Free Printable BSME SET#2

1.

If log₁₀^x / (1 - log ₁₀²) = 2, what is the value of x?

a)

1/4

b)

25

c)

4

d)

5

2.

Solve for x: $:\log6+𝑥\log4=\log4+\log(32+4𝑥)$

a)

1

b)

2

c)

3

d)

4

3.

Which of the following cannot be used as a base of a system of logarithm?

a)

e

b)

10

c)

2

d)

1

4.

If log ₅₂ 1000 = x, what is the value of x?

a)

4.19

b)

5.23

c)

3.12

d)

4.69

5.

Find the value of a in the equation log a 2187 = 7/2.

a)

3

b)

6

c)

9

d)

12

6.

If log 2 = x and log 3 = y, find log 1.2.

a)

2x + y

b)

2xy/10

c)

2x + y - 1

d)

xy - 1

7.

log $x^y$ / $log y^x$ is equal to:

a)

$x^y / y^x$

b)

y log x - x log y

c)

y log x / x log y

d)

1

8.

If $10^{(ax + b)}$ = P, what is the value of x?

a)

(1/a) (log P - b)

b)

(1/a) log (P - b)

9.

Find the value of $log (a^a)^4$ .

a)

2log a

b)

$a^2 log a$

c)

alog a^2

d)

$(alog a)^a$

10.

Solve for x: : 𝑥 = log_b 𝑎 × log _c𝑑 × log_dc

a)

log_b a

b)

log_a c

c)

log_b c

d)

log_a a

11.

Find the positive value of x if log_x 36 = 2.

a)

2

b)

4

c)

6

d)

8

12.

Find x if log_x 27 + log_x 3 = 2.

a)

9

b)

12

c)

8

d)

7

13.

Find a if log_2 (a + 2) + log_2 (a – 2) = 5.

a)

2

b)

4

c)

6

d)

8

14.

Solve for x if log_5 x = 3.

a)

115

b)

125

c)

135

d)

145

15.

Find log P if ln P = 8.

a)

2980.96

b)

2542.33

c)

3.47

d)

8.57

16.

If log₈x = –n, then x is equal to:

a)

$8^n$

b)

$\frac{1}{8^n}$

c)

$\frac{1}{8^n}$

d)

81/n

17.

If 3log₁₀x – log₁₀y = 0, find y in terms of x.

a)

y = 3√x

b)

y = $\sqrt{x^3}$

c)

$y = x^3$

d)

y = x

18.

Which of the following is correct?

a)

–2log 7 = 1/49

b)

log 7(–2) = 1/49

c)

log 7(1/49) = –2

d)

log 7(1/49) = 2

19.

Log of the nth root of x equals log of x to the 1/n power and also equal to:

a)

log (x)/n

b)

nlog (x)

c)

$log (x)^{(1/n)}$

d)

(n – 1)log (x)

20.

What is the natural logarithm of e to the xy power?

a)

1/xy

b)

2.718/xy

c)

xy

d)

2.718xy

21.

What expression is equivalent to log x – log (y + z)?

a)

log x + log y + log z

b)

log [x/(y + z)]

c)

log x – log y – log z

d)

log y + log (x + z)

22.

What is the value of $\log_{10}(1000^{3.3})$ ?

a)

9.9

b)

99.9

c)

10.9

d)

9.5

23.

If log 2 + log 2 x = 2, then the value of x is:

a)

1

b)

2

c)

3

d)

4

24.

log₆845 =?

a)

4.348

b)

6.348

c)

5.912

d)

3.761

25.

The logarithms of the quotient and the product of two numbers are 0.352182518 and 1.556302501, respectively. Find the first number:

a)

9

b)

10

c)

11

d)

12

26.

The sum of the logarithms of two numbers is 1.748188 and the difference of their logarithms is –0.0579919. One of the numbers is:

a)

9

b)

6

c)

8

d)

5

27.

Solve for y: y = $ln (\frac{e^x}{e^{(x–2)}})$

a)

2

b)

x

c)

–2

d)

x – 2

28.

