional}\:{force}\:{which}\:{will} \\ $$$${ensure}\:{that}\:{the}\:{rider}\:{successfully} \\ $$$${negotiates}\:{the}\:{track}\:{with}\:{a}\:{speed} \\ $$$${of}\:\mathrm{25}{m}/{s}.{What}\:{happens}\:{to}\:{the} \\ $$$${rider}\:{if}\:\mu=\mathrm{0}.\mathrm{3}? \\ $$

Question Number 24078    Answers: 1   Comments: 7

Question Number 24057    Answers: 1   Comments: 0

A block of ice slides down a 45° incline plane in twice the time it takes to slide down a 45° frictionless incline plane.What is the coefficient of kinetic friction between the ice block and the incline plqne.

$${A}\:{block}\:{of}\:{ice}\:{slides}\:{down}\:{a}\:\mathrm{45}° \\ $$$${incline}\:{plane}\:{in}\:{twice}\:{the}\:{time}\:{it} \\ $$$${takes}\:{to}\:{slide}\:{down}\:{a}\:\mathrm{45}°\:{frictionless} \\ $$$${incline}\:{plane}.{What}\:{is}\:{the}\:{coefficient} \\ $$$${of}\:{kinetic}\:{friction}\:{between}\:{the} \\ $$$${ice}\:{block}\:{and}\:{the}\:{incline}\:{plqne}. \\ $$

Question Number 24055    Answers: 0   Comments: 2

Any Architect in the house? please i need your help

$${Any}\:{Architect}\:{in}\:{the}\:{house}? \\ $$$$ \\ $$$${please}\:{i}\:{need}\:{your}\:{help} \\ $$

Question Number 24054    Answers: 0   Comments: 0

Compare the bond strength of S − O bond in SO_3 ^(−2) and SO_4 ^(−2) ion.

$$\mathrm{Compare}\:\mathrm{the}\:\mathrm{bond}\:\mathrm{strength}\:\mathrm{of}\:\mathrm{S}\:−\:\mathrm{O} \\ $$$$\mathrm{bond}\:\mathrm{in}\:\mathrm{SO}_{\mathrm{3}} ^{−\mathrm{2}} \:\mathrm{and}\:\mathrm{SO}_{\mathrm{4}} ^{−\mathrm{2}} \:\mathrm{ion}. \\ $$

Question Number 24069    Answers: 1   Comments: 0

Simplify (((log_2 (√5) . log_(25) 20) + log_4 (√(50)) )/(log_4 70 − log_(15) 49))

$$\mathrm{Simplify} \\ $$$$\frac{\left(\mathrm{log}_{\mathrm{2}} \:\sqrt{\mathrm{5}}\:.\:\mathrm{log}_{\mathrm{25}} \:\mathrm{20}\right)\:+\:\mathrm{log}_{\mathrm{4}} \:\sqrt{\mathrm{50}}\:\:}{\mathrm{log}_{\mathrm{4}} \:\mathrm{70}\:−\:\mathrm{log}_{\mathrm{15}} \:\mathrm{49}} \\ $$

Question Number 24042    Answers: 1   Comments: 2

f(x) = sin(sin^2 x) + cos(sin^2 x) then the range of f(x) is

$${f}\left({x}\right)\:=\:\mathrm{sin}\left(\mathrm{sin}^{\mathrm{2}} {x}\right)\:+\:\mathrm{cos}\left(\mathrm{sin}^{\mathrm{2}} {x}\right)\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{range}\:\mathrm{of}\:{f}\left({x}\right)\:\mathrm{is} \\ $$

Question Number 24037    Answers: 0   Comments: 0

Question Number 24032    Answers: 0   Comments: 7

A hemispherical bowl of radius R = 0.1 m is rotating about its own axis (which is vertical) with an angular velocity ω. A particle of mass 10^(−2) kg on the frictionless inner surface of the bowl is also rotating with the same ω. The particle is at a height h from the bottom of the bowl. It is desired to measure g (acceleration due to gravity) using the set up by measuring h accurately. Assuming that R and ω are known precisely and that the least count in the measurement of h is 10^(−4) m, what is the minimum possible error Δg in the measured value of g?

