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Question Number 21267    Answers: 0   Comments: 0

cos A+cos B+cos C=1+(r/R)

$$\mathrm{cos}\:{A}+\mathrm{cos}\:{B}+\mathrm{cos}\:{C}=\mathrm{1}+\frac{{r}}{{R}} \\ $$

Question Number 21266    Answers: 1   Comments: 0

((b^2 −c^2 )/(tan A))+((c^2 −a^2 )/(tan B))+((a^2 −b^2 )/(tan C))=0

$$\frac{{b}^{\mathrm{2}} −{c}^{\mathrm{2}} }{\mathrm{tan}\:{A}}+\frac{{c}^{\mathrm{2}} −{a}^{\mathrm{2}} }{\mathrm{tan}\:{B}}+\frac{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} }{\mathrm{tan}\:{C}}=\mathrm{0} \\ $$

Question Number 21264    Answers: 1   Comments: 0

2x+3y+2z=2

$$\mathrm{2x}+\mathrm{3y}+\mathrm{2z}=\mathrm{2} \\ $$

Question Number 21262    Answers: 0   Comments: 0

Question Number 21260    Answers: 1   Comments: 0

if (θ−ϕ) subtle and sin θ+sin ϕ=(√(3(cos ϕ)) −cos θ) so proof sin 3θ+sin 3ϕ=0

$${if}\:\left(\theta−\varphi\right)\:{subtle}\:{and}\:\mathrm{sin}\:\theta+\mathrm{sin}\:\varphi=\sqrt{\mathrm{3}\left(\mathrm{cos}\:\varphi\right.} \\ $$$$\left.−\mathrm{cos}\:\theta\right) \\ $$$${so}\:{proof}\:\mathrm{sin}\:\mathrm{3}\theta+\mathrm{sin}\:\mathrm{3}\varphi=\mathrm{0} \\ $$

Question Number 21259    Answers: 1   Comments: 0

2cos (π/(13))cos ((9π)/(13))+cos ((3π)/(13))+cos ((5π)/(13))=0

$$\mathrm{2cos}\:\frac{\pi}{\mathrm{13}}\mathrm{cos}\:\frac{\mathrm{9}\pi}{\mathrm{13}}+\mathrm{cos}\:\frac{\mathrm{3}\pi}{\mathrm{13}}+\mathrm{cos}\:\frac{\mathrm{5}\pi}{\mathrm{13}}=\mathrm{0} \\ $$

Question Number 21253    Answers: 1   Comments: 0

the hcf of two numbers is 75 and their lcm is 3375 if one of the numbers is 675 find the other number

$${the}\:{hcf}\:{of}\:{two}\:{numbers}\:{is}\:\mathrm{75}\:{and}\:{their}\:{lcm}\:{is}\:\mathrm{3375}\:{if}\:{one}\:{of}\:{the}\:{numbers}\:{is}\:\mathrm{675}\:{find}\:{the}\:{other}\:{number} \\ $$

Question Number 21252    Answers: 0   Comments: 0

prove,∀x_1 ,...,x_n y_1 ,...,y_n ∈R^+ (√(x_1 x_2 ...x_n ))+(√(y_1 y_2 ...y_n ))≤(√((x_1 +y_1 )(x_2 +y_2 )...(x_n +y_n )))

$${prove},\forall{x}_{\mathrm{1}} ,...,{x}_{{n}} {y}_{\mathrm{1}} ,...,{y}_{{n}} \in\mathbb{R}^{+} \\ $$$$\sqrt{{x}_{\mathrm{1}} {x}_{\mathrm{2}} ...{x}_{{n}} }+\sqrt{{y}_{\mathrm{1}} {y}_{\mathrm{2}} ...{y}_{{n}} }\leqslant\sqrt{\left({x}_{\mathrm{1}} +{y}_{\mathrm{1}} \right)\left({x}_{\mathrm{2}} +{y}_{\mathrm{2}} \right)...\left({x}_{{n}} +{y}_{{n}} \right)} \\ $$

