Question and Answers Forum

OthersQuestion and Answers: Page 121

Question Number 27603 Answers: 0 Comments: 1

Find the value of i^i ?

$${Find}\:\:{the}\:{value}\:{of}\:\:\:{i}^{{i}} \:\:? \\ $$$$ \\ $$$$ \\ $$

Question Number 27536 Answers: 0 Comments: 0

m_1 s_1 (x−𝛉)=m_2 s_2 (𝛉−y) ; x=? ;y=? 𝛉=? solve it as an equation....

$$\boldsymbol{\mathrm{m}}_{\mathrm{1}} \boldsymbol{\mathrm{s}}_{\mathrm{1}} \left(\boldsymbol{\mathrm{x}}−\boldsymbol{\theta}\right)=\boldsymbol{\mathrm{m}}_{\mathrm{2}} \boldsymbol{\mathrm{s}}_{\mathrm{2}} \left(\boldsymbol{\theta}−\boldsymbol{\mathrm{y}}\right)\:\:\:;\:\boldsymbol{\mathrm{x}}=?\:;\boldsymbol{\mathrm{y}}=?\:\boldsymbol{\theta}=? \\ $$$$\mathrm{solve}\:\mathrm{it}\:\mathrm{as}\:\mathrm{an}\:\mathrm{equation}.... \\ $$

Question Number 27520 Answers: 0 Comments: 0

Question Number 27430 Answers: 0 Comments: 0

A 2000kg space capsule is traveling away from the earth, determine the gravitational field strenght and gravitational force on the capsule due to the earth when it is (a) At a distance from the earth′s surface equal to the radius of the earth (b) At a very large distance away from the earth (Take g = 9.8Nkg^(−1) on earth surface)

$$\mathrm{A}\:\mathrm{2000kg}\:\mathrm{space}\:\mathrm{capsule}\:\mathrm{is}\:\mathrm{traveling}\:\mathrm{away}\:\mathrm{from}\:\mathrm{the}\:\mathrm{earth},\:\mathrm{determine}\:\mathrm{the} \\ $$$$\mathrm{gravitational}\:\mathrm{field}\:\mathrm{strenght}\:\mathrm{and}\:\mathrm{gravitational}\:\mathrm{force}\:\mathrm{on}\:\mathrm{the}\:\mathrm{capsule}\:\mathrm{due}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{earth}\:\mathrm{when}\:\mathrm{it}\:\mathrm{is} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{At}\:\mathrm{a}\:\mathrm{distance}\:\mathrm{from}\:\mathrm{the}\:\mathrm{earth}'\mathrm{s}\:\mathrm{surface}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{At}\:\mathrm{a}\:\mathrm{very}\:\mathrm{large}\:\mathrm{distance}\:\mathrm{away}\:\mathrm{from}\:\mathrm{the}\:\mathrm{earth}\:\left(\mathrm{Take}\:\:\mathrm{g}\:=\:\mathrm{9}.\mathrm{8Nkg}^{−\mathrm{1}} \:\mathrm{on}\right. \\ $$$$\left.\mathrm{earth}\:\mathrm{surface}\right) \\ $$

Question Number 27427 Answers: 0 Comments: 0

A particle of mass 2kg moves in a force field depending on a time t given by F = 24t^2 i + (36t − 16)j − 12tk assuming that at t = 0 the particle is located at r_0 = 3i − j + 4k and has v_0 = 6i + 5j − 8k. Find (a) Velocity at any time t (b) Position at any time t (c) τ (torgue) at any time t (d) Angular momentum at any time t above the Origin

