Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1517

Question Number 51372    Answers: 1   Comments: 1

Question Number 51368    Answers: 0   Comments: 8

Question Number 51367    Answers: 3   Comments: 0

Evaluate: cot^(−1) [(((√(1−sinx))+(√(1+sinx)))/((√(1−sinx))−(√(1+sinx))))] = ?

$${Evaluate}: \\ $$$$\mathrm{cot}^{−\mathrm{1}} \left[\frac{\sqrt{\mathrm{1}−\mathrm{sin}{x}}+\sqrt{\mathrm{1}+\mathrm{sin}{x}}}{\sqrt{\mathrm{1}−\mathrm{sin}{x}}−\sqrt{\mathrm{1}+\mathrm{sin}{x}}}\right]\:=\:? \\ $$

Question Number 51360    Answers: 0   Comments: 0

Question Number 51364    Answers: 0   Comments: 2

The value of x for which sin(cot^(−1) (1+x))=cos(tan^(−1) x) is ?

$${The}\:{value}\:{of}\:{x}\:{for}\:{which} \\ $$$$\mathrm{sin}\left(\mathrm{cot}^{−\mathrm{1}} \left(\mathrm{1}+{x}\right)\right)=\mathrm{cos}\left(\mathrm{tan}^{−\mathrm{1}} {x}\right)\:{is}\:? \\ $$

Question Number 51356    Answers: 2   Comments: 1

Evaluate : tan {(1/2)cos^(−1) ((√5)/3)} ?

$${Evaluate}\:: \\ $$$$\mathrm{tan}\:\left\{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}^{−\mathrm{1}} \frac{\sqrt{\mathrm{5}}}{\mathrm{3}}\right\}\:? \\ $$

Question Number 51353    Answers: 4   Comments: 1

Question Number 51403    Answers: 0   Comments: 0

Question Number 51325    Answers: 1   Comments: 0

If a number of little droplets all of the same radius r coalesce to form a single drop of radius R.show that the rise in temperature is given by ((3T)/(pJ))((1/r)−(1/R)) where T is surface tension of water and J is mechanical equivalent of heat

$${If}\:{a}\:{number}\:{of}\:{little}\: \\ $$$${droplets}\:{all}\:{of}\:{the}\:{same}\: \\ $$$${radius}\:{r}\:{coalesce}\:{to} \\ $$$${form}\:\:{a}\:{single} \\ $$$${drop}\:{of}\:{radius}\:{R}.{show} \\ $$$${that}\:{the}\:{rise}\:{in}\:{temperature} \\ $$$${is}\:{given}\:{by} \\ $$$$\frac{\mathrm{3}{T}}{{pJ}}\left(\frac{\mathrm{1}}{{r}}−\frac{\mathrm{1}}{{R}}\right) \\ $$$${where}\:\:{T}\:{is}\:{surface}\:{tension} \\ $$$${of}\:{water}\:{and}\:{J}\:{is}\:{mechanical} \\ $$$${equivalent}\:{of}\:{heat} \\ $$

Question Number 51324    Answers: 2   Comments: 0

calculate ∫_0 ^(+∞) (dx/(1+x^(2 ) +x^4 ))

$${calculate}\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}\:} \:+{x}^{\mathrm{4}} } \\ $$

Question Number 51321    Answers: 1   Comments: 0

A B C D is a parallelogram on the Argand plane. The affixes of A, B, C are 8 + 5i, − 7 − 5i, − 5 + 5i respectively . Find the affix of D

$$\mathrm{A}\:\mathrm{B}\:\mathrm{C}\:\mathrm{D}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{parallelogram}\:\mathrm{on}\:\mathrm{the}\:\mathrm{Argand}\:\mathrm{plane}.\:\mathrm{The}\: \\ $$$$\mathrm{affixes}\:\mathrm{of}\:\:\mathrm{A},\:\mathrm{B},\:\mathrm{C}\:\:\mathrm{are}\:\:\:\mathrm{8}\:+\:\mathrm{5i},\:\:−\:\mathrm{7}\:−\:\mathrm{5i},\:\:−\:\mathrm{5}\:+\:\mathrm{5i}\:\:\mathrm{respectively} \\ $$$$.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{affix}\:\mathrm{of}\:\:\mathrm{D} \\ $$