$$\mathrm{A}\:\mathrm{hemispherical}\:\mathrm{bowl}\:\mathrm{of}\:\mathrm{radius}\:{R}\:=\:\mathrm{0}.\mathrm{1} \\ $$$$\mathrm{m}\:\mathrm{is}\:\mathrm{rotating}\:\mathrm{about}\:\mathrm{its}\:\mathrm{own}\:\mathrm{axis}\:\left(\mathrm{which}\right. \\ $$$$\left.\mathrm{is}\:\mathrm{vertical}\right)\:\mathrm{with}\:\mathrm{an}\:\mathrm{angular}\:\mathrm{velocity}\:\omega. \\ $$$$\mathrm{A}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{10}^{−\mathrm{2}} \:\mathrm{kg}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{frictionless}\:\mathrm{inner}\:\mathrm{surface}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bowl}\:\mathrm{is} \\ $$$$\mathrm{also}\:\mathrm{rotating}\:\mathrm{with}\:\mathrm{the}\:\mathrm{same}\:\omega.\:\mathrm{The} \\ $$$$\mathrm{particle}\:\mathrm{is}\:\mathrm{at}\:\mathrm{a}\:\mathrm{height}\:{h}\:\mathrm{from}\:\mathrm{the}\:\mathrm{bottom} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{bowl}. \\ $$$$\mathrm{It}\:\mathrm{is}\:\mathrm{desired}\:\mathrm{to}\:\mathrm{measure}\:{g}\:\left(\mathrm{acceleration}\right. \\ $$$$\left.\mathrm{due}\:\mathrm{to}\:\mathrm{gravity}\right)\:\mathrm{using}\:\mathrm{the}\:\mathrm{set}\:\mathrm{up}\:\mathrm{by} \\ $$$$\mathrm{measuring}\:{h}\:\mathrm{accurately}.\:\mathrm{Assuming} \\ $$$$\mathrm{that}\:{R}\:\mathrm{and}\:\omega\:\mathrm{are}\:\mathrm{known}\:\mathrm{precisely}\:\mathrm{and} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{least}\:\mathrm{count}\:\mathrm{in}\:\mathrm{the}\:\mathrm{measurement} \\ $$$$\mathrm{of}\:{h}\:\mathrm{is}\:\mathrm{10}^{−\mathrm{4}} \:\mathrm{m},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{minimum} \\ $$$$\mathrm{possible}\:\mathrm{error}\:\Delta{g}\:\mathrm{in}\:\mathrm{the}\:\mathrm{measured}\:\mathrm{value} \\ $$$$\mathrm{of}\:{g}? \\ $$

Question Number 24023    Answers: 0   Comments: 0

Compounds with high heat of formation are less stable because (1) it is difficult to synthesize them (2) energy rich state leads to instability (3) high temperature is required to synthesize them (4) molecules of such compounds are distorted

$$\mathrm{Compounds}\:\mathrm{with}\:\mathrm{high}\:\mathrm{heat}\:\mathrm{of}\:\mathrm{formation} \\ $$$$\mathrm{are}\:\mathrm{less}\:\mathrm{stable}\:\mathrm{because} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{it}\:\mathrm{is}\:\mathrm{difficult}\:\mathrm{to}\:\mathrm{synthesize}\:\mathrm{them} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{energy}\:\mathrm{rich}\:\mathrm{state}\:\mathrm{leads}\:\mathrm{to}\:\mathrm{instability} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{high}\:\mathrm{temperature}\:\mathrm{is}\:\mathrm{required}\:\mathrm{to} \\ $$$$\mathrm{synthesize}\:\mathrm{them} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{molecules}\:\mathrm{of}\:\mathrm{such}\:\mathrm{compounds}\:\mathrm{are} \\ $$$$\mathrm{distorted} \\ $$

Question Number 24022    Answers: 1   Comments: 0

A one kg ball rolling on a smooth horizontal surface at 20 m s^(−1) comes to the bottom of an inclined plane making an angle of 30° with the horizontal. Calculate K.E. of the ball when it is at the bottom of incline. How far up the incline will the ball roll? Neglect friction.