Question Number 21251    Answers: 0   Comments: 0

resolve : ∀x∈R, (√(x+1))∣x−2∣=(√(x+2))∣x−1∣−2

$${resolve}\:: \\ $$$$\forall{x}\in\mathbb{R},\:\sqrt{{x}+\mathrm{1}}\mid{x}−\mathrm{2}\mid=\sqrt{{x}+\mathrm{2}}\mid{x}−\mathrm{1}\mid−\mathrm{2} \\ $$$$ \\ $$

Question Number 21249    Answers: 0   Comments: 1

A particle slides down a frictionless parabolic (y = x^2 ) track (A − B − C) starting from rest at point A. Point B is at the vertex of parabola and point C is at a height less than that of point A. After C, the particle moves freely in air as a projectile. If the particle reaches highest point at P, then (a) KE at P = KE at B (b) height at P = height at A (c) total energy at P = total energy at A (d) time of travel from A to B = time of travel from B to P.

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{slides}\:\mathrm{down}\:\mathrm{a}\:\mathrm{frictionless} \\ $$$$\mathrm{parabolic}\:\left({y}\:=\:{x}^{\mathrm{2}} \right)\:\mathrm{track}\:\left({A}\:−\:{B}\:−\:{C}\right) \\ $$$$\mathrm{starting}\:\mathrm{from}\:\mathrm{rest}\:\mathrm{at}\:\mathrm{point}\:{A}.\:\mathrm{Point}\:{B} \\ $$$$\mathrm{is}\:\mathrm{at}\:\mathrm{the}\:\mathrm{vertex}\:\mathrm{of}\:\mathrm{parabola}\:\mathrm{and}\:\mathrm{point}\:{C} \\ $$$$\mathrm{is}\:\mathrm{at}\:\mathrm{a}\:\mathrm{height}\:\mathrm{less}\:\mathrm{than}\:\mathrm{that}\:\mathrm{of}\:\mathrm{point}\:{A}. \\ $$$$\mathrm{After}\:{C},\:\mathrm{the}\:\mathrm{particle}\:\mathrm{moves}\:\mathrm{freely}\:\mathrm{in}\:\mathrm{air} \\ $$$$\mathrm{as}\:\mathrm{a}\:\mathrm{projectile}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{reaches} \\ $$$$\mathrm{highest}\:\mathrm{point}\:\mathrm{at}\:{P},\:\mathrm{then} \\ $$$$\left({a}\right)\:\mathrm{KE}\:\mathrm{at}\:{P}\:=\:\mathrm{KE}\:\mathrm{at}\:{B} \\ $$$$\left({b}\right)\:\mathrm{height}\:\mathrm{at}\:{P}\:=\:\mathrm{height}\:\mathrm{at}\:{A} \\ $$$$\left({c}\right)\:\mathrm{total}\:\mathrm{energy}\:\mathrm{at}\:{P}\:=\:\mathrm{total}\:\mathrm{energy}\:\mathrm{at} \\ $$$${A} \\ $$$$\left({d}\right)\:\mathrm{time}\:\mathrm{of}\:\mathrm{travel}\:\mathrm{from}\:{A}\:\mathrm{to}\:{B}\:=\:\mathrm{time}\:\mathrm{of} \\ $$$$\mathrm{travel}\:\mathrm{from}\:{B}\:\mathrm{to}\:{P}. \\ $$

Question Number 21248    Answers: 0   Comments: 0

The locus of the centre of a circle which touches the given circles ∣z − z_1 ∣ = ∣3 + 4i∣ and ∣z − z_2 ∣ = ∣1 + i(√3)∣ is a hyperbola, then the length of its transverse axis is

$$\mathrm{The}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{which} \\ $$$$\mathrm{touches}\:\mathrm{the}\:\mathrm{given}\:\mathrm{circles}\:\mid{z}\:−\:{z}_{\mathrm{1}} \mid\:= \\ $$$$\mid\mathrm{3}\:+\:\mathrm{4}{i}\mid\:\mathrm{and}\:\mid{z}\:−\:{z}_{\mathrm{2}} \mid\:=\:\mid\mathrm{1}\:+\:{i}\sqrt{\mathrm{3}}\mid\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{hyperbola},\:\mathrm{then}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{its} \\ $$$$\mathrm{transverse}\:\mathrm{axis}\:\mathrm{is} \\ $$

