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Question Number 25387 Answers: 1 Comments: 0

∫((12x)/((2−x)(3−x)(4−x)))dx

$$\int\frac{\mathrm{12}{x}}{\left(\mathrm{2}−{x}\right)\left(\mathrm{3}−{x}\right)\left(\mathrm{4}−{x}\right)}{dx} \\ $$$$ \\ $$

Question Number 25381 Answers: 1 Comments: 0

The first term of a sequence is 1, the second is 2 and every term is the sum of the two preceding terms. The n^(th) term is.

$$\mathrm{The}\:\mathrm{first}\:\mathrm{term}\:\mathrm{of}\:\mathrm{a}\:\mathrm{sequence}\:\mathrm{is}\:\mathrm{1},\:\mathrm{the} \\ $$$$\mathrm{second}\:\mathrm{is}\:\mathrm{2}\:\mathrm{and}\:\mathrm{every}\:\mathrm{term}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{two}\:\mathrm{preceding}\:\mathrm{terms}.\:\mathrm{The}\:{n}^{\mathrm{th}} \:\mathrm{term} \\ $$$$\mathrm{is}. \\ $$

Question Number 25379 Answers: 2 Comments: 0

lim_(x → 0) ((((1 + x)^a − 1)/x)) for a ∈ R Don′t using L′hospital rules.

$$\underset{\mathrm{x}\:\rightarrow\:\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\left(\mathrm{1}\:+\:\mathrm{x}\right)^{\mathrm{a}} \:−\:\mathrm{1}}{\mathrm{x}}\right)\:\mathrm{for}\:\mathrm{a}\:\in\:\mathbb{R} \\ $$$$ \\ $$$$\mathrm{Don}'\mathrm{t}\:\mathrm{using}\:\mathrm{L}'\mathrm{hospital}\:\mathrm{rules}. \\ $$

Question Number 25378 Answers: 1 Comments: 0

If log x, log y, log z (x,y,z > 1) are in GP then 2x+log(bx), 3x+log(by), 4x+log(bz) are in A.P. True/False?

$${If}\:\mathrm{log}\:{x},\:\mathrm{log}\:{y},\:\mathrm{log}\:{z}\:\left({x},{y},{z}\:>\:\mathrm{1}\right)\:{are}\:{in} \\ $$$${GP}\:{then}\:\mathrm{2}{x}+\mathrm{log}\left({bx}\right),\:\mathrm{3}{x}+\mathrm{log}\left({by}\right), \\ $$$$\mathrm{4}{x}+\mathrm{log}\left({bz}\right)\:{are}\:{in}\:{A}.{P}. \\ $$$$\boldsymbol{{True}}/\boldsymbol{{False}}? \\ $$

Question Number 25377 Answers: 1 Comments: 0

Question Number 25375 Answers: 1 Comments: 0

what is HCF of(1/(3 )) (2/3) (1/4) ?

$${what}\:{is}\:{HCF}\:\:{of}\frac{\mathrm{1}}{\mathrm{3}\:\:}\:\frac{\mathrm{2}}{\mathrm{3}}\:\frac{\mathrm{1}}{\mathrm{4}}\:? \\ $$

Question Number 25374 Answers: 0 Comments: 3

Question Number 25445 Answers: 0 Comments: 0

Question Number 25371 Answers: 0 Comments: 0

If sin α, sin^2 α, 1, sin^4 α and sin^5 α are in AP, where −π<α < π, then α lies in the interval

$$\mathrm{If}\:\mathrm{sin}\:\alpha,\:\mathrm{sin}^{\mathrm{2}} \alpha,\:\mathrm{1},\:\mathrm{sin}^{\mathrm{4}} \alpha\:\mathrm{and}\:\mathrm{sin}^{\mathrm{5}} \alpha\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}, \\ $$$$\mathrm{where}\:\:\:−\pi<\alpha\:<\:\pi,\:\mathrm{then}\:\alpha\:\mathrm{lies}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{interval} \\ $$

Question Number 25344 Answers: 1 Comments: 0

If A and B are two points on a circle of radius r, then prove that mAB^(−) ≤2r.

