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Question Number 49174    Answers: 1   Comments: 1

If z_1 ,z_2 and z_3 ,z_(4 ) are two pairs of conjugate complex numbers , then find value of arg((z_1 /z_4 ))+arg((z_2 /z_3 )) ?

$${If}\:{z}_{\mathrm{1}} ,{z}_{\mathrm{2}} \:{and}\:{z}_{\mathrm{3}} ,{z}_{\mathrm{4}\:} {are}\:{two}\:{pairs}\:{of}\: \\ $$$${conjugate}\:{complex}\:{numbers}\:,\:{then}\: \\ $$$${find}\:{value}\:{of}\:{arg}\left(\frac{{z}_{\mathrm{1}} }{{z}_{\mathrm{4}} }\right)+{arg}\left(\frac{{z}_{\mathrm{2}} }{{z}_{\mathrm{3}} }\right)\:? \\ $$

Question Number 49151    Answers: 1   Comments: 0

Let z is complex number satisfying the equation z^2 −(3+i)z+m+2i=0, where mεR. Suppose the equation has a real root, then find the non real root?

$${Let}\:{z}\:{is}\:{complex}\:{number}\:{satisfying} \\ $$$${the}\:{equation}\:{z}^{\mathrm{2}} −\left(\mathrm{3}+{i}\right){z}+{m}+\mathrm{2}{i}=\mathrm{0}, \\ $$$${where}\:{m}\epsilon{R}.\:{Suppose}\:{the}\:{equation} \\ $$$${has}\:{a}\:{real}\:{root},\:{then}\:{find}\:{the}\:{non}\:{real}\:{root}? \\ $$

Question Number 49147    Answers: 1   Comments: 0

Question Number 49123    Answers: 1   Comments: 1

If a^3 −a−1=0 then find the valueof a^4 +a^3 −a^2 −2a+1

$$\mathrm{If} \\ $$$$\mathrm{a}^{\mathrm{3}} −\mathrm{a}−\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{valueof} \\ $$$$\mathrm{a}^{\mathrm{4}} +\mathrm{a}^{\mathrm{3}} −\mathrm{a}^{\mathrm{2}} −\mathrm{2a}+\mathrm{1} \\ $$

Question Number 48795    Answers: 1   Comments: 1

Find the sum: ^(30) C_0 .5^(100) −^(30) C_1 .5^(98) .3^3 +^(30) C_2 .5^(96) .3^6 − ...=?

$${Find}\:{the}\:{sum}: \\ $$$$\:^{\mathrm{30}} {C}_{\mathrm{0}} .\mathrm{5}^{\mathrm{100}} −^{\mathrm{30}} {C}_{\mathrm{1}} .\mathrm{5}^{\mathrm{98}} .\mathrm{3}^{\mathrm{3}} +^{\mathrm{30}} {C}_{\mathrm{2}} .\mathrm{5}^{\mathrm{96}} .\mathrm{3}^{\mathrm{6}} −\:...=? \\ $$

Question Number 48687    Answers: 0   Comments: 0

f(x)=sin (x) f(x)+f′((1/x))=(1/2)(√2) find x?

$${f}\left({x}\right)=\mathrm{sin}\:\left({x}\right) \\ $$$${f}\left({x}\right)+{f}'\left(\frac{\mathrm{1}}{{x}}\right)=\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{2}} \\ $$$$\mathrm{find}\:{x}? \\ $$

Question Number 48705    Answers: 3   Comments: 2

Q.1→ Coefficient of a^8 b^4 c^9 d^9 in expansion of (abc+abd+acd+bcd)^(10) =? Q.2→ Coefficient of (1/x) in expansion of (1+x)^n (1+(1/x))^n =? Q.3→ If x^m occurs in expansion of (x+(1/x^2 ))^(2n) , then its coefficient=?

