Free Printable BSME SET#1

1.

What is the temperature in degree Celsius of absolute zero?

a)

-32

b)

0

c)

273

d)

-273

2.

How many degrees Celsius is 100 degrees Fahrenheit?

a)

37.8°C

b)

2.667°C

c)

1.334°C

d)

13.34°C

3.

A comfortable room temperature is 72°F. What is this temperature, expressed in degrees Kelvin?

a)

263

b)

290

c)

295

d)

275

4.

255°C is equivalent to:

a)

491°F

b)

427°F

c)

173.67°F

d)

109.67°F

5.

At what temperature will the °C and °F readings be equal?

a)

A. 40°

b)

B. -40°

c)

C. 32°

d)

D. 0°

6.

How many degree Celsius is 80 degrees Fahrenheit?

a)

26.67

b)

86.4

c)

33.33

d)

16.33

7.

What is the absolute temperature of the freezing point of water in degree Rankine?

a)

-32

b)

0

c)

428

d)

492

8.

The angle of inclination of the road is 32°. What is the angle of inclination in mils?

a)

456.23

b)

568.89

c)

125.36

d)

284.44

9.

An angle measures x degrees. What is its measure in radians?

a)

180°×x/π

b)

πx/180°

c)

180°π/x

d)

180πx

10.

Express 45° in mils.

a)

80 mils

b)

800 mils

c)

8000 mils

d)

80000 mils

11.

What is the value in degrees of π radians?

a)

180°

b)

57.3°

c)

90°

d)

45°

12.

How many degrees is 3200 mils?

a)

360°

b)

270°

c)

180°

d)

90°

13.

An angular unit equivalent to 1/400 of the circumference of a circle is called:

a)

Mil

b)

grad

c)

radian

d)

degree

14.

Carry out the following multiplication and express your answer in cubic meters: 3cm×5mm×2m.

a)

3×10⁻³

b)

3×10⁻⁴

c)

8×10⁻²

d)

8×10²

15.

Add the following and express in meters: 3m+2 cm+70 mm

a)

2.90 m

b)

3.14 m

c)

3.12 m

d)

3.09 m

16.

One nautical mile is equivalent to:

a)

5280 ft.

b)

6280 ft.

c)

1.256 statute mile

d)

1.854 km

17.

100 square meters is equal to how many square feet?

a)

1076.39

b)

1000

c)

328.08

d)

500

18.

100 m² × (3.28 ft / 1 m)² = ?

a)

328.10

b)

956.36

c)

1075.84

d)

1563.25

19.

A tank contains 1500 gallons of water. What is the equivalent in cubic meters?

a)

4.256

b)

5.856

c)

6.256

d)

5.685

20.

How many cubic feet is equivalent to 100 gallons of water?

a)

74.80

b)

1.337

c)

13.37

d)

133.7

21.

How many cubic meters is 100 gallons of liquid?

a)

0.1638 cu. meter

b)

1.638 cu. meters

c)

0.3785 cu. meter

d)

3.7850 cu. meters

22.

The number of board feet in a plank 3 inches thick, 1 foot wide, and 20 feet long is:

a)

30

b)

60

c)

120

d)

90

23.

Which of the following is correct?

a)

1 horsepower = 746 kW

b)

1 horsepower = 0.746 watts

c)

1 horsepower = 0.746 kW

d)

1 horsepower = 746 watts

24.

The acceleration due to gravity in English unit is equivalent to:

a)

32.2 ft/sec²

b)

3.22 ft/sec²

c)

9.81 ft/sec²

d)

98.17 ft/sec²

25.

The prefix nano is opposite to:

a)

mega

b)

hexa

c)

giga

d)

tera

26.

10 to the 12th power is the value of the prefix:

a)

giga

b)

pico

c)

tera

d)

peta

27.

Convert 630 degrees to its value in centesimal system.

a)

700 grade

b)

800 grade

c)

750 grade

d)

850 grade

28.

When rounded-off to four significant figures, 102.48886 becomes:

a)

102.4

b)

102.489

c)

102.4888

d)

102.5

29.

Which of the following is a prime number?

a)

221

b)

63

c)

523

d)

700

30.

The number of significant figures in the value 500.00 is:

a)

one

b)

three

c)

five

d)

six

31.

A line on a map was drawn at a scale of 1:100,000. If a line in the map is 290 mm long, the actual length of the line is:

a)

4.8 km

b)

5.8 km

c)

2.9 km

d)

6.4 km

32.

Which of the following is correct:

a)

0.001 has three significant figures

b)

100 has three significant figures

c)

100.00 has five significant figures

d)

0.000249 has six significant figures

33.

The scale on the map is 1:x. A lot having an area of 640 m² is represented by an area of 25.6 cm² on the map. What is the value of x?

a)

50

b)

100

c)

200

d)

20

34.

