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Qormaata galuumsa kutaa 12ffaa Herregaa, bara 2009 A.L.I (2017)

Gaaffilee dhugaa qormaata galuumsa yunivarsiitii kutaa 12 kan Herregaa, akkuma barattoonni bara 2009 A.L.I itti fudhatanitti. Tokkoon tokkoon gaaffii deebii sirrii fi ibsa qaba.

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  • 2009 A.L.I (2017)

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  • Gaaffilee 61 deebii waliin

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Gaaffilee qormaata kanaa yaalaa

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Gaaffii 1

If A=(aij)3×3A = (a_{ij})_{3\times 3} is a square matrix with A−1=[132113045]A^{-1} = \begin{bmatrix} 1 & 3 & 2 \\ 1 & 1 & 3 \\ 0 & 4 & 5 \end{bmatrix}, then what is the cofactor of a23a_{23}?.

  1. A.−3/14-3/14
  2. B.−2/7-2/7
  3. C.2/72/7
  4. D.−3/7-3/7
Deebii fi ibsa ilaalaa

Deebii: B −2/7-2/7

Maaliif

The cofactor of a23a_{23} is C23=det⁡(A)(A−1)32C_{23} = \det(A)(A^{-1})_{32}. Since det⁡(A−1)=−14\det(A^{-1}) = -14, we have det⁡(A)=−1/14\det(A) = -1/14, so C23=(−1/14)(4)=−2/7C_{23} = (-1/14)(4) = -2/7.

Gaaffii 2

A team of 10 researchers consist 4 biologists and 6 chemists. If 3 persons are chosen randomly from the team, what is the probability that at least one is a biologist?

  1. A.2/32/3
  2. B.2/52/5
  3. C.5/65/6
  4. D.7/107/10
Deebii fi ibsa ilaalaa

Deebii: C 5/65/6

Maaliif

Using the complement, the probability that none of the 3 chosen researchers is a biologist (all are chemists) is (63)/(103)=20/120=1/6\binom{6}{3}/\binom{10}{3} = 20/120 = 1/6, so the probability of at least one biologist is 1−1/6=5/61 - 1/6 = 5/6.

Gaaffii 3

The probability that an electronic device produced by a company does not function properly is equal to 0.1. If 2 devices are bought, then what is the probability that at least one device function properly?

  1. A.0.81
  2. B.0.09
  3. C.0.18
  4. D.0.99
Deebii fi ibsa ilaalaa

Deebii: D 0.99

Maaliif

The probability that at least one device functions properly is 1−P(both fail)=1−(0.1)2=1−0.01=0.991 - P(\text{both fail}) = 1 - (0.1)^2 = 1 - 0.01 = 0.99.

Gaaffii 5

In how many ways can a committee of 3 members be formed from 7 candidates?

  1. A.7
  2. B.21
  3. C.28
  4. D.35
Deebii fi ibsa ilaalaa

Deebii: D 35

Maaliif

The number of ways to choose a committee of 3 from 7 candidates is (73)=7×6×53×2×1=35\binom{7}{3} = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35.

Gaaffii 6

The following is a frequency distribution table of a grouped data with variable X. What is the mean (xˉ\bar{x}) and the variance (s2s^2) of the data respectively? [Figure: A two-row bordered frequency table with five columns. Top row: first cell labelled 'X', then the class intervals 3-7, 8-12, 13-17, 18-22. Bottom row: first cell labelled 'Frequency', then the values 4, 6, 8, 2 under those intervals respectively.]

  1. A.xˉ=12, s2=21\bar{x} = 12,\ s^2 = 21
  2. B.xˉ=12, s2=25\bar{x} = 12,\ s^2 = 25
  3. C.xˉ=13, s2=9\bar{x} = 13,\ s^2 = 9
  4. D.xˉ=13, s2=16\bar{x} = 13,\ s^2 = 16
Deebii fi ibsa ilaalaa

Deebii: A xˉ=12, s2=21\bar{x} = 12,\ s^2 = 21

Maaliif

With midpoints 5,10,15,205, 10, 15, 20 and frequencies 4,6,8,24, 6, 8, 2, the mean is xˉ=240/20=12\bar{x} = 240/20 = 12, and the variance is s2=∑f(x−xˉ)2/N=420/20=21s^2 = \sum f(x - \bar{x})^2 / N = 420/20 = 21.

Gaaffii 7

The expenditure of 100 families is given below. The mode of the data is 23.5, what are the values of f1 and f2 [Figure: A two-row bordered table with six columns. Top row: first cell labelled 'Expenditure', then the classes 0-9, 10-19, 20-29, 30-39, 40-49. Bottom row: first cell labelled 'No. of Families', then the values 14, 23, f1f_1, 21, f2f_2 under those classes respectively.]

  1. A.f1=27, f2=15f_1 = 27,\ f_2 = 15
  2. B.f1=15, f2=27f_1 = 15,\ f_2 = 27
  3. C.f1=25, f2=17f_1 = 25,\ f_2 = 17
  4. D.f1=17, f2=25f_1 = 17,\ f_2 = 25
Deebii fi ibsa ilaalaa

Deebii: A f1=27, f2=15f_1 = 27,\ f_2 = 15

Maaliif

The mode is 23.523.5, which lies in 19.5−29.519.5 - 29.5. Using the mode formula 23.5=19.5+f1−23(f1−23)+(f1−21)×1023.5 = 19.5 + \frac{f_1 - 23}{(f_1 - 23) + (f_1 - 21)} \times 10 yields f1=27f_1 = 27, and since the total is 100, f2=100−(14+23+27+21)=15f_2 = 100 - (14 + 23 + 27 + 21) = 15.

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Gaaffilee 61 kuusaa kana keessa jiran hunda akka waraqaa qormaataa maxxanfameetti, furtuu deebii ibsa 58 waliin immoo akka faayilii lammaffaatti. Maxxansaa yookiin daataa malee dubbisaa.

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Kunneen gaaffilee dhugaa qormaata galuumsa Herregaa bara 2009 A.L.I ti?

Eeyyee. Qormaata galuumsa yunivarsiitii biyyaalessaa kan Herregaa barattoonni bara 2009 A.L.I (2017) fudhatan irraa fudhataman. Kuusaan keenya gaaffilee isaa 61 qaba; tokkoon tokkoon isaanii deebii fi ibsa gara kitaaba barnootaatti qajeelchu qabu.

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