Question Number 51320    Answers: 1   Comments: 0

The points A, B, C represent the complex numbers z_1 , z_2 , z_3 respectively. And G is the centroid of the triangle A B C, if 4z_1 + z_2 + z_3 = 0, show that the origin is the mid point of AG.

$$\mathrm{The}\:\mathrm{points}\:\mathrm{A},\:\mathrm{B},\:\mathrm{C}\:\:\mathrm{represent}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{numbers}\:\:\mathrm{z}_{\mathrm{1}} ,\:\mathrm{z}_{\mathrm{2}} ,\:\mathrm{z}_{\mathrm{3}} \: \\ $$$$\mathrm{respectively}.\:\mathrm{And}\:\mathrm{G}\:\mathrm{is}\:\mathrm{the}\:\mathrm{centroid}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{A}\:\mathrm{B}\:\mathrm{C},\:\:\mathrm{if} \\ $$$$\mathrm{4z}_{\mathrm{1}} \:+\:\mathrm{z}_{\mathrm{2}} \:+\:\mathrm{z}_{\mathrm{3}} \:\:=\:\:\mathrm{0},\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{origin}\:\mathrm{is}\:\mathrm{the}\:\mathrm{mid}\:\mathrm{point}\:\mathrm{of}\:\:\mathrm{AG}. \\ $$

Question Number 51316    Answers: 0   Comments: 2

Question Number 51314    Answers: 0   Comments: 1

Question Number 51312    Answers: 0   Comments: 1

Question Number 51307    Answers: 0   Comments: 3

Question Number 51299    Answers: 0   Comments: 4

Is Resonance possible in Pyridine ?

$${Is}\:{Resonance}\:{possible}\:{in}\:{Pyridine}\:? \\ $$

Question Number 51289    Answers: 1   Comments: 5

Question Number 51287    Answers: 1   Comments: 0

Question Number 51286    Answers: 1   Comments: 0

Question Number 51284    Answers: 1   Comments: 1

If x is real, show that (2 + j)e^((1 + j3)x) + (2 − j)e^((1 − j3)x) is also real

$$\mathrm{If}\:\:\boldsymbol{\mathrm{x}}\:\mathrm{is}\:\mathrm{real},\:\mathrm{show}\:\mathrm{that}\:\:\left(\mathrm{2}\:+\:\mathrm{j}\right)\mathrm{e}^{\left(\mathrm{1}\:+\:\mathrm{j3}\right)\boldsymbol{\mathrm{x}}} \:+\:\left(\mathrm{2}\:−\:\boldsymbol{\mathrm{j}}\right)\boldsymbol{\mathrm{e}}^{\left(\mathrm{1}\:−\:\boldsymbol{\mathrm{j}}\mathrm{3}\right)\boldsymbol{\mathrm{x}}} \\ $$$$\mathrm{is}\:\mathrm{also}\:\mathrm{real} \\ $$

Question Number 51279    Answers: 1   Comments: 1

Question Number 51271    Answers: 1   Comments: 0

Show that the locus of a point which moves so that its distance from the point (ae,0) is e times its distance from the line x=(a/e) is given by the equation (x^2 /a^2 )+(y^2 /(a^2 (1−e^2 )))=1

$${Show}\:{that}\:{the}\:{locus}\:{of}\:{a} \\ $$$${point}\:{which}\:{moves}\:{so} \\ $$$${that}\:{its}\:{distance}\:{from} \\ $$$${the}\:{point}\:\left({ae},\mathrm{0}\right)\:{is}\:{e}\:{times} \\ $$$${its}\:{distance}\:{from}\:{the}\: \\ $$$${line}\:{x}=\frac{{a}}{{e}}\:{is}\:{given}\:{by}\:{the} \\ $$$${equation} \\ $$$$\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{a}^{\mathrm{2}} \left(\mathrm{1}−{e}^{\mathrm{2}} \right)}=\mathrm{1} \\ $$$$ \\ $$

