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Question Number 60247 Answers: 0 Comments: 0

A uniform pole PQ, 30 m long and of mass 4 kg is carried by a boy at P and a man 8 m away from Q. Find the distance from P where a mass of 20 kg should be attached so that the man′s support is twice that of the boy, if the system is in equilibrium [Take g=10ms^(−2) ]

$$\mathrm{A}\:\mathrm{uniform}\:\mathrm{pole}\:\mathrm{PQ},\:\mathrm{30}\:\mathrm{m}\:\mathrm{long}\:\mathrm{and}\:\mathrm{of}\:\mathrm{mass} \\ $$$$\mathrm{4}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{carried}\:\mathrm{by}\:\mathrm{a}\:\mathrm{boy}\:\mathrm{at}\:\mathrm{P}\:\mathrm{and}\:\mathrm{a}\:\mathrm{man}\: \\ $$$$\mathrm{8}\:\mathrm{m}\:\mathrm{away}\:\mathrm{from}\:\mathrm{Q}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{from} \\ $$$$\mathrm{P}\:\mathrm{where}\:\mathrm{a}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{20}\:\mathrm{kg}\:\mathrm{should}\:\mathrm{be}\:\mathrm{attached} \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{the}\:\mathrm{man}'\mathrm{s}\:\mathrm{support}\:\mathrm{is}\:\mathrm{twice}\:\mathrm{that} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{boy},\:\mathrm{if}\:\mathrm{the}\:\mathrm{system}\:\mathrm{is}\:\mathrm{in}\:\mathrm{equilibrium} \\ $$$$\left[\mathrm{Take}\:\mathrm{g}=\mathrm{10ms}^{−\mathrm{2}} \right] \\ $$

Question Number 60237 Answers: 0 Comments: 1

Question Number 60234 Answers: 1 Comments: 0

Question Number 60227 Answers: 0 Comments: 0

Question Number 60219 Answers: 1 Comments: 1

C=((2𝛑𝛜𝛜_0 L)/(ln((R_2 /R_1 )))). prove.

$$\boldsymbol{\mathrm{C}}=\frac{\mathrm{2}\boldsymbol{\pi\varepsilon\varepsilon}_{\mathrm{0}} \boldsymbol{\mathrm{L}}}{\boldsymbol{\mathrm{ln}}\left(\frac{\boldsymbol{\mathrm{R}}_{\mathrm{2}} }{\boldsymbol{\mathrm{R}}_{\mathrm{1}} }\right)}. \\ $$$$\boldsymbol{\mathrm{prove}}. \\ $$

Question Number 60241 Answers: 0 Comments: 1

Question Number 60240 Answers: 0 Comments: 1

∫_0 ^2 ((ln(x))/(√(4−x^2 )))dx

$$\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}\frac{\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}\right)}{\sqrt{\mathrm{4}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }}\boldsymbol{\mathrm{dx}} \\ $$

Question Number 60238 Answers: 0 Comments: 0

Question Number 60212 Answers: 1 Comments: 1

Question Number 60203 Answers: 2 Comments: 1

demonstrate ∣sin(y)−sin(x)∣≤∣y−x∣

$${demonstrate}\: \\ $$$$\mid{sin}\left({y}\right)−{sin}\left({x}\right)\mid\leqslant\mid{y}−{x}\mid \\ $$

Question Number 60202 Answers: 0 Comments: 0

construct the point M^′ =(1/2)((((z+∣z∣))/2))

$${construct}\:{the}\:{point}\:{M}^{'} =\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\left({z}+\mid{z}\mid\right)}{\mathrm{2}}\right) \\ $$

Question Number 60197 Answers: 1 Comments: 1

valculste lim_(n→+∞) (ln((Π_(k=1) ^n (1+(k^3 /n^3 )))^(1/n) )

$${valculste}\:{lim}_{{n}\rightarrow+\infty} \left({ln}\left(\left(\prod_{{k}=\mathrm{1}} ^{{n}} \left(\mathrm{1}+\frac{{k}^{\mathrm{3}} }{{n}^{\mathrm{3}} }\right)\right)^{\frac{\mathrm{1}}{{n}}} \right)\right. \\ $$

Question Number 60198 Answers: 1 Comments: 0

find lim_(n→+∞) ln(Π_(k=1) ^n (1+(k^4 /n^4 ))^(1/n) )

$${find}\:{lim}_{{n}\rightarrow+\infty} \:{ln}\left(\prod_{{k}=\mathrm{1}} ^{{n}} \left(\mathrm{1}+\frac{{k}^{\mathrm{4}} }{{n}^{\mathrm{4}} }\right)^{\frac{\mathrm{1}}{{n}}} \right) \\ $$

Question Number 60189 Answers: 0 Comments: 0

Question Number 60175 Answers: 0 Comments: 2

solving u^v =w with u, v, w ∈C finding all possible solutions I tested this with several values and found no mistake. please review and comment. I hope this will help at least some of you.

