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Question Number 27253    Answers: 0   Comments: 0

Question Number 27235    Answers: 1   Comments: 0

(1) There are 60 tickets in a bag numbered 1 through 60.If a ticket is picked at random,find the probability that the number is divisible by 3 or 4 ?

$$\left(\mathrm{1}\right)\:\:\boldsymbol{\mathrm{There}}\:\boldsymbol{\mathrm{are}}\:\mathrm{60}\:\boldsymbol{\mathrm{tickets}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{bag}} \\ $$$$\boldsymbol{\mathrm{numbered}}\:\mathrm{1}\:\boldsymbol{\mathrm{through}}\:\mathrm{60}.\boldsymbol{\mathrm{If}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{ticket}}\: \\ $$$$\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{picked}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{random}},\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\: \\ $$$$\boldsymbol{\mathrm{probability}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{is}} \\ $$$$\boldsymbol{\mathrm{divisible}}\:\boldsymbol{\mathrm{by}}\:\mathrm{3}\:\boldsymbol{\mathrm{or}}\:\mathrm{4}\:? \\ $$

Question Number 27224    Answers: 1   Comments: 4

Question Number 27215    Answers: 1   Comments: 0

find the value of ∫_(−1) ^1 (dx/((√(1−x^2 )) +(√(1+x^2 )))) .

$${find}\:{the}\:{value}\:{of}\:\int_{−\mathrm{1}} ^{\mathrm{1}} \:\:\:\:\frac{{dx}}{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:\:+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:\:. \\ $$

Question Number 27213    Answers: 1   Comments: 1

[(16x^4 −1)]/[2x−1] factorise it

$$\left[\left(\mathrm{16}{x}^{\mathrm{4}} −\mathrm{1}\right)\right]/\left[\mathrm{2}{x}−\mathrm{1}\right]\:{factorise}\:{it} \\ $$

Question Number 27204    Answers: 1   Comments: 0

if g(x)=f(x)+f(1−x) and f^((2)) (x)<0 then show that g(x) is increasing in (0,1/2) and g(x) is decreasing in (1/2,1)

$$\mathrm{if}\:{g}\left({x}\right)={f}\left({x}\right)+{f}\left(\mathrm{1}−{x}\right) \\ $$$$\mathrm{and}\:{f}^{\left(\mathrm{2}\right)} \left({x}\right)<\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{show}\:\mathrm{that}\: \\ $$$${g}\left({x}\right)\:\mathrm{is}\:\mathrm{increasing}\:\mathrm{in}\:\left(\mathrm{0},\mathrm{1}/\mathrm{2}\right)\:\mathrm{and} \\ $$$${g}\left({x}\right)\:\mathrm{is}\:\mathrm{decreasing}\:\mathrm{in}\:\left(\mathrm{1}/\mathrm{2},\mathrm{1}\right) \\ $$

Question Number 27198    Answers: 1   Comments: 0

Question Number 27197    Answers: 1   Comments: 1

Question Number 27203    Answers: 2   Comments: 0

Let S ⊂ (0, π) denote the set of values of x satisfying the equation 8^(1+∣cos x∣+cos^2 x+∣cos^3 x∣+... to ∞) = 4^3 then S =

$$\mathrm{Let}\:{S}\:\subset\:\left(\mathrm{0},\:\pi\right)\:\mathrm{denote}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:{x} \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{8}^{\mathrm{1}+\mid\mathrm{cos}\:{x}\mid+\mathrm{cos}^{\mathrm{2}} {x}+\mid\mathrm{cos}^{\mathrm{3}} {x}\mid+...\:\mathrm{to}\:\infty} =\:\mathrm{4}^{\mathrm{3}} \\ $$$$\mathrm{then}\:{S}\:=\: \\ $$

Question Number 27202    Answers: 1   Comments: 0

Question Number 27527    Answers: 0   Comments: 1

(√5)=2.236 then the valve of 100/(√(125))=?

$$\sqrt{\mathrm{5}}=\mathrm{2}.\mathrm{236}\:{then}\:{the}\:{valve}\:{of}\:\mathrm{100}/\sqrt{\mathrm{125}}=? \\ $$

Question Number 27526    Answers: 1   Comments: 0

(256)^(0.16) ×(256)^(0.09) =?

$$\left(\mathrm{256}\right)^{\mathrm{0}.\mathrm{16}} ×\left(\mathrm{256}\right)^{\mathrm{0}.\mathrm{09}} =? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 27189    Answers: 1   Comments: 0

let give S_(n ) = Σ_(p=1) ^(p=n) arctan ((1/(2p^2 )) ) find lim_(n−>∝) S_n .

$${let}\:{give}\:{S}_{{n}\:} =\:\sum_{{p}=\mathrm{1}} ^{{p}={n}} \:{arctan}\:\left(\frac{\mathrm{1}}{\mathrm{2}{p}^{\mathrm{2}} }\:\right)\:\:{find}\:{lim}_{{n}−>\propto} \:{S}_{{n}} \:\:. \\ $$

Question Number 27187    Answers: 0   Comments: 1

find I= ∫_0 ^∝ ((cosx)/(cosh(x)))dx

$${find}\:{I}=\:\:\int_{\mathrm{0}} ^{\propto} \:\frac{{cosx}}{{cosh}\left({x}\right)}{dx} \\ $$

