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AllQuestion and Answers: Page 1934

Question Number 14336 Answers: 1 Comments: 2

Question Number 14310 Answers: 0 Comments: 0

Question Number 20978 Answers: 0 Comments: 0

A particle is observed from two frames S_1 and S_2 . The frame S_2 moves with respect to S_1 with an acceleration a. Let P_1 and P_2 be the pseudo forces on the particle when seen from S_1 and S_2 respectively. Which of the following are not possible? (1) P_1 ≠ 0, P_2 ≠ 0 (2) P_1 ≠ 0, P_2 = 0 (3) P_1 = 0, P_2 ≠ 0 (4) P_1 = 0, P_2 = 0

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{observed}\:\mathrm{from}\:\mathrm{two}\:\mathrm{frames} \\ $$$${S}_{\mathrm{1}} \:\mathrm{and}\:{S}_{\mathrm{2}} .\:\mathrm{The}\:\mathrm{frame}\:{S}_{\mathrm{2}} \:\mathrm{moves}\:\mathrm{with} \\ $$$$\mathrm{respect}\:\mathrm{to}\:{S}_{\mathrm{1}} \:\mathrm{with}\:\mathrm{an}\:\mathrm{acceleration}\:{a}. \\ $$$$\mathrm{Let}\:{P}_{\mathrm{1}} \:\mathrm{and}\:{P}_{\mathrm{2}} \:\mathrm{be}\:\mathrm{the}\:\mathrm{pseudo}\:\mathrm{forces}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{particle}\:\mathrm{when}\:\mathrm{seen}\:\mathrm{from}\:{S}_{\mathrm{1}} \:\mathrm{and}\:{S}_{\mathrm{2}} \\ $$$$\mathrm{respectively}.\:\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{are} \\ $$$$\mathrm{not}\:\mathrm{possible}? \\ $$$$\left(\mathrm{1}\right)\:{P}_{\mathrm{1}} \:\neq\:\mathrm{0},\:{P}_{\mathrm{2}} \:\neq\:\mathrm{0} \\ $$$$\left(\mathrm{2}\right)\:{P}_{\mathrm{1}} \:\neq\:\mathrm{0},\:{P}_{\mathrm{2}} \:=\:\mathrm{0} \\ $$$$\left(\mathrm{3}\right)\:{P}_{\mathrm{1}} \:=\:\mathrm{0},\:{P}_{\mathrm{2}} \:\neq\:\mathrm{0} \\ $$$$\left(\mathrm{4}\right)\:{P}_{\mathrm{1}} \:=\:\mathrm{0},\:{P}_{\mathrm{2}} \:=\:\mathrm{0} \\ $$

Question Number 14306 Answers: 1 Comments: 3

Question Number 14297 Answers: 0 Comments: 8

Select the correct formulae for uniformly accelerated motion along a straight line (More than one option are correct) (1) v = u + at (2) s = (((u + v)/2))t (3) s = vt − (1/2)at^2 (4) s = ((v^2 − u^2 )/(2a))

$$\mathrm{Select}\:\mathrm{the}\:\mathrm{correct}\:\mathrm{formulae}\:\mathrm{for} \\ $$$$\mathrm{uniformly}\:\mathrm{accelerated}\:\mathrm{motion}\:\mathrm{along}\:\mathrm{a} \\ $$$$\mathrm{straight}\:\mathrm{line}\:\left(\mathrm{More}\:\mathrm{than}\:\mathrm{one}\:\mathrm{option}\right. \\ $$$$\left.\mathrm{are}\:\mathrm{correct}\right) \\ $$$$\left(\mathrm{1}\right)\:{v}\:=\:{u}\:+\:{at} \\ $$$$\left(\mathrm{2}\right)\:{s}\:=\:\left(\frac{{u}\:+\:{v}}{\mathrm{2}}\right){t} \\ $$$$\left(\mathrm{3}\right)\:{s}\:=\:{vt}\:−\:\frac{\mathrm{1}}{\mathrm{2}}{at}^{\mathrm{2}} \\ $$$$\left(\mathrm{4}\right)\:{s}\:=\:\frac{{v}^{\mathrm{2}} \:−\:{u}^{\mathrm{2}} }{\mathrm{2}{a}} \\ $$