$$\mathrm{A}\:\mathrm{one}\:\mathrm{kg}\:\mathrm{ball}\:\mathrm{rolling}\:\mathrm{on}\:\mathrm{a}\:\mathrm{smooth} \\ $$$$\mathrm{horizontal}\:\mathrm{surface}\:\mathrm{at}\:\mathrm{20}\:\mathrm{m}\:\mathrm{s}^{−\mathrm{1}} \:\mathrm{comes}\:\mathrm{to} \\ $$$$\mathrm{the}\:\mathrm{bottom}\:\mathrm{of}\:\mathrm{an}\:\mathrm{inclined}\:\mathrm{plane}\:\mathrm{making} \\ $$$$\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{30}°\:\mathrm{with}\:\mathrm{the}\:\mathrm{horizontal}. \\ $$$$\mathrm{Calculate}\:\mathrm{K}.\mathrm{E}.\:\mathrm{of}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{when}\:\mathrm{it}\:\mathrm{is}\:\mathrm{at} \\ $$$$\mathrm{the}\:\mathrm{bottom}\:\mathrm{of}\:\mathrm{incline}.\:\mathrm{How}\:\mathrm{far}\:\mathrm{up}\:\mathrm{the} \\ $$$$\mathrm{incline}\:\mathrm{will}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{roll}?\:\mathrm{Neglect} \\ $$$$\mathrm{friction}. \\ $$

Question Number 24025    Answers: 1   Comments: 4

Question Number 23996    Answers: 1   Comments: 0

z^(−4_(=1/3(1−(√(3i)))) )

$$\mathrm{z}^{−\mathrm{4}_{=\mathrm{1}/\mathrm{3}\left(\mathrm{1}−\sqrt{\left.\mathrm{3i}\right)}\right.} } \\ $$

Question Number 24010    Answers: 0   Comments: 0

Prove that Σ_(r=1) ^(2n−1) (−1)^(r−1) ∙(r/(^(2n) C_r )) = (n/(n + 1)) .

$$\mathrm{Prove}\:\mathrm{that}\:\underset{{r}=\mathrm{1}} {\overset{\mathrm{2}{n}−\mathrm{1}} {\sum}}\left(−\mathrm{1}\right)^{{r}−\mathrm{1}} \centerdot\frac{{r}}{\:^{\mathrm{2}{n}} {C}_{{r}} }\:=\:\frac{{n}}{{n}\:+\:\mathrm{1}}\:. \\ $$

Question Number 23984    Answers: 2   Comments: 0

Which of the following relation is/are correct? (1) ΔG = ΔH − TΔS (2) ΔG = ΔH + T[((δ(ΔG))/(δT))]_P (3) ΔG = ΔH + TΔS (4) ΔG = ΔH + ΔnRT

$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{relation}\:\mathrm{is}/\mathrm{are} \\ $$$$\mathrm{correct}? \\ $$$$\left(\mathrm{1}\right)\:\Delta\mathrm{G}\:=\:\Delta\mathrm{H}\:−\:\mathrm{T}\Delta\mathrm{S} \\ $$$$\left(\mathrm{2}\right)\:\Delta\mathrm{G}\:=\:\Delta\mathrm{H}\:+\:\mathrm{T}\left[\frac{\delta\left(\Delta\mathrm{G}\right)}{\delta\mathrm{T}}\right]_{\mathrm{P}} \\ $$$$\left(\mathrm{3}\right)\:\Delta\mathrm{G}\:=\:\Delta\mathrm{H}\:+\:\mathrm{T}\Delta\mathrm{S} \\ $$$$\left(\mathrm{4}\right)\:\Delta\mathrm{G}\:=\:\Delta\mathrm{H}\:+\:\Delta\mathrm{nRT} \\ $$

  Pg 1753      Pg 1754      Pg 1755      Pg 1756      Pg 1757      Pg 1758      Pg 1759      Pg 1760      Pg 1761      Pg 1762   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com