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Qormaata galuumsa kutaa 12ffaa Herregaa, bara 2008 A.L.I (2016)

Gaaffilee dhugaa qormaata galuumsa yunivarsiitii kutaa 12 kan Herregaa, akkuma barattoonni bara 2008 A.L.I itti fudhatanitti. Tokkoon tokkoon gaaffii deebii sirrii fi ibsa qaba.

Bilisaan shaakaluu jalqabaaWaraqaa gaaffii

  • Damee lamaanuu

    Eenyutu fudhata

  • 2008 A.L.I (2016)

    Bara qormaataa

  • Gaaffilee 57 deebii waliin

    Kuusaa kana keessa

Gaaffilee qormaata kanaa yaalaa

Deebii banuun dura tokkoon tokkoon gaaffii ofii keessaniin deebisaa. Ibsi gara kutaa kitaaba barnootaa sirriitti waan qajeelchuuf, yeroo gaaffii dogoggortan fuula kam irra deebi'uu akka qabdan ni beektu.

Gaaffii 1

Which one of the following is a one to one correspondence function from A=[0, 1] to B=[1, 2]?

  1. A.f(x)=xf(x) = x
  2. B.f(x)=1/3x3+1f(x) = 1/3x^{3} + 1
  3. C.f(x)=2x+1f(x) = 2x + 1
  4. D.f(x)=x2+1f(x) = x^{2} + 1
Deebii fi ibsa ilaalaa

Deebii: D f(x)=x2+1f(x) = x^{2} + 1

Maaliif

The function f(x) = x^2 + 1 is continuous and strictly increasing on [0, 1], with f(0) = 1 and f(1) = 2, making it a bijection (one-to-one correspondence) from [0, 1] onto [1, 2].

Gaaffii 2

What is the solution set of 1−1x1−1x2=3x2−x1+1x\dfrac{1-\frac{1}{x}}{1-\frac{1}{x^{2}}} = 3x^{2} - \dfrac{x}{1+\frac{1}{x}} ? ?

  1. A.{−1, 1/3}\{-1,\ 1/3\}
  2. B.{1/3}\{1/3\}
  3. C.{3, −1/3}\{3,\ -1/3\}
  4. D.{−1/3}\{-1/3\}
Deebii fi ibsa ilaalaa

Deebii: B {1/3}\{1/3\}

Maaliif

Simplifying the left-hand side gives x/(x+1) and the right-hand side gives 3x^2 - x^2/(x+1) = (3x^3 + 2x^2)/(x+1). Equating and solving yields 3x^2 - x = 0, so x = 0 or x = 1/3; however, x = 0 is not in the domain of 1/x, leaving {1/3} as the only valid solution.

Gaaffii 5

The planet Mercury's orbit around the sun is an ellipse with eccentricity 0.206, length of the major axis 1.16×1081.16 \times 10^{8} km and the sun at one focus. What is the max distance from Mercury to the sun?

  1. A.6.99×1086.99 \times 10^{8} km
  2. B.6.99×1076.99 \times 10^{7} km
  3. C.9.66×1079.66 \times 10^{7} km
  4. D.9.66×1089.66 \times 10^{8} km
Deebii fi ibsa ilaalaa

Deebii: B 6.99×1076.99 \times 10^{7} km

Maaliif

The semi-major axis is a = (1.16 × 10^8)/2 = 5.8 × 10^7 km. The maximum distance (aphelion) is r_max = a(1 + e) = 5.8 × 10^7 × (1 + 0.206) ≈ 6.99 × 10^7 km.

Gaaffii 6

The graph of a hyperbola and the lines of its asymptotes are given as shown in the following figure. Which one of the following is an equation of the hyperbola? [Figure: A scanned hand-drawn Cartesian plane. The horizontal axis is drawn as a solid arrow to the right and labelled x; the vertical axis is a solid arrow upward and labelled y. Two solid curves form a hyperbola that opens vertically (up and down): the upper branch has its vertex on the positive y-axis roughly two units above the origin and sweeps up to the left and to the right; the lower branch has its vertex on the y-axis just below the origin and sweeps down to the left and to the right. Two dashed straight lines are drawn as the asymptotes; they cross each other on the y-axis at a point about one unit above the origin (the centre of the hyperbola), and each branch approaches them. The dashed line of positive slope, running from lower left to upper right, carries the printed label y = x + 1 near its upper-right end. The dashed line of negative slope, running from upper left to lower right, carries the printed label y = -x + 1 near its lower-right end. No numeric tick marks are shown on either axis.]