Given: Map Area / Actual Area = $(1/x)^2$ 25.6 / 640 × 10^4 = $(1/x)^2$ What is the value of x?

a)

500

b)

1000

c)

50

d)

100

35.

Solve for x: x = $(-1/27)^{-2/3}$

a)

9

b)

1/9

c)

-9

d)

-1/9

36.

Solve for a in the equation: a = $64^x 4^y$

a)

$4^{x+3y}$

b)

$4^{xy}$

c)

$256^{xy}$

d)

$4^{3x+y}$

37.

Simplify $3^x - 3^{x-1} - 3^{x-2}$ .

a)

$3^{x-2}$

b)

$3^{x-3}$

c)

5 × $3^{x-2}$

d)

$13 \times 3^x$

38.

Which of the following is true?

a)

√2 × √2 = 2

b)

24 = 4√6

c)

√10 = √5 + √2

d)

$5^5 + 5^5 + 5^5 + 5^5 + 5^5 = 5^6$

39.

Solve for x: x = √18 - √72 + √50.

a)

-2√2

b)

2√2

c)

4

d)

4√3

40.

Solve for x: √x - √1-x = 1-√x

a)

-16/25 & 0

b)

25/16 & 0

c)

-25/16 & 0

d)

16/25 & 0

41.

Simplify $³√2x^4 - ³√16x^4 + 2³√54x^4$ .

a)

$5^3\sqrt{x^4}$

b)

$2^{3}\sqrt{5}x^{4}$

c)

$5^3\sqrt{2}x^4$

d)

$2^{3}\sqrt{2}x^{4}$

42.

Solve for x: $3^5\times x + 1 = 6^x + 2$ .

a)

x = 3

b)

x = 2

c)

x = 1

d)

x = 4

43.

$(a^{-2} b^{3})^{2} / a^{2} b^{-1}$

a)

$a^{-2} b^{7}$

b)

$a^{-2} b^{5}$

c)

$a^{-6} b^{7}$

d)

$a^{-6} b^{5}$

44.

$(3^X)^X$ is equal to:

a)

$3x^2$

b)

$3^X$

c)

$3 x^2$

d)

$3^{2X}$

45.

Solve for x: $3^{X+1}$ = 6561.

a)

1

b)

2

c)

3

d)

4

46.

If 3a = 7b, then $\frac{3a^2}{7b^2}$ =

a)

1

b)

3/7

c)

7/3

d)

49/9

47.

Solve for U if U =

a)

0.723

b)

0.618

c)

0.852

d)

0.453

48.

If x to the 3/4 power equals 8, then x equals to:

a)

-9

b)

6

c)

9

d)

16

49.

If $33^y = 1$ , what is the value of $y/33$ ?

a)

0

b)

1

c)

Infinity

d)

1/33

50.

Find the value of x that will satisfy the following expression: √x - 2 = -√x + 2

a)

x = 3/2

b)

x = 18/6

c)

x = 9/4

d)

none of these

51.

$e^{-3}$ is equal to:

a)

0.048787

b)

0.049001

c)

0.049787

d)

0.048902

52.

b to the m/nth power is equal to:

a)

nth root of b to the m power

b)

b to the m + n power

c)

1/n square root of b to the m power

d)

b to the m power over n

53.

Find x from the following equations: $27^x = 9^y$ $81 \times 3^{(-x)} = 243$

a)

2.5

b)

2

c)

1

d)

1.5

54.

Solve for a from the following equations: $(a^m)(a^n) = 100,000$ , $a^{mn} = 100,000$ , $(a^n)/(a^m) = 10$

a)

15.85

b)

10

c)

12

d)

12.56

55.

Simplify $((x^2 y^3 z^{-2})^2 (x^{-3} y^2 z^3)^{-1/2}) / (x y z^{-3})^{5/2}$

a)

$\frac{1}{x^2 y^2 z^3}$

b)

$\frac{1}{x^2 y^2 z^5}$

c)

$\frac{1}{x^2 y^5 z^3}$

d)

$\frac{1}{x^5 y^2 z^3}$

56.

Simplify the following: $7^{(a+2)} \cdot 8(7^{(a+1)}) + 5(7^{a}) + 49(7^{(a-2)})$

a)

$5^a$

b)

3

c)

$-7^a$

d)

$7^a$

57.

Simplify: $(x y^{-1} / x^{-2} y^2)^4 + (x^3 y^{-2} / x^{-3} y^3)^3$

a)

$x y^3$

b)

$y / x^3$

c)

$x^3 y$

d)

$\frac{1}{x^2 y}$

58.

Simplify the following: (√5 - √3) / (√5 + √3)

a)

4 + √15

b)

4 - √15

c)

8 + √8

d)

8 - √8

59.