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{2kg}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{a}\:\mathrm{force}\:\mathrm{field}\:\mathrm{depending}\:\mathrm{on}\:\mathrm{a}\:\mathrm{time}\:\mathrm{t}\:\mathrm{given}\:\mathrm{by} \\ $$$$\mathrm{F}\:=\:\mathrm{24t}^{\mathrm{2}} \mathrm{i}\:+\:\left(\mathrm{36t}\:−\:\mathrm{16}\right)\mathrm{j}\:−\:\mathrm{12tk}\:\:\:\mathrm{assuming}\:\mathrm{that}\:\mathrm{at}\:\mathrm{t}\:=\:\mathrm{0}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{located} \\ $$$$\mathrm{at}\:\:\mathrm{r}_{\mathrm{0}} \:=\:\mathrm{3i}\:−\:\mathrm{j}\:+\:\mathrm{4k}\:\:\mathrm{and}\:\:\mathrm{has}\:\:\:\mathrm{v}_{\mathrm{0}} \:=\:\mathrm{6i}\:+\:\mathrm{5j}\:−\:\mathrm{8k}.\:\mathrm{Find} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Velocity}\:\mathrm{at}\:\mathrm{any}\:\mathrm{time}\:\mathrm{t} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Position}\:\mathrm{at}\:\mathrm{any}\:\mathrm{time}\:\mathrm{t} \\ $$$$\left(\mathrm{c}\right)\:\tau\:\left(\mathrm{torgue}\right)\:\mathrm{at}\:\mathrm{any}\:\mathrm{time}\:\mathrm{t} \\ $$$$\left(\mathrm{d}\right)\:\mathrm{Angular}\:\mathrm{momentum}\:\mathrm{at}\:\mathrm{any}\:\mathrm{time}\:\mathrm{t}\:\mathrm{above}\:\mathrm{the}\:\mathrm{Origin} \\ $$

Question Number 27428 Answers: 0 Comments: 0

Find the workdone in moving an object along a vector r = 3i + 2j − 5k if the applied force is F = 2i − j − k

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{workdone}\:\mathrm{in}\:\mathrm{moving}\:\mathrm{an}\:\mathrm{object}\:\mathrm{along}\:\mathrm{a}\:\mathrm{vector} \\ $$$$\mathrm{r}\:=\:\mathrm{3i}\:+\:\mathrm{2j}\:−\:\mathrm{5k}\:\:\:\mathrm{if}\:\mathrm{the}\:\mathrm{applied}\:\mathrm{force}\:\mathrm{is}\:\:\mathrm{F}\:=\:\mathrm{2i}\:−\:\mathrm{j}\:−\:\mathrm{k} \\ $$

Question Number 27399 Answers: 1 Comments: 0

A and B are walking along a circular track.They start from same point at 8:00 am. A can walk 2 rounds per hour and B can walk 3 rounds per hour. How many times they cross each other before 9:30 am if they walk (i) Opposite to each other. (ii) In same direction. ?

$$\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{walking}\:\mathrm{along}\:\mathrm{a} \\ $$$$\mathrm{circular}\:\mathrm{track}.\mathrm{They}\:\mathrm{start}\:\mathrm{from} \\ $$$$\mathrm{same}\:\mathrm{point}\:\mathrm{at}\:\mathrm{8}:\mathrm{00}\:\mathrm{am}. \\ $$$$\mathrm{A}\:\mathrm{can}\:\mathrm{walk}\:\mathrm{2}\:\mathrm{rounds}\:\mathrm{per}\:\mathrm{hour} \\ $$$$\mathrm{and}\:\mathrm{B}\:\mathrm{can}\:\mathrm{walk}\:\mathrm{3}\:\mathrm{rounds}\:\mathrm{per}\:\mathrm{hour}. \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{times}\:\mathrm{they}\:\mathrm{cross}\:\mathrm{each} \\ $$$$\mathrm{other}\:\mathrm{before}\:\mathrm{9}:\mathrm{30}\:\mathrm{am}\:\mathrm{if}\:\mathrm{they}\:\mathrm{walk} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Opposite}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{In}\:\mathrm{same}\:\mathrm{direction}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:? \\ $$

