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AllQuestion and Answers: Page 1533

Question Number 49536    Answers: 3   Comments: 2

Question Number 49534    Answers: 1   Comments: 3

Question Number 49530    Answers: 3   Comments: 3

Question Number 49526    Answers: 1   Comments: 1

Question Number 49583    Answers: 0   Comments: 4

Question Number 49491    Answers: 1   Comments: 0

$${A}\:{rocket}\:{of}\:{mass}\:\mathrm{1000}{kg}\:{containing} \\ $$$${a}\:\:{propellant}\:{gas}\:{of}\:\mathrm{3000}{kg}\:{is}\:{to} \\ $$$${be}\:{launched}\:{vertically}.{If}\:{the}\:{fuel} \\ $$$${is}\:{consumed}\:{at}\:{a}\:{steady}\:{rate}\:{of} \\ $$$$\mathrm{60}{kg}/{s}.{Calculate}\:{the}\:{least}\:{velocith} \\ $$$${of}\:{the}\:{exhaust}\:{gases}\:{if}\:{the}\:{rocket} \\ $$$${and}\:{the}\:{content}\:{will}\:{just}\:{lift}\:{off} \\ $$$${the}\:{launching}\:{pad}\:{immediately} \\ $$$${after}\:{firing}? \\ $$

Question Number 49487    Answers: 0   Comments: 2

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sequence}:\:\:\mathrm{5},\:\:\mathrm{5},\:\:\mathrm{35},\:\mathrm{65},\:\:\mathrm{275},\:... \\ $$$$ \\ $$$$\mathrm{Answer}:\:\:\:\:\:\mathrm{3}^{\boldsymbol{\mathrm{n}}} \:−\:\left(−\:\mathrm{2}\right)^{\boldsymbol{\mathrm{n}}} \:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{ple}}\mathrm{1ase}\:\mathrm{how} \\ $$

Question Number 49482    Answers: 1   Comments: 14

$${Find}\:{number}\:{of}\:\mathrm{4}−{letter}\:{words}\:{which} \\ $$$${can}\:{be}\:{formed}\:{using}\:{the}\:{letters}\:{of}\: \\ $$$${the}\:{word}\:'{ALLAHABAD}'\:{such}\:{that}: \\ $$$${NO}\:{repetition}\:{of}\:{letter}\:{and}\:{word}\:{should} \\ $$$${start}\:``{either}''\:{from}\:{H}\:``{or}''\:{ends}\:{with}\:{D}\:? \\ $$

Question Number 49468    Answers: 1   Comments: 0

Question Number 49466    Answers: 0   Comments: 0

$${show}\:{that}\:{the}\:{area}\:{of}\:{the}\:{triangle}\:{whose}\:{vertics}\:{area}\:\left(\mathrm{0},\mathrm{0},\mathrm{0}\right)\:,\:\left({x}_{\mathrm{1}} ,{y}_{\mathrm{1}} ,{z}_{\mathrm{1}} \right)\:,\:\left({x}_{\mathrm{2}} ,{y}_{\mathrm{2},} {z}_{\mathrm{2}} \right)\:{is}\:\mathrm{1}/\mathrm{2}\left(\sqrt{\Sigma\left({y}_{\mathrm{1}} {z}_{\mathrm{2}} −{y}_{\mathrm{2}} {z}_{\mathrm{1}} \right)^{\mathrm{2}} \:.}\right. \\ $$

Question Number 49464    Answers: 2   Comments: 2

$$\mathrm{If}\:\:\mathrm{9}\sqrt{{x}}=\sqrt{\mathrm{12}}+\sqrt{\mathrm{147}},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:{x}\:\mathrm{is} \\ $$

Question Number 49463    Answers: 1   Comments: 0

$$\mathrm{If}\:\:\:\mathrm{7}^{\mathrm{log}\:_{\mathrm{7}} \left({x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{5}\right)} =\:{x}−\mathrm{1},\:\:{x}\:\mathrm{may}\:\mathrm{have} \\ $$$$\mathrm{values} \\ $$