$$\mathrm{If}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{two}\:\mathrm{points}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{circle}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{r},\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{m}\overline {\mathrm{AB}}\leqslant\mathrm{2r}. \\ $$

Question Number 25343 Answers: 1 Comments: 5

Question Number 25334 Answers: 1 Comments: 0

Three dice are rolled. The number of possible outcomes in which at least one die shows 5 is

$$\mathrm{Three}\:\mathrm{dice}\:\mathrm{are}\:\mathrm{rolled}.\:\mathrm{The}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{possible}\:\mathrm{outcomes}\:\mathrm{in}\:\mathrm{which}\:\mathrm{at}\:\mathrm{least} \\ $$$$\mathrm{one}\:\mathrm{die}\:\mathrm{shows}\:\mathrm{5}\:\mathrm{is} \\ $$

Question Number 25335 Answers: 2 Comments: 0

∫((tan(x))/((1+Cos(x))))dx=? Need help??

$$\int\frac{{tan}\left({x}\right)}{\left(\mathrm{1}+{Cos}\left({x}\right)\right)}{dx}=? \\ $$$${Need}\:{help}?? \\ $$$$ \\ $$

Question Number 25328 Answers: 0 Comments: 2

find the area of a rhombus whose side is 6cm and altitude is 44m. If one of the diagonal is 8cm long then find the length of the other diagonal.

$${find}\:{the}\:{area}\:{of}\:{a}\:{rhombus}\:{whose}\:{side}\:{is}\:\mathrm{6}{cm}\:{and}\:{altitude}\:{is}\:\mathrm{44}{m}.\:{If}\:{one}\:{of}\:{the}\:{diagonal}\:{is}\:\mathrm{8}{cm}\:{long}\:{then}\:{find}\:{the}\:{length}\:{of}\:{the}\:{other}\:{diagonal}. \\ $$

Question Number 25367 Answers: 1 Comments: 1

Question Number 25317 Answers: 2 Comments: 0

solvd for x:((√(2+(√3))))^x +((√(2−(√3))))^x =4

$${solvd}\:{for}\:{x}:\left(\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\right)^{{x}} +\left(\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}\right)^{{x}} =\mathrm{4} \\ $$

Question Number 25315 Answers: 2 Comments: 0

if log_(a ) ^b =log_b ^c =log_c ^a . show that a=b=c

$${if}\:{log}_{{a}\:} ^{{b}} ={log}_{{b}} ^{{c}} ={log}_{{c}} ^{{a}} .\:{show}\:{that}\:{a}={b}={c} \\ $$

Question Number 25314 Answers: 1 Comments: 1

prove that 0!=1

$${prove}\:{that}\:\mathrm{0}!=\mathrm{1} \\ $$

Question Number 25313 Answers: 1 Comments: 0

show tbat log_a ^((a^2 −x^(2)) ) =2+log_a [1−(x^2 /a^2 )]

$${show}\:{tbat}\:{log}_{{a}} ^{\left({a}^{\mathrm{2}} −{x}^{\left.\mathrm{2}\right)} \right.} =\mathrm{2}+{log}_{{a}} \left[\mathrm{1}−\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }\right] \\ $$

Question Number 25308 Answers: 1 Comments: 0

A man pushes a box of 40kg up an incline of 15°.If the man applied a horizontal force 200N and the box moves up the plane a distance of 20m at a constant velocity and the coefficient of friction is 0.10, find a)workdone by the man on the box b)workdone against friction.

$${A}\:{man}\:{pushes}\:{a}\:{box}\:{of}\:\mathrm{40}{kg}\:{up}\:{an} \\ $$$${incline}\:{of}\:\mathrm{15}°.{If}\:{the}\:{man}\:{applied} \\ $$$${a}\:{horizontal}\:{force}\:\mathrm{200}{N}\:{and}\:{the} \\ $$$${box}\:{moves}\:{up}\:{the}\:{plane}\:{a}\:{distance} \\ $$$${of}\:\mathrm{20}{m}\:{at}\:{a}\:{constant}\:{velocity}\:{and} \\ $$$${the}\:{coefficient}\:{of}\:{friction}\:{is}\:\mathrm{0}.\mathrm{10}, \\ $$$${find} \\ $$$$\left.{a}\right){workdone}\:{by}\:{the}\:{man}\:{on}\:{the} \\ $$$${box} \\ $$$$\left.{b}\right){workdone}\:{against}\:{friction}. \\ $$