$${Q}.\mathrm{1}\rightarrow \\ $$$${Coefficient}\:{of}\:{a}^{\mathrm{8}} {b}^{\mathrm{4}} {c}^{\mathrm{9}} {d}^{\mathrm{9}} \:{in}\:{expansion} \\ $$$${of}\:\left({abc}+{abd}+{acd}+{bcd}\right)^{\mathrm{10}} \:=? \\ $$$$ \\ $$$${Q}.\mathrm{2}\rightarrow \\ $$$${Coefficient}\:{of}\:\frac{\mathrm{1}}{{x}}\:{in}\:{expansion}\:{of} \\ $$$$\left(\mathrm{1}+{x}\right)^{{n}} \left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{n}} =? \\ $$$$ \\ $$$${Q}.\mathrm{3}\rightarrow \\ $$$${If}\:{x}^{{m}} \:{occurs}\:{in}\:{expansion}\:{of}\: \\ $$$$\left({x}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)^{\mathrm{2}{n}} ,\:{then}\:{its}\:{coefficient}=? \\ $$

Question Number 48678    Answers: 0   Comments: 0

Question Number 48675    Answers: 2   Comments: 0

Find remainder when 27^(40) is divided by 12 ?

$${Find}\:{remainder}\:{when}\:\mathrm{27}^{\mathrm{40}} \:{is}\:{divided} \\ $$$${by}\:\mathrm{12}\:? \\ $$

Question Number 48559    Answers: 3   Comments: 0

Question Number 48553    Answers: 1   Comments: 2

In a hospital unit,there are 8 nurses and 5 physicians. 7 of them are female nurses and 3 of them are male physicians. what is the the probability of selecting a staff who is Nurse or Male? plzz help

$$\mathrm{In}\:\mathrm{a}\:\mathrm{hospital}\:\mathrm{unit},\mathrm{there}\:\mathrm{are}\:\mathrm{8}\:\mathrm{nurses} \\ $$$$\mathrm{and}\:\mathrm{5}\:\mathrm{physicians}.\:\mathrm{7}\:\mathrm{of}\:\mathrm{them}\:\mathrm{are} \\ $$$$\mathrm{female}\:\mathrm{nurses}\:\mathrm{and}\:\mathrm{3}\:\mathrm{of}\:\mathrm{them}\:\mathrm{are} \\ $$$$\mathrm{male}\:\mathrm{physicians}. \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of} \\ $$$$\mathrm{selecting}\:\mathrm{a}\:\mathrm{staff}\:\mathrm{who}\:\mathrm{is}\:\mathrm{Nurse}\:\mathrm{or} \\ $$$$\mathrm{Male}? \\ $$$$\mathrm{plzz}\:\mathrm{help} \\ $$$$ \\ $$$$ \\ $$

Question Number 48509    Answers: 0   Comments: 0

For every natural numbers n Find the value of Σ_(0≤j≤i≤n) (((−1)^j )/((n − i)! j!))

$${For}\:\:{every}\:\:{natural}\:\:{numbers}\:\:{n}\:\: \\ $$$${Find}\:\:\:{the}\:\:{value}\:\:{of} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{\mathrm{0}\leqslant{j}\leqslant{i}\leqslant{n}} {\sum}\:\:\frac{\left(−\mathrm{1}\right)^{{j}} }{\left({n}\:−\:{i}\right)!\:{j}!} \\ $$

Question Number 48482    Answers: 0   Comments: 0

(at−h)^2 +((a/t)−k)^2 =R^( 2) where a, h, k, R are constants. Then find s^2 =(t_1 −t_2 )^2 (1+(1/(t_1 ^2 t_2 ^2 ))) where t_1 , t_2 are roots of eq. at top.

$$\left({at}−{h}\right)^{\mathrm{2}} +\left(\frac{{a}}{{t}}−{k}\right)^{\mathrm{2}} ={R}^{\:\mathrm{2}} \\ $$$${where}\:\:\:{a},\:{h},\:{k},\:{R}\:{are}\:{constants}. \\ $$$${Then}\:{find}\: \\ $$$$\:\:\:{s}^{\mathrm{2}} \:=\left({t}_{\mathrm{1}} −{t}_{\mathrm{2}} \right)^{\mathrm{2}} \left(\mathrm{1}+\frac{\mathrm{1}}{{t}_{\mathrm{1}} ^{\mathrm{2}} {t}_{\mathrm{2}} ^{\mathrm{2}} }\right)\: \\ $$$${where}\:{t}_{\mathrm{1}} ,\:{t}_{\mathrm{2}} \:{are}\:{roots}\:{of}\:{eq}.\:{at}\:{top}. \\ $$

Question Number 48447    Answers: 0   Comments: 4

Find the sum Σ_(k=0) ^(10) ^(20) C_k .

