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Question Number 9080 Answers: 0 Comments: 1

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Question Number 9069 Answers: 0 Comments: 2

Question Number 9061 Answers: 2 Comments: 1

Question Number 9057 Answers: 4 Comments: 0

Question Number 9049 Answers: 0 Comments: 5

Prove that every even number can be expressed as sum of two primes or give an counter example.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{every}\:\mathrm{even}\:\mathrm{number}\:\mathrm{can}\:\mathrm{be}\: \\ $$$$\mathrm{expressed}\:\mathrm{as}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{two}\:\mathrm{primes}\:\mathrm{or} \\ $$$$\mathrm{give}\:\mathrm{an}\:\mathrm{counter}\:\mathrm{example}. \\ $$

Question Number 9048 Answers: 1 Comments: 0

Question Number 9041 Answers: 0 Comments: 2

Question Number 9032 Answers: 0 Comments: 2

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Question Number 9030 Answers: 0 Comments: 0

f(x ,y)=f(2x+2y, 2y−2x) IF f(2^x ,0)=f(2^(x+k) ,0) Find minimum value of k>0.

$${f}\left({x}\:,{y}\right)={f}\left(\mathrm{2}{x}+\mathrm{2}{y},\:\mathrm{2}{y}−\mathrm{2}{x}\right) \\ $$$$\mathrm{I}{F}\:{f}\left(\mathrm{2}^{{x}} ,\mathrm{0}\right)={f}\left(\mathrm{2}^{{x}+{k}} ,\mathrm{0}\right) \\ $$$$\boldsymbol{\mathrm{F}}\mathrm{ind}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{k}>\mathrm{0}. \\ $$

Question Number 9029 Answers: 2 Comments: 0

2cos(x+Π/4)=cos(x−Π/4)

$$ \\ $$$$\mathrm{2}{cos}\left({x}+\Pi/\mathrm{4}\right)={cos}\left({x}−\Pi/\mathrm{4}\right) \\ $$

Question Number 9025 Answers: 0 Comments: 7

Determine number/s that is/are comprised of four distinct prime factors such that difference of largest and smallest prime factors is equal to the sum of remaining two factors. _(Propsed by Rasheed Soomro)

$$\mathrm{Determine}\:\mathrm{number}/\mathrm{s}\:\mathrm{that}\:\mathrm{is}/\mathrm{are}\:\mathrm{comprised} \\ $$$$\mathrm{of}\:\mathrm{four}\:\mathrm{distinct}\:\mathrm{prime}\:\mathrm{factors}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{difference}\:\mathrm{of}\:\mathrm{largest}\:\mathrm{and}\:\mathrm{smallest}\:\mathrm{prime} \\ $$$$\mathrm{factors}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{remaining} \\ $$$$\mathrm{two}\:\mathrm{factors}.\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:_{\mathrm{Propsed}\:\mathrm{by}\:\mathrm{Rasheed}\:\mathrm{Soomro}} \\ $$

Question Number 9021 Answers: 1 Comments: 0

What is the remainder when (13^5 + 14^5 + 15^5 + 16^5 ) is divided by 29 ?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\: \\ $$$$\left(\mathrm{13}^{\mathrm{5}} \:+\:\mathrm{14}^{\mathrm{5}} \:+\:\mathrm{15}^{\mathrm{5}} \:+\:\mathrm{16}^{\mathrm{5}} \right)\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{29}\:?\: \\ $$

Question Number 9020 Answers: 2 Comments: 1

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Question Number 9011 Answers: 0 Comments: 0

Show that for any arbitary constants A and B y = A(sinx + (1/x)cosx) + B(cosx − (1/x)sinx) satisfy the differential equation (d^2 y/dx^2 ) + (1 − (2/x^2 ))y = 0

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{for}\:\mathrm{any}\:\mathrm{arbitary}\:\mathrm{constants}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B} \\ $$$$\mathrm{y}\:=\:\mathrm{A}\left(\mathrm{sinx}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\mathrm{cosx}\right)\:+\:\mathrm{B}\left(\mathrm{cosx}\:−\:\frac{\mathrm{1}}{\mathrm{x}}\mathrm{sinx}\right)\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}\:\:\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:+\:\left(\mathrm{1}\:−\:\frac{\mathrm{2}}{\mathrm{x}^{\mathrm{2}} }\right)\mathrm{y}\:=\:\mathrm{0} \\ $$

Question Number 9009 Answers: 1 Comments: 0

If : x = ((3y + 6z)/(7z − 2)) and y = (((1/2)z + 6y)/((3/2)z + 6y)) Find : x^3 + y^3

$$\mathrm{If}\::\:\:\mathrm{x}\:=\:\frac{\mathrm{3y}\:+\:\mathrm{6z}}{\mathrm{7z}\:−\:\mathrm{2}}\:\:\mathrm{and}\:\:\mathrm{y}\:=\:\frac{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{z}\:+\:\mathrm{6y}}{\frac{\mathrm{3}}{\mathrm{2}}\mathrm{z}\:+\:\mathrm{6y}} \\ $$$$\mathrm{Find}\::\:\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \\ $$

Question Number 9008 Answers: 0 Comments: 0

What is the value of ε_(ijk) ε_(ijk) δ_(mn) δ_(mn) ?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\epsilon_{\mathrm{ijk}} \epsilon_{\mathrm{ijk}} \delta_{\mathrm{mn}} \delta_{\mathrm{mn}} \:? \\ $$

Question Number 9226 Answers: 1 Comments: 0

Solve: (x^2 + 1)dy = (4x + xy^2 )dx y(0) = 2

$$\mathrm{Solve}:\:\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}\right)\mathrm{dy}\:=\:\left(\mathrm{4x}\:+\:\mathrm{xy}^{\mathrm{2}} \right)\mathrm{dx} \\ $$$$\mathrm{y}\left(\mathrm{0}\right)\:=\:\mathrm{2} \\ $$

Question Number 9004 Answers: 1 Comments: 0

prove (1/2)∙(3/4)∙(5/6)∙∙∙∙∙((2n−1)/(2n))≤(1/(√(3n+1)))