Question Number 25307 Answers: 0 Comments: 0

An object constrained to move along the x-axis is acted upon by a force F(x) where a=5N/m, b=−2N/m. F(x)=ax+bx^2 The object is observed to proceed directly from x=1m to x=3m. How much work was done by the object by the force?Does the process of integration take into account the fact that the force F(x) changes sign in interval.

$${An}\:{object}\:{constrained}\:{to}\:{move} \\ $$$${along}\:{the}\:{x}-{axis}\:{is}\:{acted}\:{upon}\:{by} \\ $$$${a}\:{force}\:{F}\left({x}\right)\:{where}\:{a}=\mathrm{5}{N}/{m}, \\ $$$${b}=−\mathrm{2}{N}/{m}.\:{F}\left({x}\right)={ax}+{bx}^{\mathrm{2}} \\ $$$${The}\:{object}\:{is}\:{observed}\:{to}\:{proceed} \\ $$$${directly}\:{from}\:{x}=\mathrm{1}{m}\:{to}\:{x}=\mathrm{3}{m}. \\ $$$${How}\:{much}\:{work}\:{was}\:{done}\:{by}\:{the} \\ $$$${object}\:{by}\:{the}\:{force}?{Does}\:{the} \\ $$$${process}\:{of}\:{integration}\:{take}\:{into} \\ $$$${account}\:{the}\:{fact}\:{that}\:{the}\:{force} \\ $$$${F}\left({x}\right)\:{changes}\:{sign}\:{in}\:{interval}. \\ $$

Question Number 25350 Answers: 0 Comments: 0

If A and B are two points in the plane of a circle having radius r and mAB>2r ,prove that at least one of A or B is outside the circle.

$$\mathrm{If}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{two}\:\mathrm{points}\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{plane}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{having} \\ $$$$\mathrm{radius}\:\mathrm{r}\:\mathrm{and}\:\mathrm{mAB}>\mathrm{2r}\:,\mathrm{prove}\:\mathrm{that}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one} \\ $$$$\mathrm{of}\:\mathrm{A}\:\mathrm{or}\:\mathrm{B}\:\mathrm{is}\:\mathrm{outside}\:\mathrm{the}\:\mathrm{circle}. \\ $$

Question Number 25300 Answers: 0 Comments: 2

Question Number 25295 Answers: 1 Comments: 0

X and Y can do a work in 30 days and 60 days respectively. If they work on alternate days beginning with X, in how many days will the work be completed?

$$\mathrm{X}\:\mathrm{and}\:\mathrm{Y}\:\mathrm{can}\:\mathrm{do}\:\mathrm{a}\:\mathrm{work}\:\mathrm{in}\:\mathrm{30}\:\mathrm{days}\:\mathrm{and} \\ $$$$\mathrm{60}\:\mathrm{days}\:\mathrm{respectively}.\:\mathrm{If}\:\mathrm{they}\:\mathrm{work}\:\mathrm{on} \\ $$$$\mathrm{alternate}\:\mathrm{days}\:\mathrm{beginning}\:\mathrm{with}\:\mathrm{X},\:\mathrm{in} \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{days}\:\mathrm{will}\:\mathrm{the}\:\mathrm{work}\:\mathrm{be} \\ $$$$\mathrm{completed}? \\ $$

Question Number 25310 Answers: 0 Comments: 0

Question Number 25290 Answers: 2 Comments: 0

∫((x dx)/(√(a^4 +x^4 )))

$$\int\frac{{x}\:{dx}}{\sqrt{{a}^{\mathrm{4}} +{x}^{\mathrm{4}} }} \\ $$

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