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Question Number 25129 Answers: 1 Comments: 1

Question Number 25122 Answers: 0 Comments: 1

3_C_1 + 4_C_2 + 5_C_3 +...........+ 49_C_(47) = ? where n_C_r = ((n!)/(r!×(n−r)!)) .

$$\:\mathrm{3}_{{C}_{\mathrm{1}} } \:+\:\mathrm{4}_{{C}_{\mathrm{2}} } \:+\:\mathrm{5}_{{C}_{\mathrm{3}} } \:+...........+\:\mathrm{49}_{{C}_{\mathrm{47}} } \:=\:? \\ $$$${where}\:{n}_{{C}_{{r}} } \:=\:\frac{{n}!}{{r}!×\left({n}−{r}\right)!}\:. \\ $$

Question Number 25125 Answers: 1 Comments: 1

A vertical stick 12 cm long casts a shadow of 8 cm long on the ground . At the same time, a tower casts a shadow of 40 m long on the ground. find the hight of the tower ?

$$\boldsymbol{\mathrm{A}}\:\mathrm{vertical}\:\mathrm{stick}\:\mathrm{12}\:\boldsymbol{\mathrm{cm}}\:\mathrm{long}\:\mathrm{casts}\:\mathrm{a}\: \\ $$$$\mathrm{shadow}\:\mathrm{of}\:\mathrm{8}\:\boldsymbol{\mathrm{cm}}\:\mathrm{long}\:\mathrm{on}\:\mathrm{the}\:\mathrm{ground}\:. \\ $$$$\mathrm{At}\:\mathrm{the}\:\mathrm{same}\:\mathrm{time},\:\mathrm{a}\:\mathrm{tower}\:\mathrm{casts}\:\mathrm{a}\: \\ $$$$\mathrm{shadow}\:\mathrm{of}\:\mathrm{40}\:\boldsymbol{\mathrm{m}}\:\mathrm{long}\:\mathrm{on}\:\mathrm{the}\:\mathrm{ground}.\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{hight}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tower}\:? \\ $$

Question Number 25114 Answers: 0 Comments: 1

Question Number 25113 Answers: 0 Comments: 1

Question Number 25112 Answers: 0 Comments: 1

Question Number 25109 Answers: 1 Comments: 0

Question Number 25103 Answers: 1 Comments: 0

Question Number 25091 Answers: 1 Comments: 0

A particle of mass m moving with speed u collides perfectly inelastically with a sphere of radius R and same mass, at rest, at an impact parameter d. Find (a) Angle between their final velocities (b) Magnitude of their final velocities

$${A}\:{particle}\:{of}\:{mass}\:{m}\:{moving}\:{with} \\ $$$${speed}\:{u}\:{collides}\:{perfectly}\:{inelastically} \\ $$$${with}\:{a}\:{sphere}\:{of}\:{radius}\:{R}\:{and}\:{same} \\ $$$${mass},\:{at}\:{rest},\:{at}\:{an}\:{impact}\:{parameter} \\ $$$${d}.\:{Find} \\ $$$$\left({a}\right)\:{Angle}\:{between}\:{their}\:{final}\:{velocities} \\ $$$$\left({b}\right)\:{Magnitude}\:{of}\:{their}\:{final} \\ $$$${velocities} \\ $$

Question Number 25094 Answers: 1 Comments: 0

Question Number 25088 Answers: 1 Comments: 1

Q...((x+7)/(x+4))>1, x∈R

$$ \\ $$$$ \\ $$$$ \\ $$$${Q}...\frac{{x}+\mathrm{7}}{{x}+\mathrm{4}}>\mathrm{1},\:\:\:\:\:{x}\in{R} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 25086 Answers: 0 Comments: 4