  1. A.y2−2y−x2=0y^{2} - 2y - x^{2} = 0
  2. B.y2−3y−x2=0y^{2} - 3y - x^{2} = 0
  3. C.x2−(y−1)2=1x^{2} - (y-1)^{2} = 1
  4. D.(x−1)2−y2=1(x-1)^{2} - y^{2} = 1
Deebii fi ibsa ilaalaa

Deebii: A y2−2y−x2=0y^{2} - 2y - x^{2} = 0

Maaliif

The asymptotes intersect at the center (0, 1) and have slopes ±1. Since the hyperbola opens vertically, its equation is (y - 1)^2 - x^2 = 1, which expands to y^2 - 2y - x^2 = 0.

Gaaffii 7

If the truth value of a proposition p is False, then which one of the following compound proposition has a truth value True?

  1. A.¬p∧p\neg p \wedge p
  2. B.¬p⇒p\neg p \Rightarrow p
  3. C.¬(¬p∨p)\neg(\neg p \vee p)
  4. D.p⇒¬pp \Rightarrow \neg p
Deebii fi ibsa ilaalaa

Deebii: D p⇒¬pp \Rightarrow \neg p

Maaliif

When p is False, ¬p is True. The conditional statement p ⇒ ¬p has a False hypothesis, which makes the implication vacuously True.

Gaaffii 9

Which one of the following compound propositions is a tautology?

  1. A.(q∨¬q)⇒p(q \vee \neg q) \Rightarrow p
  2. B.p⇒(p∨¬q)p \Rightarrow (p \vee \neg q)
  3. C.p∨(q∧¬q)p \vee (q \wedge \neg q)
  4. D.p⇒(q∧¬q)p \Rightarrow (q \wedge \neg q)
Deebii fi ibsa ilaalaa

Deebii: B p⇒(p∨¬q)p \Rightarrow (p \vee \neg q)

Maaliif

By the rule of addition, p implies p ∨ ¬q regardless of the truth values of p and q, making p ⇒ (p ∨ ¬q) a tautology.

Qormaata guutuu PDF dhaan buufadhaa

Gaaffilee 57 kuusaa kana keessa jiran hunda akka waraqaa qormaataa maxxanfameetti, furtuu deebii ibsa 54 waliin immoo akka faayilii lammaffaatti. Maxxansaa yookiin daataa malee dubbisaa.

Bilisa; herregas hin gaafatu.

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Herregni Temari bilisaa qormaata Herregaa guutuu fi kan waggoota biroo hunda qormaatilee fakkeenyaa sa'aatiin daangeffaman godhee qabxii battalumaa waliin isiniif kenna. Bilbila kamiyyuu irratti, walitti hidhamiinsa laafaa irrattillee ni hojjeta.

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Qormaata kana taa'uu dura Herregaa qayyabadhu

Yaadannoon gabaabaan Herregaa kutaa 12 kaardii 33 qaba. Tokkoon tokkoon boqonnaa boqonnaadhaan kitaaba biyyaalessaa irraa qophaa'ee seericha, mallattoowwan isaa maal bakka akka bu'an fi dogoggora qabxii nama dhabsiisu ni ibsa.

Yaadannoo Herregaa bani
Kunneen gaaffilee dhugaa qormaata galuumsa Herregaa bara 2008 A.L.I ti?

Eeyyee. Qormaata galuumsa yunivarsiitii biyyaalessaa kan Herregaa barattoonni bara 2008 A.L.I (2016) fudhatan irraa fudhataman. Kuusaan keenya gaaffilee isaa 57 qaba; tokkoon tokkoon isaanii deebii fi ibsa gara kitaaba barnootaatti qajeelchu qabu.

Qormaata guutuu akkamittan shaakala?

Lakkoofsa bilbilaatiin herrega bilisaa banadhaa. Qormaatichi guutuun qormaata fakkeenyaa sa'aatiin daangeffame ta'ee qabxii battalumaa kenna; fooyya'iinsi gargaaraa AI ji'atti qarshii 199 kan ta'e waan isin jalaa darbe hunda isinii ibsa.

Qormaata Herregaa bara 2008 A.L.I PDF dhaan buufachuu nan danda'aa?

Eeyyee; bilisas. Waraqaan gaaffii faayilii tokko, furtuun deebii ibsa isaa waliin immoo faayilii biraa ti; kanaaf qormaata dursitanii yaaluu dandeessu. Maxxansaa, yookiin yeroo daataan hin jirre irra deebiif bilbila keessan irratti kaa'adhaa.

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