What is the value of (log 5 to the base 2) + (log 5 to the base 3)?

a)

3.97

b)

7.39

c)

9.37

d)

3.79

29.

The logarithm of a negative number is:

a)

irrational number

b)

real number

c)

imaginary number

d)

complex number

30.

38.5^x = 6.5^x–2, solve for x using logarithms.

a)

2.70

b)

2.10

c)

–2.10

d)

–2.02

31.

Find the 6th term of the expansion of $(\frac{1}{2} a - 3)^{16}$ .

a)

22113/256411 66339

b)

128411/22113 66339/256411

c)

128411/22113

d)

66339/256411

32.

In the expansion of (x + 4y)^12, the numerical coefficient of the 5th term is:

a)

253,440

b)

126,720

c)

63,360

d)

506,880

33.

The middle term in the expansion of (x^2 – 3)^8 is:

a)

$-70x^8$

b)

$70x^8$

c)

–5670x^8

d)

$5670x^8$

34.

The term involving $x^9$ in the expansion of $(x^2 + 2/x)^{12}$ is:

a)

25434x^9

b)

52344x^9

c)

$25344x^9$

d)

23544x^9

35.

The constant term in the expansion of $(x + 1/x^{3/2})^{15}$ is:

a)

3003

b)

5005

c)

6435

d)

7365

36.

Find the sum of the coefficients in the expansion of $(x + 2y – z)^8$ .

a)

256

b)

1024

c)

1

d)

6

37.

The sum of the coefficients in the expansion of $(x + 2y + z)^4(x + 3y)^5$ is:

a)

524,288

b)

65,536

c)

131,072

d)

262,144

38.

The sum of the coefficients in the expansion of $(x + y - z)^8$ is:

a)

less than 2

b)

above 10

c)

from 2 to 5

d)

from 5 to 10

39.

What is the sum of the coefficients of the expansion of $(2x – 1)^{20}$ ?

a)

1

b)

0

c)

215

d)

225

40.

In the quadratic equation $Ax^2 + Bx + C = 0$ , the product of the roots is:

a)

C/A

b)

–B/A

c)

–C/A

d)

B/A

41.

If $\frac{1}{4}$ and $–\frac{7}{2}$ are the roots of the quadratic equation Ax^2 + Bx + C = 0, what is the value of B?

a)

–28

b)

4

c)

–7

d)

26

42.

In the equation $3x^2 + 4x + (2h – 5) = 0$ , find h if the product of the roots is 4.

a)

–7/2

b)

–10/2

c)

17/2

d)

7/2

43.

If the roots of $ax^2 + bx + c = 0$ are u and v, then the roots of $cx^2 + bx + a = 0$ are:

a)

A. u and v

b)

B. –u and v

c)

C. 1/u and 1/v

d)

D. –1/u and –1/v

44.

If the roots of the quadratic equation $ax^2 + bx + c = 0$ are 3 and 2 and a, b, c are all whole numbers, find a + b + c.

a)

12

b)

–2

c)

2

d)

6

45.

The equation whose roots are the reciprocals of the roots of $2x^2 - 3x - 5 = 0$ is:

a)

$5x^2 + 3x - 2 = 0$

b)

$3x^2 – 5x – 2 = 0$

c)

$5x^2 – 2x – 3 = 0$

d)

$2x^2 – 5x – 3 = 0$

46.

The roots of a quadratic equation are 1/3 and 1/4. What is the equation?

a)

$12x^2 + 7x + 1 = 0$

b)

$12x^2 + 7x – 1 = 0$

47.

Find k so that the expression $kx^2 - 3kx + 9$ is a perfect square.

a)

3

b)

4

c)

12

d)

6

48.

Find k so that $4x^2 + kx + 1 = 0$ will only have one real solution.

a)

1

b)

4

c)

3

d)

2

49.

The only root of the equation $x^2 - 6x + k = 0$ is:

a)

3

b)

2

c)

6

d)

1

50.

