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Question Number 24351 Answers: 0 Comments: 0

Question Number 24347 Answers: 0 Comments: 2

Question Number 24352 Answers: 0 Comments: 1

for what value of y will ((x^2 + 4)/(6x − 8)) lies between a positive integer.

$$\mathrm{for}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:\mathrm{y}\:\mathrm{will}\:\:\frac{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4}}{\mathrm{6x}\:−\:\mathrm{8}}\:\:\mathrm{lies}\:\mathrm{between}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer}. \\ $$

Question Number 24233 Answers: 2 Comments: 0

if (d^2 y/dx^2 )=ksiny then y=?

$${if}\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }={ksiny}\:{then}\:{y}=? \\ $$

Question Number 24227 Answers: 3 Comments: 1

Question Number 24186 Answers: 0 Comments: 4

(n − 1) equal point masses each of mass m are placed at the vertices of a regular n-polygon. The vacant vertex has a position vector a with respect to the centre of the polygon. Find the position vector of centre of mass.

$$\left({n}\:−\:\mathrm{1}\right)\:\mathrm{equal}\:\mathrm{point}\:\mathrm{masses}\:\mathrm{each}\:\mathrm{of}\:\mathrm{mass} \\ $$$${m}\:\mathrm{are}\:\mathrm{placed}\:\mathrm{at}\:\mathrm{the}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{a}\:\mathrm{regular} \\ $$$${n}-\mathrm{polygon}.\:\mathrm{The}\:\mathrm{vacant}\:\mathrm{vertex}\:\mathrm{has}\:\mathrm{a} \\ $$$$\mathrm{position}\:\mathrm{vector}\:{a}\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{centre}\:\mathrm{of}\:\mathrm{the}\:\mathrm{polygon}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{position} \\ $$$$\mathrm{vector}\:\mathrm{of}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{mass}. \\ $$

Question Number 24184 Answers: 0 Comments: 9

Question Number 24181 Answers: 1 Comments: 0

if the points C(−1,2) divides internally the line segment joining the points A(2,5) and B(x,y) in the ratio 3:4 find the value of x^2 +y^2

$${if}\:{the}\:{points}\:{C}\left(−\mathrm{1},\mathrm{2}\right)\:{divides}\:{internally}\:{the}\:{line}\:{segment}\:{joining}\:{the}\:{points}\:{A}\left(\mathrm{2},\mathrm{5}\right)\:{and}\:{B}\left({x},{y}\right)\:{in}\:{the}\:{ratio}\:\mathrm{3}:\mathrm{4}\:{find}\:{the}\:{value}\:{of}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \\ $$

Question Number 24178 Answers: 0 Comments: 6

A block is released from rest at the top of a frictionless incline plane 16.00m long.It reaches the bottom 4.0s later.A second block is projected up the plane from the bottom at the instant the first one is released in such a way that it returns to the bottom simultaneously with the first block.Find: a)the acceleration of each block on the incline plane b)the initial velocity of the first block. c)how far up the incline plane did the second block travel. d)What angle does the plane makes with the horizontal. (g=10m/s^2 )

$${A}\:{block}\:{is}\:{released}\:{from}\:{rest}\:{at}\:{the} \\ $$$${top}\:{of}\:{a}\:{frictionless}\:{incline} \\ $$$${plane}\:\mathrm{16}.\mathrm{00}{m}\:{long}.{It}\:{reaches}\:{the} \\ $$$${bottom}\:\mathrm{4}.\mathrm{0}{s}\:{later}.{A}\:{second}\:{block} \\ $$$${is}\:{projected}\:{up}\:{the}\:{plane}\:{from}\:{the} \\ $$$${bottom}\:{at}\:{the}\:{instant}\:{the}\:{first}\:{one} \\ $$$${is}\:{released}\:{in}\:{such}\:{a}\:{way}\:{that}\:{it} \\ $$$${returns}\:{to}\:{the}\:{bottom}\:{simultaneously} \\ $$$${with}\:{the}\:{first}\:{block}.{Find}: \\ $$$$\left.{a}\right){the}\:{acceleration}\:{of}\:{each}\:{block} \\ $$$${on}\:{the}\:{incline}\:{plane} \\ $$$$\left.{b}\right){the}\:{initial}\:{velocity}\:{of}\:{the}\:{first} \\ $$$${block}. \\ $$$$\left.{c}\right){how}\:{far}\:{up}\:{the}\:{incline}\:{plane} \\ $$$${did}\:{the}\:{second}\:{block}\:{travel}. \\ $$$$\left.{d}\right){What}\:{angle}\:{does}\:{the}\:{plane}\:{makes} \\ $$$${with}\:{the}\:{horizontal}. \\ $$$$\left({g}=\mathrm{10}{m}/{s}^{\mathrm{2}} \right) \\ $$