Question Number 14291 Answers: 1 Comments: 3

Is the equation correct for uniformly accelerated motion along a straight line? s = vt − (1/2)at^2

$$\mathrm{Is}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{correct}\:\mathrm{for}\:\mathrm{uniformly} \\ $$$$\mathrm{accelerated}\:\mathrm{motion}\:\mathrm{along}\:\mathrm{a}\:\mathrm{straight} \\ $$$$\mathrm{line}? \\ $$$${s}\:=\:{vt}\:−\:\frac{\mathrm{1}}{\mathrm{2}}{at}^{\mathrm{2}} \\ $$

Question Number 14288 Answers: 1 Comments: 0

Solve: y′ + (y/x) = 0

$$\mathrm{Solve}:\:\:\mathrm{y}'\:+\:\frac{\mathrm{y}}{\mathrm{x}}\:=\:\mathrm{0} \\ $$

Question Number 14287 Answers: 0 Comments: 5

∫_( 3) ^( ∞) (dx/((x − 3)^2 ))

$$\int_{\:\:\mathrm{3}} ^{\:\:\infty} \:\:\frac{\mathrm{dx}}{\left(\mathrm{x}\:−\:\mathrm{3}\right)^{\mathrm{2}} } \\ $$

Question Number 14284 Answers: 1 Comments: 0

Question Number 14274 Answers: 1 Comments: 0

Question Number 14273 Answers: 1 Comments: 0

Question Number 14269 Answers: 1 Comments: 0

In ΔABC, if sinA+sinB+sinC.=cosA+cosB+cosC+1, then prove that ΔABC is a right triangle.

$${In}\:\Delta{ABC},\:{if}\:{sinA}+{sinB}+{sinC}.={cosA}+{cosB}+{cosC}+\mathrm{1}, \\ $$$${then}\:{prove}\:{that}\:\Delta{ABC}\:{is}\:{a}\:{right}\:{triangle}. \\ $$

Question Number 14268 Answers: 1 Comments: 0

If tanθ + tan2θ = tan3θ, find the exhaustive set of values of θ satisfying the given equation.

$$\mathrm{If}\:\mathrm{tan}\theta\:+\:\mathrm{tan2}\theta\:=\:\mathrm{tan3}\theta,\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{exhaustive}\:\mathrm{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:\theta\:\mathrm{satisfying} \\ $$$$\mathrm{the}\:\mathrm{given}\:\mathrm{equation}. \\ $$

Question Number 14267 Answers: 1 Comments: 0

If sin^3 x + cos^3 x + 3sinxcosx − 1 = 0, then find x.

$$\mathrm{If}\:\mathrm{sin}^{\mathrm{3}} {x}\:+\:\mathrm{cos}^{\mathrm{3}} {x}\:+\:\mathrm{3sin}{x}\mathrm{cos}{x}\:−\:\mathrm{1}\:=\:\mathrm{0}, \\ $$$$\mathrm{then}\:\mathrm{find}\:{x}. \\ $$

Question Number 14246 Answers: 1 Comments: 3

Question Number 14245 Answers: 0 Comments: 0

pls no; 6,7,10,11,and 13

$$\mathrm{pls}\:\mathrm{no};\:\mathrm{6},\mathrm{7},\mathrm{10},\mathrm{11},\mathrm{and}\:\mathrm{13} \\ $$

Question Number 14244 Answers: 1 Comments: 0

Question Number 14219 Answers: 1 Comments: 0

Question Number 14211 Answers: 0 Comments: 11

x^2 +y^2 +xy=4 y^2 +z^2 +yz=9 z^2 +x^2 +zx=16

$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{xy}=\mathrm{4} \\ $$$${y}^{\mathrm{2}} +{z}^{\mathrm{2}} +{yz}=\mathrm{9} \\ $$$${z}^{\mathrm{2}} +{x}^{\mathrm{2}} +{zx}=\mathrm{16} \\ $$

