etf questions (eng)

8/15/2019 ETF Questions (Eng)

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Elektrotehnički fakultet u Sarajevu akademska 2011/12

PRIJEMNI ISPIT IZ MATEMATIKE GRUPA: A

1

ŠIFRA KANDIDATA _ _ _ _ _

Problem 1. Expression is given: 2 2 3 22 6 1

22 3 2

a a aa a a

a a a

Which of the following expressions is equivalent to the given expression? (Answer: A)

a)

24

a

a

b)2

4

a

a

c)

3

2 2

a

a a

d)2

2

4

a

a

Problem 2. Choosing randomly we choose number n from set of natural numbers smaller or equal to10. What is the probability that the number will satisfy the relation 5 3 14n ? (Answer C)

a)

2

5 b)

1

10 c)

1

5 d)

3

10


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Problem 3. Sum of three numbers is 80. If we divide first number with second we get quotient 3 and

remainder 3, if we divide third number with first we again get the same quotient 3 and remainder 3.

None of the numbers is equal to zero. Adding difference of first and second number to the third

number we get: (Answer: D)

a) 41 b) 53 c) 66 d) 70

Problem 4. Complete solution of 1 2 2 x x is given as: (Answer: A)

a) 1 5 x b) 1,5 x c) 1,5 x d) 2 5 x


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Problem 5. Values of parameter m , for which solutions of quadratic equation

23 3 0 x mx m both from set and opposite signs, are: (Answer B)

a) 3m b) 3m c) 0m d) 2 4m i m

Problem 6. Equation

23 3 2 7 3 2 0k x k x k has only one solution with respect to

unknown x. Product of parameter k, k and the solution of equation x, x is: (Answer C)

a) 0 b) 1

2 c)

4

3 d)

19 53

24


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Problem 7. Value of unknown x which satisfies the equation 7 77 3 6

26 7 3 3 7

x x

x x x

is:

(Answer: B)

a) 1 x b) 1 2 x c) 13 4 x d) 3 x

Problem 8. The sides of cuboid are given 3a cm

,4b cm

and 5c cm

. Surface of cuboid, if everyside becomes longer for 25%, will change for: (Answer C)

a) 23,50 cm2

b)

117,50 cm2

c) 52,87 cm2

d) 146,9 cm2

a

b

c


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Problem 9. Equation is given:2 1 11 1

3 4 9 6 4 93 2

x x x x

. Which of the following equations is

equivalent to the given equation? (Answer: D)

a) 2 1 1 x b) 2 2

60 3 42 2 x x

c)

3 1

41

3

x

d)

2 1

21

3

x

Problem 10. In arithmetic sequence first term is 4, and eight term is 25. Sum of third and fifth term of

that sequence is: (Answer: B)

a) 29 b)26 c)36 d)23


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Problem 11. Goods are on discount of 20%. What is percentage of price that must be increased to

make the price of the goods same as it was in the beginning? (Answer: B)

a)

20% b) 25% c)30% d)50%

Problem 12. Possible solution of equation 6 3 3 5 x i is: (Answer: A)

a) 6 x b)1

6 x c) 1 x d) 3 x


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Problem 13. If 2 1

21

Z

Z

and8

Re 1 Z

Z

than complex number Z x iy is equal to:

(Answer: C)

a) 1

4 Z i b) 4 Z i c) 0.25 Z i d)

12

4 Z i

Problem 14. Solution of logarithmic equation log 5 2 log 3 1 x x is: (Answer: A)

a)

4 11 b) 4 11 c)8 22

2

d) 4 44


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Problem 15. If we know that5

log 2 a and 5log 3 b , value of logarithm 45log 100 with respect

to parameters a and b is: (Answer: B)

a)

2

2

1

ab

b b)

2 1

2 1

a

b

c) 25log 4a b d)

21

2 1

a

b

Problem 16. Values of variable x for which the inequality is satisfied

24 cos 3 0 x

are: (Answer: B)

a) 3 3

2 2 x b) ,

6 6k x k k

c) ,

3 3k x k k

d) ,6 6

x k ili x k k


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Problem 17. By simplifying the expression

sin cos2

sin sin2

tg

ctg

we get:

(Answer: B)

a) -1 b)3 c) sin d) 2tg

Problem 18. Equation of the line, which touches the circle described by equation

2 2

3 2 1 x y and is parallel to line with equation 2 y x , is given: (Answer: A)

a) 1 2 y x or 1 2 y x b)

2 2

1 2 1 x y

c) 2 3 y x or 2 3 y x d) 4 y x or 7 y x


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Problem 19. Notation ba is notation for the number a in numerical system b. Sum of

7 7344 266 is: (Answer: D)

a) 52304 b) 2101000100 c) 10326 d) 7643

Problem 20. Notation ba is notation for the number a in numerical system b. Base of unknown

numerical system, in which holds

23 32 121 x x x

, is: (Answer: D)

a) 7 x b) 6 x c) 5 x d) 4 x

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