Question Number 24177 Answers: 2 Comments: 1

A lorry goes round an unbanked curve.If the radius of the curve is 30m and the coefficient of friction between the ground and the tyre is 0.6. Calculate the maximum speed of the lorry. (g=10m/s^2 ) please buddies help

$${A}\:{lorry}\:{goes}\:{round}\:{an}\:{unbanked} \\ $$$${curve}.{If}\:{the}\:{radius}\:{of}\:{the}\:{curve} \\ $$$${is}\:\mathrm{30}{m}\:{and}\:{the}\:{coefficient}\:{of} \\ $$$${friction}\:{between}\:{the}\:{ground}\:{and} \\ $$$${the}\:{tyre}\:{is}\:\mathrm{0}.\mathrm{6}.\:{Calculate}\:{the} \\ $$$${maximum}\:{speed}\:{of}\:{the}\:{lorry}. \\ $$$$\left({g}=\mathrm{10}{m}/{s}^{\mathrm{2}} \right) \\ $$$$ \\ $$$$ \\ $$$${please}\:{buddies}\:{help} \\ $$

Question Number 24172 Answers: 1 Comments: 1

Question Number 24168 Answers: 0 Comments: 4

A plank of mass M kg is sliding on the smooth horizontal surface with constant velocity of 10 ms^(−1) . A another block of mass M kg is gently placed on it. The coefficient of friction between the block and the upper surface of the plank is 0.2. Assuming that plank is long enough such that the block does not fall from it. The velocity-time graph of the block is [Take g = 10 m/s^2 ]

$$\mathrm{A}\:\mathrm{plank}\:\mathrm{of}\:\mathrm{mass}\:{M}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{sliding}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{smooth}\:\mathrm{horizontal}\:\mathrm{surface}\:\mathrm{with}\:\mathrm{constant} \\ $$$$\mathrm{velocity}\:\mathrm{of}\:\mathrm{10}\:\mathrm{ms}^{−\mathrm{1}} .\:\mathrm{A}\:\mathrm{another}\:\mathrm{block}\:\mathrm{of} \\ $$$$\mathrm{mass}\:{M}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{gently}\:\mathrm{placed}\:\mathrm{on}\:\mathrm{it}.\:\mathrm{The} \\ $$$$\mathrm{coefficient}\:\mathrm{of}\:\mathrm{friction}\:\mathrm{between}\:\mathrm{the} \\ $$$$\mathrm{block}\:\mathrm{and}\:\mathrm{the}\:\mathrm{upper}\:\mathrm{surface}\:\mathrm{of}\:\mathrm{the}\:\mathrm{plank} \\ $$$$\mathrm{is}\:\mathrm{0}.\mathrm{2}.\:\mathrm{Assuming}\:\mathrm{that}\:\mathrm{plank}\:\mathrm{is}\:\mathrm{long} \\ $$$$\mathrm{enough}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{block}\:\mathrm{does}\:\mathrm{not}\:\mathrm{fall} \\ $$$$\mathrm{from}\:\mathrm{it}.\:\mathrm{The}\:\mathrm{velocity}-\mathrm{time}\:\mathrm{graph}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{block}\:\mathrm{is}\:\left[\mathrm{Take}\:{g}\:=\:\mathrm{10}\:\mathrm{m}/\mathrm{s}^{\mathrm{2}} \right] \\ $$