Question Number 27186    Answers: 1   Comments: 1

find I=∫_0 ^π (dx/(cosx +2sinx)) .

$${find}\:{I}=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dx}}{{cosx}\:+\mathrm{2}{sinx}}\:. \\ $$

Question Number 27185    Answers: 0   Comments: 0

find ∫∫_D (x+y)^2 e^(x^2 −y^2 ) dxdy with D={(x,y)∈R^(2 ) /0<x<1 and 0<y<1−x }.

$${find}\:\:\int\int_{{D}} \left({x}+{y}\right)^{\mathrm{2}} \:{e}^{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } {dxdy}\:{with} \\ $$$${D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}\:} /\mathrm{0}<{x}<\mathrm{1}\:{and}\:\mathrm{0}<{y}<\mathrm{1}−{x}\:\right\}. \\ $$

Question Number 27184    Answers: 0   Comments: 1

calculate in terms of x f(x)= ∫_0 ^(π/(2 )) (dt/(1+xsint)) .

$${calculate}\:{in}\:{terms}\:{of}\:{x}\:\:\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}\:}} \frac{{dt}}{\mathrm{1}+{xsint}}\:. \\ $$

Question Number 27183    Answers: 1   Comments: 0

find the value of I= ∫_0 ^1 ((t−1)/(lnt))dt .

$${find}\:{the}\:{value}\:{of}\:{I}=\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{t}−\mathrm{1}}{{lnt}}{dt}\:. \\ $$

Question Number 27182    Answers: 0   Comments: 1

find the value of I_a = ∫∫_D_a e^(−((x^2 +y^2 )/2)) dxdy with D_a ={(x,y)∈R^2 / x^2 +y^2 ≤ a^2 }

$$\:{find}\:{the}\:{value}\:{of}\:{I}_{{a}} =\:\int\int_{{D}_{{a}} } {e}^{−\frac{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }{\mathrm{2}}} {dxdy}\:\:{with} \\ $$$${D}_{{a}} \:=\left\{\left({x},{y}\right)\in\mathbb{R}^{\mathrm{2}} \:/\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \leqslant\:{a}^{\mathrm{2}} \:\:\right\} \\ $$

Question Number 27168    Answers: 0   Comments: 4

Question Number 27159    Answers: 0   Comments: 0

(√(1−x^(6 ) )) +(√(1−y^6 )) =k^3 (x^3 −y^3 ) then prove that (dy/dx)=((x^2 (√(1−x^2 )))/(y^2 (√(1−y^(2Δ) ))))

$$\sqrt{\mathrm{1}−{x}^{\mathrm{6}\:} \:}\:+\sqrt{\mathrm{1}−{y}^{\mathrm{6}} }\:={k}^{\mathrm{3}} \left({x}^{\mathrm{3}} −{y}^{\mathrm{3}} \right)\:\:\:{then}\:{prove}\:{that}\:\:\:\frac{{dy}}{{dx}}=\frac{{x}^{\mathrm{2}} \sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{{y}^{\mathrm{2}} \sqrt{\mathrm{1}−{y}^{\mathrm{2}\Delta} }} \\ $$$$ \\ $$$$ \\ $$

Question Number 27144    Answers: 1   Comments: 1

Let A={x,y,z} and B={1,2}. Find the number of relations from A to B.

$${Let}\:{A}=\left\{{x},{y},{z}\right\}\:{and}\:{B}=\left\{\mathrm{1},\mathrm{2}\right\}.\:{Find} \\ $$$${the}\:{number}\:{of}\:{relations}\:{from}\:{A}\:{to} \\ $$$${B}. \\ $$

Question Number 27128    Answers: 1   Comments: 0

A body resting on a rough horizontal plane require a pull of 18N inclined at 30° to the plane first to move it.It was found that a push of 22N inclined at 30° to the plane just moved the body. Determine the weight and coefficient of friction.

$${A}\:{body}\:{resting}\:{on}\:{a}\:{rough} \\ $$$${horizontal}\:{plane}\:{require}\:{a}\:{pull}\:{of} \\ $$$$\mathrm{18}{N}\:{inclined}\:{at}\:\mathrm{30}°\:{to}\:{the}\:{plane} \\ $$$${first}\:{to}\:{move}\:{it}.{It}\:{was}\:{found} \\ $$$${that}\:{a}\:{push}\:{of}\:\mathrm{22}{N}\:{inclined}\:{at}\:\mathrm{30}° \\ $$$${to}\:{the}\:{plane}\:{just}\:{moved}\:{the}\:{body}. \\ $$$${Determine}\:{the}\:{weight}\:{and}\: \\ $$$${coefficient}\:{of}\:{friction}. \\ $$

Question Number 27117    Answers: 1   Comments: 0

Question Number 27112    Answers: 0   Comments: 2

Question Number 27104    Answers: 0   Comments: 1

sin45^(o ) cos45^o +(√(3 sin 60°=?))

$$\mathrm{sin45}^{{o}\:} \mathrm{cos45}^{{o}} +\sqrt{\mathrm{3}\:\:\:\mathrm{sin}\:\mathrm{60}°=?} \\ $$

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