Two engineering students are solving a problem leading to a quadratic equation. One student made a mistake in the coefficient of the first-degree term, got roots of 2 and -3. The other student made a mistake in the coefficient of the constant term, got roots of -1 and 4. What is the correct equation?

a)

$x^2 - 6x - 3 = 0$

b)

$x^2 + 6x + 3 = 0$

c)

$x^2 + 3x + 6 = 0$

d)

$x^2 - 3x - 6 = 0$

51.

Two times the father's age is 8 more than six times his son's age. Ten years ago, the sum of their ages was 44. The age of the son is:

a)

49

b)

15

c)

20

d)

18

52.

Peter's age 13 years ago was 1/3 of his age 7 years hence. How old is Peter?

a)

15

b)

21

c)

23

d)

27

53.

A man is 41 years old and in seven years he will be four times as old as his son is at that time. How old is his son now?

a)

9

b)

4

c)

5

d)

8

54.

A father is three times as old as his son. Four years ago, he was four times as old as his son was at that time. How old is his son?

a)

36 years

b)

24 years

c)

32 years

d)

12 years

55.

The ages of the mother and her daughter are 45 and 5 years, respectively. How many years will the mother be three times as old as her daughter?

a)

5

b)

10

c)

15

d)

20

56.

Mary is 24 years old. Mary is twice as old as Ana was when Mary was as old as Ana is now. How old is Ana?

a)

16

b)

18

c)

19

d)

20

57.

The sum of the parent's ages is twice the sum of their children's ages. Five years ago, the sum of the parent's ages is four times the sum of their children's ages. In fifteen years, the sum of the parent's ages will be equal to the sum of their children's ages. How many children were in the family?

a)

2

b)

3

c)

4

d)

5

58.

Two thousand (2000) kg of steel containing 8% nickel is to be made by mixing a steel containing 14% nickel with another steel containing 6% nickel. How much of the steel containing 14% nickel is needed?

a)

1500 kg

b)

800 kg

c)

750 kg

d)

500 kg

59.

A 40-gram alloy containing 35% gold is to be melted with a 20-gram alloy containing 50% gold. How much percentage of gold is the resulting alloy?

a)

40%

b)

30%

c)

45%

d)

35%

60.

In what ratio must a peanut costing P 240.00 per kg be mixed with a peanut costing P 340.00 per kg so that a profit of 20% is made by selling the mixture at P 360.00 per kg?

a)

1:2

b)

3:2

c)

2:3

d)

3:5

61.

A 100-kilogram salt solution originally 4% by weight. Salt in water is boiled to reduce water content until the concentration is 5% by weight salt. How much water is evaporated?

a)

10

b)

15

62.

A pound of alloy of lead and nickel weighs 14.4 ounces in water, where lead losses 1/11 of its weight and nickel losses 1/9 of its weight. How much of each metal is in the alloy?

a)

Lead = 7.2 ounces; Nickel = 8.8 ounces

b)

Lead = 8.8 ounces; Nickel = 7.2 ounces

c)

Lead = 6.5 ounces; Nickel = 5.4 ounces

d)

Lead = 7.8 ounces; Nickel = 4.2 ounces

63.

An alloy of silver and gold weighs 15 oz. in air and 14 oz. in water. Assuming that silver losses 1/10 of its weight in water and gold losses 1/18 of its weight, how many oz at each metal are in the alloy?

a)

silver = 4.5 oz.; gold = 10.5 oz.

b)

silver = 3.75 oz.; gold = 11.25 oz.

c)

silver = 5 oz.; gold = 10 oz.

d)

silver = 2.75 oz.; gold = 12.25 oz.

64.

A pump can pump out a tank in 11 hours. Another pump can pump out the same tank in 20 hours. How long will it take both pumps together to pump out the tank?

a)

1/2 hours

b)

1/2 hour

c)

6 hours

d)

7 hours

65.

Mr. Brown can wash his car in 15 minutes, while his son John takes twice as long to do the same job. If they work together, how many minutes can they do the washing?

a)

6

b)

8

c)

10

d)

12

66.