Question Number 24164 Answers: 0 Comments: 1

Five moles of an ideal gas expand isothermally and reversibly from a pressure of 10 atm to 2 atm at 300 K. What is the largest mass (approx) which can be lifted through a height of 1 m in this expansion?

$$\mathrm{Five}\:\mathrm{moles}\:\mathrm{of}\:\mathrm{an}\:\mathrm{ideal}\:\mathrm{gas}\:\mathrm{expand} \\ $$$$\mathrm{isothermally}\:\mathrm{and}\:\mathrm{reversibly}\:\mathrm{from}\:\mathrm{a} \\ $$$$\mathrm{pressure}\:\mathrm{of}\:\mathrm{10}\:\mathrm{atm}\:\mathrm{to}\:\mathrm{2}\:\mathrm{atm}\:\mathrm{at}\:\mathrm{300}\:\mathrm{K}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{mass}\:\left(\mathrm{approx}\right) \\ $$$$\mathrm{which}\:\mathrm{can}\:\mathrm{be}\:\mathrm{lifted}\:\mathrm{through}\:\mathrm{a}\:\mathrm{height}\:\mathrm{of} \\ $$$$\mathrm{1}\:\mathrm{m}\:\mathrm{in}\:\mathrm{this}\:\mathrm{expansion}? \\ $$

Question Number 24161 Answers: 2 Comments: 1

A door is hinged at one end and is free to rotate about a vertical axis. Does its weight cause any torque about this axis? Give reason for your answer.

$$\mathrm{A}\:\mathrm{door}\:\mathrm{is}\:\mathrm{hinged}\:\mathrm{at}\:\mathrm{one}\:\mathrm{end}\:\mathrm{and}\:\mathrm{is}\:\mathrm{free} \\ $$$$\mathrm{to}\:\mathrm{rotate}\:\mathrm{about}\:\mathrm{a}\:\mathrm{vertical}\:\mathrm{axis}.\:\mathrm{Does}\:\mathrm{its} \\ $$$$\mathrm{weight}\:\mathrm{cause}\:\mathrm{any}\:\mathrm{torque}\:\mathrm{about}\:\mathrm{this} \\ $$$$\mathrm{axis}?\:\mathrm{Give}\:\mathrm{reason}\:\mathrm{for}\:\mathrm{your}\:\mathrm{answer}. \\ $$

Question Number 24179 Answers: 1 Comments: 0

the line segment joining the points (3,−4) and (1,2) is trisected at the points P and Q if the coordinates of P and Q are (p,−2) and (5/3,q) respectively find the values of p and q.

$${the}\:{line}\:{segment}\:{joining}\:{the}\:{points}\:\left(\mathrm{3},−\mathrm{4}\right)\:{and}\:\left(\mathrm{1},\mathrm{2}\right)\:{is}\:{trisected}\:{at}\:{the}\:{points}\:{P}\:{and}\:{Q}\:{if}\:{the}\:{coordinates}\:{of}\:{P}\:{and}\:{Q}\:{are}\:\left({p},−\mathrm{2}\right)\:{and}\:\left(\mathrm{5}/\mathrm{3},{q}\right)\:{respectively}\:{find}\:{the}\:{values}\:{of}\:{p}\:{and}\:{q}. \\ $$

Question Number 24152 Answers: 0 Comments: 1

Let matrice A = ((a,b),(c,d) ), and A^T = A^(−1) Find d − bc

$$\mathrm{Let}\:\mathrm{matrice}\:{A}\:=\:\begin{pmatrix}{{a}}&{{b}}\\{{c}}&{{d}}\end{pmatrix},\:\mathrm{and}\:{A}^{{T}} \:=\:{A}^{−\mathrm{1}} \\ $$$$\mathrm{Find}\:{d}\:−\:{bc} \\ $$