Question Number 49462    Answers: 2   Comments: 0

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{2}\mid{x}\mid^{\mathrm{2}} −\:\mathrm{7}\mid{x}\mid\:+\:\mathrm{6}=\mathrm{0}. \\ $$

Question Number 49461    Answers: 2   Comments: 0

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{for}\:{x}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{equation}\:{x}^{\mathrm{2}} −\mid{x}\mid−\mathrm{2}=\mathrm{0}\:\:\mathrm{is} \\ $$

Question Number 49460    Answers: 0   Comments: 2

$$\mathrm{If}\:\:{x}=\mathrm{1}+{i}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{root}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$${x}^{\mathrm{3}} −{ix}+\mathrm{1}−{i}=\mathrm{0}\:,\:\mathrm{then}\:\mathrm{the}\:\mathrm{other}\:\mathrm{real} \\ $$$$\mathrm{root}\:\mathrm{is} \\ $$

Question Number 49459    Answers: 2   Comments: 0

$$\mathrm{If}\:\mathrm{tan}\:\theta=\frac{\mathrm{cos}\:\mathrm{9}°+\mathrm{sin}\:\mathrm{9}°}{\mathrm{cos}\:\mathrm{9}°−\mathrm{sin}\:\mathrm{9}°}\:\mathrm{then}\:\theta\:=\:\_\_\_ \\ $$

Question Number 49457    Answers: 0   Comments: 0

$${evaluate}\:\int{x}^{\mathrm{3}\:} {J}_{\mathrm{3}} \left({x}\right){dx} \\ $$

Question Number 49433    Answers: 3   Comments: 6

Question Number 49430    Answers: 0   Comments: 1

Question Number 49427    Answers: 0   Comments: 1

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sequence}:\:\:\:\mathrm{5},\:\:\mathrm{5},\:\:\mathrm{35},\:\:\mathrm{65},\:\:\mathrm{275},\:... \\ $$

Question Number 49408    Answers: 1   Comments: 3

$${Find}\:{the}\:{number}\:{of}\:{all}\:{such}\:\mathrm{7}−{digit} \\ $$$${no}.\:{which}\:{satisfy}\:{conditions}: \\ $$$$\left.\mathrm{1}\right)\:{divisible}\:{by}\:\mathrm{3} \\ $$$$\left.\mathrm{2}\right)\:{repetition}\:{allowed} \\ $$$$\left.\mathrm{3}\right)\:{zero}\:{is}\:{not}\:{used}. \\ $$

Question Number 49396    Answers: 0   Comments: 0

$${Here}\:{is}\:{floods}\:{of}\:{questions}...{number}\:{of}\:{batsman} \\ $$$${limited}\:{but}\:{bowlers}\:{are}\:{all}...\:{so}\:{pls}\:{limit}\:{your} \\ $$$${questions}...{if}\:{everybody}\:{posts}\:{questions}\:{who} \\ $$$${will}\:{answer}... \\ $$$${so}\:{pls}\:{limit}\:{questions}... \\ $$

Question Number 49394    Answers: 1   Comments: 1

Question Number 49392    Answers: 1   Comments: 0

Question Number 49389    Answers: 2   Comments: 0

$${for}\:{x}\neq\mathrm{0},{y}\neq\mathrm{0},\mathrm{xy}\neq−\mathrm{1},{f}\left(\mathrm{1}\right)=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)+\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{y}}\right)=\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\right)+\frac{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}}{\mathrm{1}+\boldsymbol{\mathrm{xy}}} \\ $$$$\mathrm{1}.{find}:\:{f}\left({x}\right),\left[{if}\:{possible}\right] \\ $$$$\mathrm{2}.{find}\::{f}^{−\mathrm{1}} \left(\mathrm{1}\right),\left[{if}\:{possible}\right]. \\ $$

Question Number 49384    Answers: 1   Comments: 1

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