One pipe can fill a tank in 5 hours and another pipe can fill the same tank in 4 hours. A drainpipe can empty the full content of the tank in 20 hours. With all the pipes open, how long will it take to fill the tank?

a)

2 hours

b)

2.5 hours

c)

1.92 hours

d)

1.8 hours

67.

A swimming pool is filled through its inlet pipe and then emptied through its outlet pipe in a total of 8 hours. If water enters through its inlet and simultaneously allowed to leave through its outlet, the pool is filled in 7 1/2 hours. Find how long will it take to fill the pool with the outlet closed

a)

6

b)

2

c)

3

d)

5

68.

Three persons can do a piece of work alone in 3 hours, 4 hours, and 6 hours, respectively. What fraction of the job can they finish in one hour working together?

a)

3/4

b)

4/3

c)

1/2

d)

2/3

69.

A father and his son can dig a well if the father works 6 hours and his son works 12 hours or they can do it if the father works 9 hours and the son works 8 hours. How long will it take for the son to dig the well alone?

a)

5 hours

b)

10 hours

c)

15 hours

d)

20 hours

70.

Peter and Paul can do a certain job in 3 hours. On a given day, they worked together for 1 hour then Paul left and Peter finishes the rest of the work in 8 more hours. How long will it take for Peter to do the job alone?

a)

A. 10 hours

b)

B. 11 hours

c)

C. 12 hours

d)

D. 13 hours

71.

Pedro can paint a fence 50% faster than Juan and 20% faster than Pilar and together they can paint a given fence in 4 hours. How long will it take Pedro to paint the same fence if he had to work alone?

a)

10 hrs.

b)

11 hrs.

c)

13 hrs.

d)

15 hrs.

72.

Nonoy can finish a certain job in 10 days if Imelda will help for 6 days. The same work can be done by Imelda in 12 days if Nonoy helps for 6 days. If they work together, how long will it take for them to do the job?

a)

8.9

b)

8.4

c)

9.2

d)

8.8

73.

A pipe can fill up a tank with the drain open in three hours. If the pipe runs with the drain open for one hour and then the drain is closed, it will take 45 more minutes for the pipe to fill the tank. If the drain will be closed right at the start of filling, how long will it take for the pipe to fill the tank?

a)

1.15 hrs

b)

1.125 hrs

c)

1.325 hrs

d)

1.525 hrs

74.

Delia can finish a job in 8 hours. Daisy can do it in 5 hours. If Delia worked for 3 hours and then Daisy was asked to help her finish it, how long will Daisy have to work with Delia to finish the job?

a)

2/5 hour

b)

25/14 hours

c)

28 hours

d)

1.923 hours

75.

A job could be done by eleven workers in 15 days. Five workers started the job. They were reinforced with four more workers at the beginning of the 6th day. Find the total number of days it took them to finish the job.

a)

22.36

b)

21.42

c)

23.22

d)

20.56

76.

On one job, two power shovels excavate 20,000 m3 of earth, the larger shovel working for 40 hours and the smaller for 35 hours. Another job, they removed 40,000 m3 with the larger shovel working 70 hours and the smaller working 90 hours. How much earth can the larger shovel move in one hour?

a)

173.91

b)

347.83

c)

368.12

d)

162.22

77.

A and B can do a piece of work in 42 days, B and C in 31 days, and A and C in 20 days. Working together, how many days can all of them finish the work?

a)

A. 18.9

b)

B. 19.4

c)

C. 17.8

d)

D. 20.9

78.

Eight men can dig 150 ft of trench in 7 hrs. Three men can backfill 100 ft of the trench in 4 hrs. The time that it will take 10 men to dig and fill 200 ft of trench is:

a)

9.867 hrs

b)

9.867 hrs

c)

8.967 hrs

d)

8.867 hrs

79.

In two hours, the minute hand of the clock rotates through an angle of:

a)

45°

b)

90°

c)

360°

d)

720°

80.

In one day (24 hours), how many times will the hour-hand and minute-hand of a continuously driven clock be together?