Question Number 24151 Answers: 0 Comments: 1

y=f(t) and y′′=ksiny y=?

$${y}={f}\left({t}\right)\:{and}\:{y}''={ksiny}\:{y}=? \\ $$

Question Number 24211 Answers: 1 Comments: 13

Question Number 24142 Answers: 0 Comments: 2

Prove that Σ_(r=1) ^(2n−1) (−1)^(r−1) (∫_0 ^1 x^r (1−x)^(2n−r) dx) =∫_0 ^1 [(1−x)^(2n) +x^(2n) −(1−x)^(2n+1) −x^(2n+1) ]dx

$${Prove}\:{that} \\ $$$$\underset{{r}=\mathrm{1}} {\overset{\mathrm{2}{n}−\mathrm{1}} {\sum}}\left(−\mathrm{1}\right)^{{r}−\mathrm{1}} \left(\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}^{{r}} \left(\mathrm{1}−{x}\right)^{\mathrm{2}{n}−{r}} {dx}\right) \\ $$$$=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\left[\left(\mathrm{1}−{x}\right)^{\mathrm{2}{n}} +{x}^{\mathrm{2}{n}} −\left(\mathrm{1}−{x}\right)^{\mathrm{2}{n}+\mathrm{1}} −{x}^{\mathrm{2}{n}+\mathrm{1}} \right]{dx} \\ $$

Question Number 24127 Answers: 1 Comments: 1

Question Number 24125 Answers: 1 Comments: 1

Question Number 24150 Answers: 0 Comments: 0

if y is a function of t then solve this y′′=ksiny diff.equ

$${if}\:{y}\:{is}\:{a}\:{function}\:{of}\:{t}\:{then}\:{solve}\:{this}\:{y}''={ksiny}\:{diff}.{equ} \\ $$

Question Number 24149 Answers: 1 Comments: 0

Question Number 24111 Answers: 1 Comments: 1

Question Number 24100 Answers: 1 Comments: 1

The distance between point P(lat 65°S, long 25°E) and Q(lat 65°S, long X) on the earth surface along the parallel of latitute is 2502.5 km. If π = ((22)/2) and earth radius is 6370 km, find the two possible values of x.

$$\mathrm{The}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{point}\:\:\mathrm{P}\left(\mathrm{lat}\:\mathrm{65}°\mathrm{S},\:\:\mathrm{long}\:\mathrm{25}°\mathrm{E}\right)\:\mathrm{and}\:\mathrm{Q}\left(\mathrm{lat}\:\mathrm{65}°\mathrm{S},\:\mathrm{long}\:\mathrm{X}\right) \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{earth}\:\mathrm{surface}\:\mathrm{along}\:\mathrm{the}\:\mathrm{parallel}\:\mathrm{of}\:\mathrm{latitute}\:\mathrm{is}\:\:\mathrm{2502}.\mathrm{5}\:\mathrm{km}.\:\mathrm{If}\:\:\pi\:=\:\frac{\mathrm{22}}{\mathrm{2}} \\ $$$$\mathrm{and}\:\mathrm{earth}\:\mathrm{radius}\:\mathrm{is}\:\:\mathrm{6370}\:\mathrm{km},\:\mathrm{find}\:\mathrm{the}\:\mathrm{two}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}. \\ $$

Question Number 24098 Answers: 1 Comments: 0

sin^(−1) ((ax)/c)+sin^(−1) ((bx)/c)=sin^(−1) x [When a^2 +b^2 =c^2 ]

$$\mathrm{sin}^{−\mathrm{1}} \frac{{ax}}{{c}}+\mathrm{sin}^{−\mathrm{1}} \frac{{bx}}{{c}}=\mathrm{sin}^{−\mathrm{1}} {x}\:\:\:\:\:\left[{When}\:\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={c}^{\mathrm{2}} \:\right] \\ $$

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