Question Number 51269    Answers: 1   Comments: 0

Find the ecentricity If (1)lactus rectum is half major axis (2)lactus rectum is half minor axis

$${Find}\:{the}\:{ecentricity}\:{If} \\ $$$$\left(\mathrm{1}\right){lactus}\:{rectum}\:{is}\:{half} \\ $$$${major}\:{axis} \\ $$$$\left(\mathrm{2}\right){lactus}\:{rectum}\:{is}\:{half} \\ $$$${minor}\:{axis} \\ $$

Question Number 51263    Answers: 1   Comments: 0

If P = 2 + j3 and Q = 2 − j3 and R = j1 Show that angle PRQ is right angle

$$\mathrm{If}\:\:\mathrm{P}\:=\:\mathrm{2}\:+\:\mathrm{j3}\:\mathrm{and}\:\mathrm{Q}\:=\:\mathrm{2}\:−\:\mathrm{j3}\:\mathrm{and}\:\mathrm{R}\:=\:\mathrm{j1} \\ $$$$\mathrm{Show}\:\mathrm{that}\:\:\mathrm{angle}\:\:\mathrm{PRQ}\:\mathrm{is}\:\mathrm{right}\:\mathrm{angle} \\ $$

Question Number 51250    Answers: 1   Comments: 0

Given that z_1 = R_1 + R + jωL ; z_2 = R_2 ; z_3 = (1/(jωC_3 )) and z_4 = R_4 + (1/(jωC_4 )) and also that z_1 z_3 = z_2 z_4 , express R and L in terms of the real constants R_1 , R_2 , R_4 , C_3 and C_4 Answer: R = ((R_2 C_3 − R_1 C_4 )/C_4 ) , L = R_2 R_4 C_3

$$\mathrm{Given}\:\mathrm{that}\:\:\:\mathrm{z}_{\mathrm{1}} \:=\:\mathrm{R}_{\mathrm{1}} \:+\:\mathrm{R}\:+\:\mathrm{j}\omega\mathrm{L}\:;\:\:\:\mathrm{z}_{\mathrm{2}} \:=\:\mathrm{R}_{\mathrm{2}} \:;\:\:\mathrm{z}_{\mathrm{3}} \:=\:\frac{\mathrm{1}}{\mathrm{j}\omega\mathrm{C}_{\mathrm{3}} } \\ $$$$\mathrm{and}\:\:\mathrm{z}_{\mathrm{4}} \:=\:\mathrm{R}_{\mathrm{4}} \:+\:\frac{\mathrm{1}}{\mathrm{j}\omega\mathrm{C}_{\mathrm{4}} }\:\:\mathrm{and}\:\mathrm{also}\:\mathrm{that}\:\:\:\mathrm{z}_{\mathrm{1}} \mathrm{z}_{\mathrm{3}} \:\:=\:\:\mathrm{z}_{\mathrm{2}} \mathrm{z}_{\mathrm{4}} \:,\:\:\:\mathrm{express}\: \\ $$$$\mathrm{R}\:\mathrm{and}\:\mathrm{L}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{real}\:\mathrm{constants}\:\:\mathrm{R}_{\mathrm{1}} ,\:\mathrm{R}_{\mathrm{2}} ,\:\mathrm{R}_{\mathrm{4}} ,\:\mathrm{C}_{\mathrm{3}} \:\mathrm{and}\:\mathrm{C}_{\mathrm{4}} \\ $$$$ \\ $$$$\mathrm{Answer}:\:\:\:\:\:\:\mathrm{R}\:=\:\frac{\mathrm{R}_{\mathrm{2}} \mathrm{C}_{\mathrm{3}} \:−\:\mathrm{R}_{\mathrm{1}} \mathrm{C}_{\mathrm{4}} }{\mathrm{C}_{\mathrm{4}} }\:,\:\:\:\:\:\:\:\:\mathrm{L}\:=\:\mathrm{R}_{\mathrm{2}} \mathrm{R}_{\mathrm{4}} \mathrm{C}_{\mathrm{3}} \\ $$

  Pg 1512      Pg 1513      Pg 1514      Pg 1515      Pg 1516      Pg 1517      Pg 1518      Pg 1519      Pg 1520      Pg 1521   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com