Question Number 21247    Answers: 1   Comments: 0

If [ ] represents the greatest integer function and f(x) = x − [x] then number of real roots of the equation f(x) + f((1/x)) = 1 are infinite. True/False

$$\mathrm{If}\:\left[\:\right]\:\mathrm{represents}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{integer} \\ $$$$\mathrm{function}\:\mathrm{and}\:{f}\left({x}\right)\:=\:{x}\:−\:\left[{x}\right]\:\mathrm{then} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{real}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$${f}\left({x}\right)\:+\:{f}\left(\frac{\mathrm{1}}{{x}}\right)\:=\:\mathrm{1}\:\mathrm{are}\:\mathrm{infinite}. \\ $$$$\boldsymbol{\mathrm{True}}/\boldsymbol{\mathrm{False}} \\ $$

Question Number 21353    Answers: 1   Comments: 0

A censusman on duty visited a house which the lady inmates declined to reveal their individual ages, but said − “we do not mind giving you the sum of the ages of any two ladies you may choose”. Thereupon the censusman said − “In that case please give me the sum of the ages of every possible pair of you”. The gave the sums as follows : 30, 33, 41, 58, 66, 69. The censusman took these figures and happily went away. How did he calculate the individual ages of the ladies from these figures?

$$\mathrm{A}\:\mathrm{censusman}\:\mathrm{on}\:\mathrm{duty}\:\mathrm{visited}\:\mathrm{a}\:\mathrm{house} \\ $$$$\mathrm{which}\:\mathrm{the}\:\mathrm{lady}\:\mathrm{inmates}\:\mathrm{declined}\:\mathrm{to} \\ $$$$\mathrm{reveal}\:\mathrm{their}\:\mathrm{individual}\:\mathrm{ages},\:\mathrm{but}\:\mathrm{said}\:− \\ $$$$``\mathrm{we}\:\mathrm{do}\:\mathrm{not}\:\mathrm{mind}\:\mathrm{giving}\:\mathrm{you}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{ages}\:\mathrm{of}\:\mathrm{any}\:\mathrm{two}\:\mathrm{ladies}\:\mathrm{you}\:\mathrm{may} \\ $$$$\mathrm{choose}''.\:\mathrm{Thereupon}\:\mathrm{the}\:\mathrm{censusman} \\ $$$$\mathrm{said}\:−\:``\mathrm{In}\:\mathrm{that}\:\mathrm{case}\:\mathrm{please}\:\mathrm{give}\:\mathrm{me}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ages}\:\mathrm{of}\:\mathrm{every}\:\mathrm{possible}\:\mathrm{pair}\:\mathrm{of} \\ $$$$\mathrm{you}''.\:\mathrm{The}\:\mathrm{gave}\:\mathrm{the}\:\mathrm{sums}\:\mathrm{as}\:\mathrm{follows}\:: \\ $$$$\mathrm{30},\:\mathrm{33},\:\mathrm{41},\:\mathrm{58},\:\mathrm{66},\:\mathrm{69}.\:\mathrm{The}\:\mathrm{censusman} \\ $$$$\mathrm{took}\:\mathrm{these}\:\mathrm{figures}\:\mathrm{and}\:\mathrm{happily}\:\mathrm{went} \\ $$$$\mathrm{away}.\:\mathrm{How}\:\mathrm{did}\:\mathrm{he}\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{individual} \\ $$$$\mathrm{ages}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ladies}\:\mathrm{from}\:\mathrm{these}\:\mathrm{figures}? \\ $$

Question Number 21241    Answers: 1   Comments: 0

Find y in 3rd quadrant tan(y − 30) = cot(y)

$$\mathrm{Find}\:\mathrm{y}\:\mathrm{in}\:\mathrm{3rd}\:\mathrm{quadrant} \\ $$$$\mathrm{tan}\left(\mathrm{y}\:−\:\mathrm{30}\right)\:=\:\mathrm{cot}\left(\mathrm{y}\right) \\ $$