Question Number 14330 Answers: 0 Comments: 1

tanθ+tan2θ=tan3θ ((tanθ+tan2θ)/(1−tanθtan2θ))(1−tanθtan2θ)=tan3θ tan3θ(1−tanθtan2θ)=tan3θ tanθtan2θtan3θ 0 3θ=kπ, where k=0,1,2,3,... θ=((kπ)/3) tanθ=0 or tan2θ=0 or tan 3θ = 0 θ=mπ, where m=0,1,2,3,... 2θ=nπ, where n=0,1,2,3,... θ=((nπ)/2) but θ∉(((p+1)π)/2), p=0,1,2,3,... The exhaustive set ={θ/θ=((kπ)/3) or θ=mπ}

$${tan}\theta+{tan}\mathrm{2}\theta={tan}\mathrm{3}\theta \\ $$$$\frac{{tan}\theta+{tan}\mathrm{2}\theta}{\mathrm{1}−{tan}\theta{tan}\mathrm{2}\theta}\left(\mathrm{1}−{tan}\theta{tan}\mathrm{2}\theta\right)={tan}\mathrm{3}\theta \\ $$$${tan}\mathrm{3}\theta\left(\mathrm{1}−{tan}\theta{tan}\mathrm{2}\theta\right)={tan}\mathrm{3}\theta \\ $$$${tan}\theta{tan}\mathrm{2}\theta{tan}\mathrm{3}\theta\:\mathrm{0} \\ $$$$\mathrm{3}\theta={k}\pi,\:{where}\:{k}=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},... \\ $$$$\theta=\frac{{k}\pi}{\mathrm{3}} \\ $$$${tan}\theta=\mathrm{0}\:\:{or}\:\:{tan}\mathrm{2}\theta=\mathrm{0}\:{or}\:{tan}\:\mathrm{3}\theta\:=\:\mathrm{0} \\ $$$$\theta={m}\pi,\:{where}\:{m}=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},... \\ $$$$\mathrm{2}\theta={n}\pi,\:{where}\:{n}=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},... \\ $$$$\theta=\frac{{n}\pi}{\mathrm{2}}\:{but}\:\theta\notin\frac{\left({p}+\mathrm{1}\right)\pi}{\mathrm{2}},\:{p}=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},... \\ $$$${The}\:{exhaustive}\:{set}\:=\left\{\theta/\theta=\frac{{k}\pi}{\mathrm{3}}\:{or}\:\theta={m}\pi\right\} \\ $$

Question Number 14215 Answers: 1 Comments: 0

Question Number 14243 Answers: 2 Comments: 0

∫ [x (lnx)^2 ] dx

$$\int\:\left[\mathrm{x}\:\left(\mathrm{lnx}\right)^{\mathrm{2}} \right]\:\mathrm{dx} \\ $$

Question Number 14189 Answers: 2 Comments: 0

Solve: (√(sinx)) + (√(cosx)) = 1 x ∈ R

$$\mathrm{Solve}:\:\:\:\sqrt{\mathrm{sinx}}\:+\:\sqrt{\mathrm{cosx}}\:=\:\mathrm{1} \\ $$$$\mathrm{x}\:\in\:\mathrm{R} \\ $$

Question Number 14181 Answers: 1 Comments: 0

∫ sec^6 (x) dx

$$\int\:\mathrm{sec}^{\mathrm{6}} \left(\mathrm{x}\right)\:\:\mathrm{dx}\:\: \\ $$

Question Number 14174 Answers: 1 Comments: 0

xtan(cos^(−1) x)=cos(sin^(−1) x) prove it.....

$$\:\:{xtan}\left({cos}^{−\mathrm{1}} {x}\right)={cos}\left({sin}^{−\mathrm{1}} {x}\right) \\ $$$${prove}\:{it}..... \\ $$

Question Number 14172 Answers: 0 Comments: 0

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