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Question Number 111125 Answers: 1 Comments: 0

Question Number 111152 Answers: 0 Comments: 0

Question Number 111282 Answers: 1 Comments: 0

A particle of mass 500g is placed on a plane inclined at an angle 30° to the horizontal. What force is (i) acting parallel to the plane (ii) acting horizontally is required to hold the particle at rest (g=10m/s^2 )

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{500g}\:\mathrm{is}\:\mathrm{placed}\:\mathrm{on}\:\mathrm{a}\: \\ $$$$\mathrm{plane}\:\mathrm{inclined}\:\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{30}° \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{horizontal}.\:\mathrm{What}\:\mathrm{force}\:\mathrm{is} \\ $$$$\left(\mathrm{i}\right)\:\mathrm{acting}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the}\:\mathrm{plane} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{acting}\:\mathrm{horizontally}\:\mathrm{is}\:\mathrm{required}\:\mathrm{to} \\ $$$$\mathrm{hold}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{at}\:\mathrm{rest}\:\left(\mathrm{g}=\mathrm{10m}/\mathrm{s}^{\mathrm{2}} \right) \\ $$

Question Number 111278 Answers: 1 Comments: 0

Towns A,B,C and D are located on the vertices of a square whose area is 1000km^2 . There is a straight line highway passing through the centre of the square but not through any of the towns. Find the sum of the squares of the distances of the towns to the highway.

$$\mathrm{Towns}\:\mathrm{A},\mathrm{B},\mathrm{C}\:\mathrm{and}\:\mathrm{D}\:\mathrm{are}\:\mathrm{located}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{a}\:\mathrm{square}\:\mathrm{whose}\:\mathrm{area}\:\mathrm{is} \\ $$$$\mathrm{1000km}^{\mathrm{2}} .\:\mathrm{There}\:\mathrm{is}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line} \\ $$$$\mathrm{highway}\:\mathrm{passing}\:\mathrm{through}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{square}\:\mathrm{but}\:\mathrm{not}\:\mathrm{through}\:\mathrm{any}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{towns}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{squares} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{distances}\:\mathrm{of}\:\mathrm{the}\:\mathrm{towns}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{highway}. \\ $$

Question Number 111114 Answers: 2 Comments: 0

4 sin 36° cos 72° sin 108° ?

$$\mathrm{4}\:\mathrm{sin}\:\mathrm{36}°\:\mathrm{cos}\:\mathrm{72}°\:\mathrm{sin}\:\mathrm{108}°\:?\: \\ $$

Question Number 111109 Answers: 0 Comments: 0

Question Number 111105 Answers: 1 Comments: 1

y′′+2y′+y=e^(−2x) +2x+3

$$\mathrm{y}''+\mathrm{2y}'+\mathrm{y}=\mathrm{e}^{−\mathrm{2x}} +\mathrm{2x}+\mathrm{3} \\ $$

Question Number 111104 Answers: 2 Comments: 2

Question Number 111103 Answers: 3 Comments: 0

(√(bemath)) lim_(x→0) ((ln (sin 3x))/(ln (sin 8x))) ? [ Without L′Hopital ]

$$\:\:\sqrt{\mathrm{bemath}} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\left(\mathrm{sin}\:\mathrm{3x}\right)}{\mathrm{ln}\:\left(\mathrm{sin}\:\mathrm{8x}\right)}\:? \\ $$$$\left[\:\mathrm{Without}\:\mathrm{L}'\mathrm{Hopital}\:\right] \\ $$$$ \\ $$

Question Number 111100 Answers: 2 Comments: 0

lim_(x→1^+ ) ((x−1)/( (√(x^2 −1)))) ?

$$\underset{{x}\rightarrow\mathrm{1}^{+} } {\mathrm{lim}}\:\frac{\mathrm{x}−\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}}\:? \\ $$