Question Number 25085 Answers: 1 Comments: 0

If a_n −a_(n−1) =1 for every positive integer greater than 1, then a_1 +a_2 +a_3 +...a_(100) equals (1) 5000 . a_1 (2) 5050 . a_1 (3) 5051 . a_1 (3) 5052 . a_2

$${If}\:{a}_{{n}} −{a}_{{n}−\mathrm{1}} =\mathrm{1}\:{for}\:{every}\:{positive} \\ $$$${integer}\:{greater}\:{than}\:\mathrm{1},\:{then}\:{a}_{\mathrm{1}} +{a}_{\mathrm{2}} +{a}_{\mathrm{3}} \\ $$$$+...{a}_{\mathrm{100}} \:{equals} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{5000}\:.\:{a}_{\mathrm{1}} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{5050}\:.\:{a}_{\mathrm{1}} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{5051}\:.\:{a}_{\mathrm{1}} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{5052}\:.\:{a}_{\mathrm{2}} \\ $$

Question Number 25068 Answers: 1 Comments: 0

Evaluate lim_(x→(π/2)) (((tan2x)/(x−π/2)))

$${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\left(\frac{{tan}\mathrm{2}{x}}{{x}−\pi/\mathrm{2}}\right) \\ $$

Question Number 25074 Answers: 0 Comments: 1

Question Number 25075 Answers: 1 Comments: 0

Let z_1 and z_2 be two roots of the equation z^2 +az+b=0, z being complex. Further assume that the origin, z_1 and z_2 form an equilateral triangle. Then,

$$\mathrm{Let}\:{z}_{\mathrm{1}} \mathrm{and}\:{z}_{\mathrm{2}} \:\mathrm{be}\:\mathrm{two}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$${z}^{\mathrm{2}} +{az}+{b}=\mathrm{0},\:{z}\:\mathrm{being}\:\mathrm{complex}.\:\mathrm{Further} \\ $$$$\mathrm{assume}\:\mathrm{that}\:\mathrm{the}\:\mathrm{origin},\:{z}_{\mathrm{1}} \:\mathrm{and}\:{z}_{\mathrm{2}} \:\mathrm{form} \\ $$$$\mathrm{an}\:\mathrm{equilateral}\:\mathrm{triangle}.\:\mathrm{Then}, \\ $$

Question Number 25066 Answers: 1 Comments: 0

let a,b,c,x,y and z be complex number such that a=((b+c)/(x−2)) ,b=((c+a)/(y−2)) c=((a+b)/(z−2)). xy +yz +zx=1000 and x+y+z=2016 find the value of xyz.

$${let}\:{a},{b},{c},{x},{y}\:{and}\:{z}\:{be}\:{complex}\:{number} \\ $$$${such}\:{that}\:{a}=\frac{{b}+{c}}{{x}−\mathrm{2}}\:,{b}=\frac{{c}+{a}}{{y}−\mathrm{2}}\:\:\:\:{c}=\frac{{a}+{b}}{{z}−\mathrm{2}}. \\ $$$${xy}\:+{yz}\:+{zx}=\mathrm{1000}\:{and}\:{x}+{y}+{z}=\mathrm{2016} \\ $$$${find}\:{the}\:{value}\:{of}\:{xyz}. \\ $$

Question Number 25076 Answers: 1 Comments: 0

A man can row 6 km/h in still water. When the river is running at 1.2 km/h, it takes]him 1 hour to row to a place and back. How far is the place?

$$\mathrm{A}\:\mathrm{man}\:\mathrm{can}\:\mathrm{row}\:\mathrm{6}\:\mathrm{km}/\mathrm{h}\:\mathrm{in}\:\mathrm{still}\:\mathrm{water}. \\ $$$$\mathrm{When}\:\mathrm{the}\:\mathrm{river}\:\mathrm{is}\:\mathrm{running}\:\mathrm{at}\:\mathrm{1}.\mathrm{2}\:\mathrm{km}/\mathrm{h}, \\ $$$$\left.\mathrm{it}\:\mathrm{takes}\right]\mathrm{him}\:\mathrm{1}\:\mathrm{hour}\:\mathrm{to}\:\mathrm{row}\:\mathrm{to}\:\mathrm{a}\:\mathrm{place}\: \\ $$$$\mathrm{and}\:\mathrm{back}.\:\mathrm{How}\:\mathrm{far}\:\mathrm{is}\:\mathrm{the}\:\mathrm{place}? \\ $$