$${Find}\:{the}\:{sum}\:\underset{{k}=\mathrm{0}} {\overset{\mathrm{10}} {\sum}}\:^{\mathrm{20}} {C}_{{k}} \:. \\ $$

Question Number 48443    Answers: 1   Comments: 3

Coefficient of x^4 in (2−x+3x^2 )^6 =?

$${Coefficient}\:{of}\:{x}^{\mathrm{4}} \:{in}\:\left(\mathrm{2}−{x}+\mathrm{3}{x}^{\mathrm{2}} \right)^{\mathrm{6}} =? \\ $$

Question Number 48368    Answers: 1   Comments: 0

Question Number 48367    Answers: 2   Comments: 0

Question Number 48306    Answers: 1   Comments: 0

x^2 +4x+1=9

$$\mathrm{x}^{\mathrm{2}} +\mathrm{4x}+\mathrm{1}=\mathrm{9} \\ $$

Question Number 48295    Answers: 1   Comments: 0

Question Number 48294    Answers: 2   Comments: 3

Question Number 48272    Answers: 0   Comments: 1

z^5 =32 find all root z

$$\mathrm{z}^{\mathrm{5}} =\mathrm{32} \\ $$$$\mathrm{find}\:\mathrm{all}\:{root}\:{z} \\ $$

Question Number 48225    Answers: 1   Comments: 0

prove that exp(((2+πi)/4))=(√(e/2))(1+i) cos (z_1 +z_2 )=cos z_1 cos z_2 −sin z_1 sin z_2

$$\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{exp}\left(\frac{\mathrm{2}+\pi\mathrm{i}}{\mathrm{4}}\right)=\sqrt{\frac{{e}}{\mathrm{2}}}\left(\mathrm{1}+{i}\right) \\ $$$$\mathrm{cos}\:\left({z}_{\mathrm{1}} +{z}_{\mathrm{2}} \right)=\mathrm{cos}\:{z}_{\mathrm{1}} \mathrm{cos}\:{z}_{\mathrm{2}} −\mathrm{sin}\:{z}_{\mathrm{1}} \mathrm{sin}\:{z}_{\mathrm{2}} \\ $$

Question Number 48224    Answers: 1   Comments: 0

e^z =1−(√3)i z=..

$${e}^{{z}} =\mathrm{1}−\sqrt{\mathrm{3}}{i} \\ $$$${z}=.. \\ $$

Question Number 48222    Answers: 0   Comments: 0

f(x)=Σ_(i=0) ^(n) a_i x^i =a_n x^n +a_(n−1) x^(n−1) +a_(n−2) x^(n−2) +…+a_2 x^2 +a_1 x+a_0 f^(−1) (x)=...

$${f}\left({x}\right)=\underset{{i}=\mathrm{0}} {\overset{{n}} {\Sigma}}{a}_{{i}} {x}^{{i}} ={a}_{{n}} {x}^{{n}} +{a}_{{n}−\mathrm{1}} {x}^{{n}−\mathrm{1}} +{a}_{{n}−\mathrm{2}} {x}^{{n}−\mathrm{2}} +\ldots+{a}_{\mathrm{2}} {x}^{\mathrm{2}} +{a}_{\mathrm{1}} {x}+{a}_{\mathrm{0}} \\ $$$${f}^{−\mathrm{1}} \left({x}\right)=... \\ $$

Question Number 48204    Answers: 1   Comments: 0

2(x^4 −2x^2 +3)(y^4 −3y^2 +4)=7 Find (x,y) .

$$\mathrm{2}\left({x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}\right)\left({y}^{\mathrm{4}} −\mathrm{3}{y}^{\mathrm{2}} +\mathrm{4}\right)=\mathrm{7} \\ $$$${Find}\:\left({x},{y}\right)\:. \\ $$

Question Number 48161    Answers: 1   Comments: 1

f(z)=((1−z)/(1+z)) u(x,y)=.. v(x,y)=..

$${f}\left({z}\right)=\frac{\mathrm{1}−{z}}{\mathrm{1}+{z}} \\ $$$${u}\left({x},{y}\right)=.. \\ $$$${v}\left({x},{y}\right)=.. \\ $$$$ \\ $$$$ \\ $$

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