Question Number 111069 Answers: 0 Comments: 0

θ′′(t)+(g/l)sinθ=0

$$\theta''\left({t}\right)+\frac{{g}}{{l}}{sin}\theta=\mathrm{0} \\ $$

Question Number 111067 Answers: 0 Comments: 2

Question Number 111062 Answers: 0 Comments: 2

Question Number 111048 Answers: 0 Comments: 0

Question Number 111047 Answers: 0 Comments: 0

Question Number 111046 Answers: 0 Comments: 1

Question Number 111045 Answers: 0 Comments: 0

Question Number 111044 Answers: 1 Comments: 4

Question Number 111043 Answers: 0 Comments: 0

solve the integral ∫_0 ^∞ (dx/((√x)(1+x^2 +x^4 )^(3/4) ))dx

$${solve}\:{the}\:{integral} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{\sqrt{{x}}\left(\mathrm{1}+{x}^{\mathrm{2}} +{x}^{\mathrm{4}} \right)^{\frac{\mathrm{3}}{\mathrm{4}}} }{dx} \\ $$

Question Number 111039 Answers: 1 Comments: 0

solve ∫_0 ^1 (√(1+x^6 ))dx mr abbo your question

$${solve}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}+{x}^{\mathrm{6}} }{dx} \\ $$$${mr}\:\:{abbo}\:{your}\:{question}\: \\ $$

Question Number 111035 Answers: 1 Comments: 0

If b∈Z^+ ∀ both the roots of equation x^2 −bx+132=0 are integers. Find (1)the largest possible value of b (2)the smallest possible value of b.

$$\mathrm{If}\:{b}\in\mathbb{Z}^{+} \:\forall\:\mathrm{both}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{equation} \\ $$$${x}^{\mathrm{2}} −{bx}+\mathrm{132}=\mathrm{0}\:\mathrm{are}\:\mathrm{integers}. \\ $$$$\mathrm{Find} \\ $$$$\left(\mathrm{1}\right)\mathrm{the}\:\mathrm{largest}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:{b} \\ $$$$\left(\mathrm{2}\right)\mathrm{the}\:\mathrm{smallest}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:{b}. \\ $$

Question Number 111029 Answers: 1 Comments: 0

Question Number 111083 Answers: 2 Comments: 0

(√(bemath)) (1)∫ (dx/(3sin x+sin^3 x)) (2) lim_(x→∞) x(5^(1/x) −1) (3) find the asymptotes (x^2 /a^2 ) − (y^2 /b^2 ) = 1

$$\:\:\:\sqrt{\mathrm{bemath}} \\ $$$$\left(\mathrm{1}\right)\int\:\frac{\mathrm{dx}}{\mathrm{3sin}\:\mathrm{x}+\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}} \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{x}\left(\mathrm{5}^{\frac{\mathrm{1}}{\mathrm{x}}} \:−\mathrm{1}\right)\: \\ $$$$\left(\mathrm{3}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{asymptotes}\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{a}^{\mathrm{2}} }\:−\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} }\:=\:\mathrm{1}\: \\ $$

Question Number 111082 Answers: 1 Comments: 1

[∫_0 ^∞ JS dx ] ∫_0 ^(π/2) ((sin (x)(4+sin^2 (x)))/((4−sin^2 (x))^2 )) dx ?

$$\:\:\:\left[\int_{\mathrm{0}} ^{\infty} {JS}\:{dx}\:\right] \\ $$$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{sin}\:\left({x}\right)\left(\mathrm{4}+\mathrm{sin}\:^{\mathrm{2}} \left({x}\right)\right)}{\left(\mathrm{4}−\mathrm{sin}\:^{\mathrm{2}} \left({x}\right)\right)^{\mathrm{2}} }\:{dx}\:? \\ $$

Question Number 111080 Answers: 1 Comments: 0

(√(bemath)) (1)Σ_(k=50) ^(100) (1/(k(151−k))) ? (2) without L′Hopital and series find the value of lim_(x→0) ((xcos x−sin x)/(x^2 sin x))

$$\:\:\sqrt{\mathrm{bemath}} \\ $$$$\left(\mathrm{1}\right)\underset{\mathrm{k}=\mathrm{50}} {\overset{\mathrm{100}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{k}\left(\mathrm{151}−\mathrm{k}\right)}\:? \\ $$$$\left(\mathrm{2}\right)\:\mathrm{without}\:\mathrm{L}'\mathrm{Hopital}\:\mathrm{and}\:\mathrm{series}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{xcos}\:\mathrm{x}−\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{2}} \mathrm{sin}\:\mathrm{x}} \\ $$

Question Number 111079 Answers: 1 Comments: 0

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