Question Number 21236    Answers: 1   Comments: 0

If (1/a) + (1/(2a)) + (1/(3a)) = (1/(b^2 − 2b)) a and b are positive integers Find minimum value of a + b

$$\mathrm{If}\:\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{\mathrm{2}{a}}\:+\:\frac{\mathrm{1}}{\mathrm{3}{a}}\:=\:\frac{\mathrm{1}}{{b}^{\mathrm{2}} \:−\:\mathrm{2}{b}} \\ $$$${a}\:\mathrm{and}\:{b}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{integers} \\ $$$$\mathrm{Find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:{a}\:+\:{b} \\ $$

Question Number 21235    Answers: 1   Comments: 0

For any integer k, let α_k = cos (((kπ)/7)) + i sin (((kπ)/7)), where i = (√(−1)). The value of the expression ((Σ_(k=1) ^(12) ∣α_(k+1) − α_k ∣)/(Σ_(k=1) ^3 ∣α_(4k−1) − α_(4k−2) ∣)) is

$$\mathrm{For}\:\mathrm{any}\:\mathrm{integer}\:{k},\:\mathrm{let}\:\alpha_{{k}} \:=\:\mathrm{cos}\:\left(\frac{{k}\pi}{\mathrm{7}}\right)\:+ \\ $$$${i}\:\mathrm{sin}\:\left(\frac{{k}\pi}{\mathrm{7}}\right),\:\mathrm{where}\:{i}\:=\:\sqrt{−\mathrm{1}}.\:\mathrm{The}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{expression}\:\frac{\underset{{k}=\mathrm{1}} {\overset{\mathrm{12}} {\sum}}\mid\alpha_{{k}+\mathrm{1}} \:−\:\alpha_{{k}} \mid}{\underset{{k}=\mathrm{1}} {\overset{\mathrm{3}} {\sum}}\mid\alpha_{\mathrm{4}{k}−\mathrm{1}} \:−\:\alpha_{\mathrm{4}{k}−\mathrm{2}} \mid}\:\mathrm{is} \\ $$

Question Number 21234    Answers: 1   Comments: 0

Let f(x) = ax^2 + bx + c, where a, b, c are real numbers. If the numbers 2a, a + b, and c are all integers, then the number of integral values between 1 and 5 that f(x) can take is

$$\mathrm{Let}\:{f}\left({x}\right)\:=\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c},\:\mathrm{where}\:{a},\:{b},\:{c} \\ $$$$\mathrm{are}\:\mathrm{real}\:\mathrm{numbers}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{numbers}\:\mathrm{2}{a}, \\ $$$${a}\:+\:{b},\:\mathrm{and}\:{c}\:\mathrm{are}\:\mathrm{all}\:\mathrm{integers},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{integral}\:\mathrm{values}\:\mathrm{between}\:\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{5}\:\mathrm{that}\:{f}\left({x}\right)\:\mathrm{can}\:\mathrm{take}\:\mathrm{is} \\ $$

Question Number 21232    Answers: 0   Comments: 0

Question Number 21231    Answers: 0   Comments: 0

Consider the areas of the four triangles obtained by drawing the diagonals AC and BD of a trapezium ABCD. The product of these areas, taken two at time, are computed. If among the six products so obtained, two products are 1296 and 576, determine the square root of the maximum possible area of the trapezium to the nearest integer.

$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{areas}\:\mathrm{of}\:\mathrm{the}\:\mathrm{four}\:\mathrm{triangles} \\ $$$$\mathrm{obtained}\:\mathrm{by}\:\mathrm{drawing}\:\mathrm{the}\:\mathrm{diagonals}\:{AC} \\ $$$$\mathrm{and}\:{BD}\:\mathrm{of}\:\mathrm{a}\:\mathrm{trapezium}\:{ABCD}.\:\mathrm{The} \\ $$$$\mathrm{product}\:\mathrm{of}\:\mathrm{these}\:\mathrm{areas},\:\mathrm{taken}\:\mathrm{two}\:\mathrm{at} \\ $$$$\mathrm{time},\:\mathrm{are}\:\mathrm{computed}.\:\mathrm{If}\:\mathrm{among}\:\mathrm{the}\:\mathrm{six} \\ $$$$\mathrm{products}\:\mathrm{so}\:\mathrm{obtained},\:\mathrm{two}\:\mathrm{products}\:\mathrm{are} \\ $$$$\mathrm{1296}\:\mathrm{and}\:\mathrm{576},\:\mathrm{determine}\:\mathrm{the}\:\mathrm{square} \\ $$$$\mathrm{root}\:\mathrm{of}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{possible}\:\mathrm{area}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{trapezium}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{integer}. \\ $$