Question Number 25058 Answers: 1 Comments: 0

Two objects slide over a frictionless horizontal surface. The first object, mass m_1 = 5 kg, is propelled with a speed u = 4.5 m/s towards the second object, mass m_2 = 5 kg, which is initially at rest. After the collision, both objects have velocities which are directed at θ = 60° on either side of the original line of motion of the first object. What can you say about the elasticity of collision?

$${Two}\:{objects}\:{slide}\:{over}\:{a}\:{frictionless} \\ $$$${horizontal}\:{surface}.\:{The}\:{first}\:{object}, \\ $$$${mass}\:{m}_{\mathrm{1}} \:=\:\mathrm{5}\:{kg},\:{is}\:{propelled}\:{with}\:{a} \\ $$$${speed}\:{u}\:=\:\mathrm{4}.\mathrm{5}\:{m}/{s}\:{towards}\:{the}\:{second} \\ $$$${object},\:{mass}\:{m}_{\mathrm{2}} \:=\:\mathrm{5}\:{kg},\:{which}\:{is} \\ $$$${initially}\:{at}\:{rest}.\:{After}\:{the}\:{collision}, \\ $$$${both}\:{objects}\:{have}\:{velocities}\:{which}\:{are} \\ $$$${directed}\:{at}\:\theta\:=\:\mathrm{60}°\:{on}\:{either}\:{side}\:{of} \\ $$$${the}\:{original}\:{line}\:{of}\:{motion}\:{of}\:{the} \\ $$$${first}\:{object}.\:{What}\:{can}\:{you}\:{say}\:{about} \\ $$$${the}\:{elasticity}\:{of}\:{collision}? \\ $$

Question Number 25054 Answers: 1 Comments: 0

If x:y=5:2, then find the value of (8x+9y)/(8x+27)

$${If}\:{x}:{y}=\mathrm{5}:\mathrm{2},\:{then}\:{find}\:{the}\:{value}\:{of}\:\left(\mathrm{8}{x}+\mathrm{9}{y}\right)/\left(\mathrm{8}{x}+\mathrm{27}\right) \\ $$

Question Number 25053 Answers: 2 Comments: 0

If 2A=3B=4C find the value of A:B:C

$${If}\:\mathrm{2}{A}=\mathrm{3}{B}=\mathrm{4}{C}\:{find}\:{the}\:{value}\:{of}\:{A}:{B}:{C} \\ $$

Question Number 25049 Answers: 1 Comments: 1

If I = Σ_(k=1) ^(98) ∫_k ^(k+1) ((k + 1)/(x(x + 1)))dx, then (1) I > ((49)/(50)) (2) I < ((49)/(50)) (3) I < log_e 99 (4) I > log_e 99

$$\mathrm{If}\:{I}\:=\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{98}} {\sum}}\underset{{k}} {\overset{{k}+\mathrm{1}} {\int}}\frac{{k}\:+\:\mathrm{1}}{{x}\left({x}\:+\:\mathrm{1}\right)}{dx},\:\mathrm{then} \\ $$$$\left(\mathrm{1}\right)\:{I}\:>\:\frac{\mathrm{49}}{\mathrm{50}} \\ $$$$\left(\mathrm{2}\right)\:{I}\:<\:\frac{\mathrm{49}}{\mathrm{50}} \\ $$$$\left(\mathrm{3}\right)\:{I}\:<\:\mathrm{log}_{{e}} \mathrm{99} \\ $$$$\left(\mathrm{4}\right)\:{I}\:>\:\mathrm{log}_{{e}} \mathrm{99} \\ $$

Question Number 25046 Answers: 1 Comments: 0

Show that (a) N=((10^(143) −1)/9) is composite, and (b) N has two factors each of which is a series of a G.P.