$$\mathrm{solving}\:{u}^{{v}} ={w}\:\mathrm{with}\:{u},\:{v},\:{w}\:\in\mathbb{C} \\ $$$$\mathrm{finding}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solutions} \\ $$$$\mathrm{I}\:\mathrm{tested}\:\mathrm{this}\:\mathrm{with}\:\mathrm{several}\:\mathrm{values}\:\mathrm{and}\:\mathrm{found} \\ $$$$\mathrm{no}\:\mathrm{mistake}.\:\mathrm{please}\:\mathrm{review}\:\mathrm{and}\:\mathrm{comment}. \\ $$$$\mathrm{I}\:\mathrm{hope}\:\mathrm{this}\:\mathrm{will}\:\mathrm{help}\:\mathrm{at}\:\mathrm{least}\:\mathrm{some}\:\mathrm{of}\:\mathrm{you}. \\ $$

Question Number 60170 Answers: 0 Comments: 0

∫xsec^3 xdx

$$\int{x}\mathrm{sec}\:^{\mathrm{3}} {xdx} \\ $$

Question Number 60156 Answers: 3 Comments: 2

Prove by principle of mathematical induction sin(x) + sin(2x) + sin(3x) + ... + sin(nx) = ((cos((1/2)x) − cos(n + (1/2))x)/(2 sin((1/2)x)))

$$\mathrm{Prove}\:\mathrm{by}\:\mathrm{principle}\:\mathrm{of}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{sin}\left(\mathrm{x}\right)\:+\:\mathrm{sin}\left(\mathrm{2x}\right)\:+\:\mathrm{sin}\left(\mathrm{3x}\right)\:+\:...\:+\:\mathrm{sin}\left(\mathrm{nx}\right)\:\:=\:\:\frac{\mathrm{cos}\left(\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}\right)\:−\:\mathrm{cos}\left(\mathrm{n}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{x}}{\mathrm{2}\:\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}\right)} \\ $$

Question Number 60152 Answers: 0 Comments: 16

Join Telegram group @booksforjee To get evry books pdfs related to NEET, JEE(MAIN ADVANCED) and all engineering entrance exam books Also Books for class XII,XI,X,IX

$${Join}\:{Telegram}\:{group} \\ $$$$@{booksforjee} \\ $$$${To}\:{get}\:{evry}\:{books}\:{pdfs} \\ $$$${related}\:{to}\:{NEET},\:{JEE}\left({MAIN}\:{ADVANCED}\right) \\ $$$${and}\:{all}\:{engineering}\:{entrance}\:{exam}\:{books} \\ $$$${Also} \\ $$$${Books}\:{for}\:{class}\:{XII},{XI},{X},{IX} \\ $$

Question Number 60155 Answers: 1 Comments: 0

Show that: (1/2) + cos(x) + cos(2x) + ... + cos(nx) = ((sin(n + (1/2))x)/(2 sin((1/2))x)) By principle of mathematical induction

$$\mathrm{Show}\:\mathrm{that}: \\ $$$$\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\:+\:\mathrm{cos}\left(\mathrm{x}\right)\:+\:\mathrm{cos}\left(\mathrm{2x}\right)\:+\:...\:+\:\mathrm{cos}\left(\mathrm{nx}\right)\:\:=\:\:\frac{\mathrm{sin}\left(\mathrm{n}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{x}}{\mathrm{2}\:\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{x}} \\ $$$$\mathrm{By}\:\mathrm{principle}\:\mathrm{of}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$

Question Number 60143 Answers: 1 Comments: 0

Two passenger trains, A and B, 450km apart, start to move towards each other at the same time and meet after 2 hours. If train B, travels (8/7) as fast as train A, find the speed of each train.

$$\mathrm{Two}\:\mathrm{passenger}\:\mathrm{trains},\:\mathrm{A}\:\mathrm{and}\:\mathrm{B},\:\mathrm{450km}\:\mathrm{apart}, \\ $$$$\mathrm{start}\:\mathrm{to}\:\mathrm{move}\:\mathrm{towards}\:\mathrm{each}\:\mathrm{other}\:\mathrm{at}\:\mathrm{the} \\ $$$$\mathrm{same}\:\mathrm{time}\:\mathrm{and}\:\mathrm{meet}\:\mathrm{after}\:\mathrm{2}\:\mathrm{hours}.\:\mathrm{If}\:\mathrm{train}\:\mathrm{B}, \\ $$$$\mathrm{travels}\:\frac{\mathrm{8}}{\mathrm{7}}\:\mathrm{as}\:\mathrm{fast}\:\mathrm{as}\:\mathrm{train}\:\mathrm{A},\:\mathrm{find}\:\mathrm{the}\:\mathrm{speed} \\ $$$$\mathrm{of}\:\mathrm{each}\:\mathrm{train}. \\ $$

Question Number 60135 Answers: 1 Comments: 0

Question Number 60133 Answers: 2 Comments: 1

Question Number 60132 Answers: 0 Comments: 1

Question Number 60121 Answers: 2 Comments: 3

Question Number 60115 Answers: 0 Comments: 2

Question Number 60095 Answers: 1 Comments: 1

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