Question Number 27335 Answers: 0 Comments: 1

if 2 chords of ellipse have the same distance from the centre of ellipse and the eccentric angle of the end points of the chords are respectivly α β γ δ then prove that tan (α/2)×tan (β/2)×tan (γ/2)×tan (δ/2)=1

$${if}\:\mathrm{2}\:{chords}\:{of}\:{ellipse}\:{have}\:{the}\:{same} \\ $$$${distance}\:{from}\:{the}\:{centre}\:{of}\:{ellipse} \\ $$$${and}\:{the}\:{eccentric}\:{angle}\:{of}\:{the}\:{end}\:{points}\:{of}\:{the}\:{chords} \\ $$$${are}\:{respectivly}\:\alpha\:\beta\:\gamma\:\delta\:{then}\:{prove}\:{that} \\ $$$$\mathrm{tan}\:\frac{\alpha}{\mathrm{2}}×\mathrm{tan}\:\frac{\beta}{\mathrm{2}}×\mathrm{tan}\:\frac{\gamma}{\mathrm{2}}×\mathrm{tan}\:\frac{\delta}{\mathrm{2}}=\mathrm{1} \\ $$

Question Number 27334 Answers: 1 Comments: 0

(q_1 /q_2 )=((x/(0.8−x)))^2 ; x=?

$$\frac{\mathrm{q}_{\mathrm{1}} }{\mathrm{q}_{\mathrm{2}} }=\left(\frac{\mathrm{x}}{\mathrm{0}.\mathrm{8}−\mathrm{x}}\right)^{\mathrm{2}} \:\:\:\:;\:\boldsymbol{\mathrm{x}}=? \\ $$

Question Number 27332 Answers: 1 Comments: 1

Question Number 27293 Answers: 1 Comments: 0

L^(−1) ((s^3 /(s^4 +4)))=?

$${L}^{−\mathrm{1}} \left(\frac{{s}^{\mathrm{3}} }{{s}^{\mathrm{4}} +\mathrm{4}}\right)=? \\ $$

Question Number 27254 Answers: 1 Comments: 0

Question Number 27253 Answers: 0 Comments: 0

Question Number 27204 Answers: 1 Comments: 0

if g(x)=f(x)+f(1−x) and f^((2)) (x)<0 then show that g(x) is increasing in (0,1/2) and g(x) is decreasing in (1/2,1)

$$\mathrm{if}\:{g}\left({x}\right)={f}\left({x}\right)+{f}\left(\mathrm{1}−{x}\right) \\ $$$$\mathrm{and}\:{f}^{\left(\mathrm{2}\right)} \left({x}\right)<\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{show}\:\mathrm{that}\: \\ $$$${g}\left({x}\right)\:\mathrm{is}\:\mathrm{increasing}\:\mathrm{in}\:\left(\mathrm{0},\mathrm{1}/\mathrm{2}\right)\:\mathrm{and} \\ $$$${g}\left({x}\right)\:\mathrm{is}\:\mathrm{decreasing}\:\mathrm{in}\:\left(\mathrm{1}/\mathrm{2},\mathrm{1}\right) \\ $$

Question Number 27159 Answers: 0 Comments: 0

(√(1−x^(6 ) )) +(√(1−y^6 )) =k^3 (x^3 −y^3 ) then prove that (dy/dx)=((x^2 (√(1−x^2 )))/(y^2 (√(1−y^(2Δ) ))))

$$\sqrt{\mathrm{1}−{x}^{\mathrm{6}\:} \:}\:+\sqrt{\mathrm{1}−{y}^{\mathrm{6}} }\:={k}^{\mathrm{3}} \left({x}^{\mathrm{3}} −{y}^{\mathrm{3}} \right)\:\:\:{then}\:{prove}\:{that}\:\:\:\frac{{dy}}{{dx}}=\frac{{x}^{\mathrm{2}} \sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{{y}^{\mathrm{2}} \sqrt{\mathrm{1}−{y}^{\mathrm{2}\Delta} }} \\ $$$$ \\ $$$$ \\ $$

Question Number 27073 Answers: 1 Comments: 0

∫ln x×cos 2ln xdx

$$\int\mathrm{ln}\:{x}×\mathrm{cos}\:\mathrm{2ln}\:{xdx} \\ $$

Question Number 26909 Answers: 1 Comments: 0

∫((e^x ((1/x)−(2/x^3 )))/(−2))dx

$$\int\frac{{e}^{{x}} \left(\frac{\mathrm{1}}{{x}}−\frac{\mathrm{2}}{{x}^{\mathrm{3}} }\right)}{−\mathrm{2}}{dx} \\ $$