Question Number 21230    Answers: 1   Comments: 0

For each positive integer n, consider the highest common factor h_n of the two numbers n! + 1 and (n + 1)!. For n < 100, find the largest value of h_n .

$$\mathrm{For}\:\mathrm{each}\:\mathrm{positive}\:\mathrm{integer}\:{n},\:\mathrm{consider} \\ $$$$\mathrm{the}\:\mathrm{highest}\:\mathrm{common}\:\mathrm{factor}\:{h}_{{n}} \:\mathrm{of}\:\mathrm{the}\:\mathrm{two} \\ $$$$\mathrm{numbers}\:{n}!\:+\:\mathrm{1}\:\mathrm{and}\:\left({n}\:+\:\mathrm{1}\right)!.\:\mathrm{For}\:{n}\:<\:\mathrm{100}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{value}\:\mathrm{of}\:{h}_{{n}} . \\ $$

Question Number 21229    Answers: 0   Comments: 0

Let p, q be prime numbers such that n^(3pq) − n is a multiple of 3pq for all positive integers n. Find the least possible value of p + q.

$$\mathrm{Let}\:{p},\:{q}\:\mathrm{be}\:\mathrm{prime}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that} \\ $$$${n}^{\mathrm{3}{pq}} \:−\:{n}\:\mathrm{is}\:\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{3}{pq}\:\mathrm{for}\:\boldsymbol{\mathrm{all}} \\ $$$$\mathrm{positive}\:\mathrm{integers}\:{n}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{least} \\ $$$$\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:{p}\:+\:{q}. \\ $$

Question Number 21228    Answers: 0   Comments: 0

Let P be an interior point of a triangle ABC whose sidelengths are 26, 65, 78. The line through P parallel to BC meets AB in K and AC in L. The line through P parallel to CA meets BC in M and BA in N. The line through P parallel to AB meets CA in S and CB in T. If KL, MN, ST, are of equal lengths, find this common length.

$$\mathrm{Let}\:{P}\:\mathrm{be}\:\mathrm{an}\:\mathrm{interior}\:\mathrm{point}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle} \\ $$$${ABC}\:\mathrm{whose}\:\mathrm{sidelengths}\:\mathrm{are}\:\mathrm{26},\:\mathrm{65},\:\mathrm{78}. \\ $$$$\mathrm{The}\:\mathrm{line}\:\mathrm{through}\:{P}\:\mathrm{parallel}\:\mathrm{to}\:{BC}\:\mathrm{meets} \\ $$$${AB}\:\mathrm{in}\:{K}\:\mathrm{and}\:{AC}\:\mathrm{in}\:{L}.\:\mathrm{The}\:\mathrm{line}\:\mathrm{through} \\ $$$${P}\:\mathrm{parallel}\:\mathrm{to}\:{CA}\:\mathrm{meets}\:{BC}\:\mathrm{in}\:{M}\:\mathrm{and}\:{BA} \\ $$$$\mathrm{in}\:{N}.\:\mathrm{The}\:\mathrm{line}\:\mathrm{through}\:{P}\:\mathrm{parallel}\:\mathrm{to}\:{AB} \\ $$$$\mathrm{meets}\:{CA}\:\mathrm{in}\:{S}\:\mathrm{and}\:{CB}\:\mathrm{in}\:{T}.\:\mathrm{If}\:{KL},\:{MN}, \\ $$$${ST},\:\mathrm{are}\:\mathrm{of}\:\mathrm{equal}\:\mathrm{lengths},\:\mathrm{find}\:\mathrm{this} \\ $$$$\mathrm{common}\:\mathrm{length}. \\ $$

Question Number 21223    Answers: 1   Comments: 0

lim_(x→π/2) (π−2x)tan (x)

$$\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\left(\pi−\mathrm{2}{x}\right)\mathrm{tan}\:\left({x}\right) \\ $$