(a)

81.

How many minutes after 3:00 PM will the minute hand of the clock overtakes the hour hand?

a)

14-1/12 minutes

b)

16-1/12 minutes

c)

16-4/11 minutes

d)

14/11 minutes

82.

How many minutes after 10:00 o'clock will the hands of the clock be opposite each other for the first time?

a)

21.41

b)

22.31

c)

21.81

d)

22.61

83.

What time between the hours of 12:00 noon and 1:00 pm would the hour-hand and the minute-hand of a continuously driven clock be in straight line?

a)

12:33 pm

b)

12:30 pm

c)

12:37 pm

d)

12:287 pm

84.

At what time after 12:00 noon will the hour hand and the minute hand of a clock first form an angle of 120°?

a)

21.818

b)

12:21.181

c)

21.181

d)

12:21.818

85.

From the time 6:15 PM to the time 7:45 PM of the same day, the minute hand of a standard clock describe an arc of:

a)

360°

b)

180°

c)

540°

d)

720°

86.

It is now between 3 and 4 o'clock and in twenty minutes the minute-hand will be as much as the hour-hand as it is now behind it. What is the time now?

a)

3:06.36

b)

3:07.36

c)

3:09.36

d)

3:08.36

87.

A man left his home at past 3:00 o'clock PM as indicated in his wall clock. Between two to three hours after, he returned home and noticed that the hands of the clock interchanged. At what time did he left his home?

a)

3:27.27

b)

3:31.47

c)

3:22.22

d)

3:44.44

88.

The sum of the reciprocals of two numbers is 11. Three times the reciprocal of one of the numbers is three more than twice the reciprocal of the other number. Find the numbers.

a)

5 and 6

b)

7 and 4

c)

1/5 and 1/6

d)

1/7 and 1/4

89.

If a two-digit number has x for its unit's digit and y for its ten's digit, represent the number.

a)

yx

b)

10y + x

c)

10x + y

d)

x* y

90.

One number is five less than the other number. If their sum is 135, what are the numbers?

a)

A. 70 & 75

b)

B. 60 & 65

c)

C. 65 & 70

d)

D. 75 & 80

91.

In a two-digit number, the unit’s digit is 3 greater than the ten’s digit. Find the number if it is 4 times as large as the sum of its digits.

a)

47

b)

58

c)

63

d)

25

92.

Find two consecutive even integers such that the square of the larger is 44 greater than the square of the smaller integer.

a)

10 & 12

b)

12 & 14

c)

8 & 10

d)

14 & 16

93.

Twice the middle digit of a three-digit number is the sum of the other two. If the number is divided by the sum of its digit, the answer is 56 and the reminder is 12. If the digits are reversed, the number becomes smaller by 594. Find the number.

a)

258

b)

567

c)

852

d)

741

94.

The product of three consecutive integers is 9240. Find the third integer.

a)

20

b)

21

c)

22

d)

23

95.

The product of two numbers is 1400. If three (3) is subtracted from each number, their product becomes 1175. Find the bigger number.

a)

28

b)

50

c)

32

d)

40

96.

The sum of the digits of a three-digit number is 14. The hundreds digit being 4 times the units digit. If 594 is subtracted from the number, the order of the digits will be reversed. Find the number.

a)

743

b)

563

c)

653

d)

842

97.

The sum of two numbers is 21, and one number is twice the other. Find the numbers.

a)

7 and 14

b)

6 and 15

c)

8 and 13

d)

9 and 12

98.

Ten less than four times a certain number is 14. Determine the number.

a)

4

b)

5

c)

6

d)

7

99.

The denominator of a certain fraction is three more than twice the numerator. If 7 is added to both terms of the fraction, the resulting fraction is 3/5. Find the original fraction.

a)

8/5

b)

5/13

c)

13/5

d)

3/5

100.

Three times the first of three consecutive odd integers is three more than twice the third. Find the third integer.

a)

9

b)

11

c)

13

d)

15

BSME SET#2

Total questions: 100

Worksheet time: 50mins

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