Question Number 26839 Answers: 1 Comments: 0

a=3 b=6 a−b=?

$$\mathrm{a}=\mathrm{3}\:\mathrm{b}=\mathrm{6} \\ $$$$\mathrm{a}−\mathrm{b}=? \\ $$

Question Number 26812 Answers: 1 Comments: 0

sum of infinite seris tan^(−1) (2/n^2 )

$${sum}\:{of}\:{infinite}\:{seris} \\ $$$$\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{2}/{n}^{\mathrm{2}} \right) \\ $$

Question Number 26801 Answers: 0 Comments: 0

find expansion of α^3 +β^3 +γ^3

$${find}\:{expansion}\:{of}\:\alpha^{\mathrm{3}} +\beta^{\mathrm{3}} +\gamma^{\mathrm{3}} \\ $$

Question Number 26686 Answers: 1 Comments: 1

Question Number 26681 Answers: 0 Comments: 1

f:R×R→R such that f(x+iy)=(√(x^2 +y^2 .)) Then f is a) many−one and into function b) one−one and onto function c) many−one and onto function d) one−one and into function

$${f}:{R}×{R}\rightarrow{R}\:{such}\:{that}\:{f}\left({x}+{iy}\right)=\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} .} \\ $$$${Then}\:{f}\:{is} \\ $$$$\left.{a}\right)\:{many}−{one}\:{and}\:{into}\:{function} \\ $$$$\left.{b}\right)\:{one}−{one}\:{and}\:{onto}\:{function} \\ $$$$\left.{c}\right)\:{many}−{one}\:{and}\:{onto}\:{function} \\ $$$$\left.{d}\right)\:{one}−{one}\:{and}\:{into}\:{function} \\ $$

Question Number 26634 Answers: 1 Comments: 1

Question Number 26625 Answers: 1 Comments: 0

3y−2x+7=0 x^2 −4y^2 −21=0

$$\mathrm{3y}−\mathrm{2x}+\mathrm{7}=\mathrm{0} \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{4y}^{\mathrm{2}} −\mathrm{21}=\mathrm{0} \\ $$

Question Number 26623 Answers: 2 Comments: 0

distance between 2 places A and B on road is 70 km. a car starts from A and other from B .if they travel in same direction they will meet after 7 hours. if they travel towards each other they will meet after 1 hour then find their speeds

$$\mathrm{distance}\:\mathrm{between}\:\mathrm{2}\:\mathrm{places}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{on} \\ $$$$\mathrm{road}\:\mathrm{is}\:\mathrm{70}\:\mathrm{km}.\:\mathrm{a}\:\mathrm{car}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{A}\:\mathrm{and}\:\mathrm{other}\: \\ $$$$\mathrm{from}\:\mathrm{B}\:.\mathrm{if}\:\mathrm{they}\:\mathrm{travel}\:\mathrm{in}\:\mathrm{same}\:\mathrm{direction} \\ $$$$\mathrm{they}\:\mathrm{will}\:\mathrm{meet}\:\mathrm{after}\:\mathrm{7}\:\mathrm{hours}.\:\mathrm{if}\:\mathrm{they}\:\mathrm{travel} \\ $$$$\mathrm{towards}\:\mathrm{each}\:\mathrm{other}\:\mathrm{they}\:\mathrm{will}\:\mathrm{meet}\:\mathrm{after} \\ $$$$\mathrm{1}\:\mathrm{hour}\:\mathrm{then}\:\mathrm{find}\:\mathrm{their}\:\mathrm{speeds} \\ $$

Question Number 26581 Answers: 0 Comments: 0

Pg 116 Pg 117 Pg 118 Pg 119 Pg 120 Pg 121 Pg 122 Pg 123 Pg 124 Pg 125

Contact: info@tinkutara.com