Question Number 21224    Answers: 0   Comments: 1

One mole of a monoatomic real gas satisfies the equation p(V − b) = RT where b is a constant. The relationship of interatomic potential V(r) and interatomic distance r for the gas is given by

$$\mathrm{One}\:\mathrm{mole}\:\mathrm{of}\:\mathrm{a}\:\mathrm{monoatomic}\:\mathrm{real}\:\mathrm{gas} \\ $$$$\mathrm{satisfies}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{p}\left(\mathrm{V}\:−\:\mathrm{b}\right)\:=\:\mathrm{RT} \\ $$$$\mathrm{where}\:\mathrm{b}\:\mathrm{is}\:\mathrm{a}\:\mathrm{constant}.\:\mathrm{The}\:\mathrm{relationship} \\ $$$$\mathrm{of}\:\mathrm{interatomic}\:\mathrm{potential}\:\mathrm{V}\left(\mathrm{r}\right)\:\mathrm{and} \\ $$$$\mathrm{interatomic}\:\mathrm{distance}\:\mathrm{r}\:\mathrm{for}\:\mathrm{the}\:\mathrm{gas}\:\mathrm{is} \\ $$$$\mathrm{given}\:\mathrm{by} \\ $$

Question Number 21219    Answers: 1   Comments: 0

(A) If ∣w∣ = 2, then the set of points z = w − (1/w) is contained in or equal to (B) If ∣w∣ = 1, then the set of points z = w + (1/w) is contained in or equal to Options for both A and B: (p) An ellipse with eccentricity (4/5) (q) The set of points z satisfying Im z = 0 (r) The set of points z satisfying ∣Im z∣ ≤ 1 (s) The set of points z satisfying ∣Re z∣ ≤ 2 (t) The set of points z satisfying ∣z∣ ≤ 3

$$\left(\mathrm{A}\right)\:\mathrm{If}\:\mid{w}\mid\:=\:\mathrm{2},\:\mathrm{then}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{points} \\ $$$${z}\:=\:{w}\:−\:\frac{\mathrm{1}}{{w}}\:\mathrm{is}\:\mathrm{contained}\:\mathrm{in}\:\mathrm{or}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left(\mathrm{B}\right)\:\mathrm{If}\:\mid{w}\mid\:=\:\mathrm{1},\:\mathrm{then}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{points} \\ $$$${z}\:=\:{w}\:+\:\frac{\mathrm{1}}{{w}}\:\mathrm{is}\:\mathrm{contained}\:\mathrm{in}\:\mathrm{or}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\mathrm{Options}\:\mathrm{for}\:\mathrm{both}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}: \\ $$$$\left(\mathrm{p}\right)\:\mathrm{An}\:\mathrm{ellipse}\:\mathrm{with}\:\mathrm{eccentricity}\:\frac{\mathrm{4}}{\mathrm{5}} \\ $$$$\left(\mathrm{q}\right)\:\mathrm{The}\:\mathrm{set}\:\mathrm{of}\:\mathrm{points}\:{z}\:\mathrm{satisfying}\:\mathrm{Im}\:{z} \\ $$$$=\:\mathrm{0} \\ $$$$\left(\mathrm{r}\right)\:\mathrm{The}\:\mathrm{set}\:\mathrm{of}\:\mathrm{points}\:{z}\:\mathrm{satisfying}\:\mid\mathrm{Im}\:{z}\mid \\ $$$$\leqslant\:\mathrm{1} \\ $$$$\left(\mathrm{s}\right)\:\mathrm{The}\:\mathrm{set}\:\mathrm{of}\:\mathrm{points}\:{z}\:\mathrm{satisfying}\:\mid\mathrm{Re}\:{z}\mid \\ $$$$\leqslant\:\mathrm{2} \\ $$$$\left(\mathrm{t}\right)\:\mathrm{The}\:\mathrm{set}\:\mathrm{of}\:\mathrm{points}\:{z}\:\mathrm{satisfying}\:\mid{z}\mid\:\leqslant\:\mathrm{3} \\ $$

Question Number 21212    Answers: 0   Comments: 0

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