Which of the following is equivalent to m√n√a

a)

$n\sqrt{a^m}$

b)

$\sqrt{a^m}$

c)

$\sqrt{a^{mn}}$

d)

mn√a

60.

Find the value of x in $(3^5)(9^6) = 3^{(2x)}$

a)

8.5

b)

9

c)

9.5

d)

8

61.

Solve for x: $x^{x^{x^{x}}} = 10$

a)

1.2589

b)

2.4156

c)

1.1745

d)

Cannot be solved

62.

Change 0.2272727… to a common fraction.

a)

7/44

b)

5/48

c)

5/22

d)

9/34

63.

What is the value of 7! Or 7 factorial?

a)

5040

b)

2540

c)

5020

d)

2520

64.

The reciprocal of 20 is:

a)

0.50

b)

20

c)

0.20

d)

0.05

65.

If p is an odd number and q is an even number, which of the following expressions must be even?

a)

p + q

b)

p − q

c)

pq

d)

p/q

66.

MCMXCIV is a Roman Numeral equivalent to:

a)

2974

b)

3974

c)

2174

d)

1994

67.

What is the lowest common factor of 10 & 32

a)

320

b)

40

c)

180

d)

10

68.

4xy - 4x^2 - y^2 is equal to:

a)

$(2x - y)^2$

b)

$(-2x - y)^2$

c)

$(-2x + y)^2$

d)

$-(2x - y)^2$

69.

Factor x^4 - y^2 + y - x^2 as completely as possible.

a)

$(x^2 + y)(x^2 + y - 1)$

b)

$(x^2 + y)(x^2 - y - 1)$

c)

$(x^2 - y)(x^2 - y - 1)$

d)

$(x^2 - y)(x^2 + y - 1)$

70.

Factor the expression x^2 + 6x + 8 as completely as possible.

a)

(x + 8)(x - 2)

b)

(x + 4)(x + 2)

c)

(x + 4)(x - 2)

d)

(x - 8)(x - 2)

71.

Factor the expression $x^3 + 8$ as completely as possible:

a)

$(x - 2)(x^2 + 2x + 4)$

b)

$(x + 4)(x^2 + 2x + 2)$

c)

$(-x + 2)(-x^2 + 2x + 2)$

d)

$(x + 2)(x^2 - 2x + 4)$

72.

Factor the expression (x^4 - y^4) as completely as possible:

a)

$(x + y)(x^2 + 2xy + y^2)$

b)

$(x^2 + y^2)(x^2 - y^2)$

c)

$(x^2 + y^2)(x + y)(x - y)$

d)

$(1 + x^2)(1 + y)(1 - y^2)$

73.

Factor the expression $3x^3 + 3x^2 - 18x$ as completely as possible

a)

3x(x + 2)(x - 3)

b)

3x(x - 2)(x + 3)

c)

3x(x - 3)(x + 6)

d)

$(3x^2 - 6x)(x - 1)$

74.

Factor the expression $16 - 10x + x^2$ :

a)

(x + 8)(x - 2)

b)

(x - 8)(x - 2)

c)

(x - 8)(x + 2)

d)

(x + 8)(x + 2)

75.

Factor the expression $x^6 - 1$ as completely as possible.

a)

$(x + 1)(x - 1)(x^4 + x^2 - 1)$

b)

$(x + 1)(x - 1)(x^4 + 2x^2 + 1)$

c)

$(x + 1)(x - 1)(x^4 - x^2 + 1)$

d)

$(x + 1)(x - 1)(x^4 + x^2 + 1)$

76.

The roots of the equation $(x - 4)^2(x + 2) = (x + 2)^2(x - 4)$ are:

a)

A. 4 and -2 only

b)

B. 1 only

c)

C. -2 and 4 only

d)

D. 1, -2 and 4 only

77.

If f(x) = $x^2 + x + 1$ , then f(x) - f(x - 1) =

a)

0

b)

x

c)

2x

d)

3

78.

Which of the following is not an identity?

a)

$(x - 1)^2 = x^2 - 2x + 1$

b)

$(x + 3)(2x - 2) = 2(x^2 + 2x - 3)$

c)

$x^2 - (x - 1)^2 = 2x - 1$

d)

2(x - 1) + 3(x + 1) = 5x + 4

79.

Solve for x: $4 + \frac{x+3}{x-3} - \frac{4x^2}{x^2-9} = \frac{x+9}{x+3}$

a)

-18 = -18

b)

12 =12 or -3 = -3

c)

Any value

d)

-27 = -27 or 0 = 0

80.

Solve the simultaneous equations: 3x - y = 6; 9x - y = 12.

a)

x = 3; y = 1

b)

x = 1; y = -3

c)

x = 2; y = 2

d)

x = 4; y = 2

81.

Solve algebraically: $4x^2 + 7y^2 = 32$ ; $11y^2 - 3x^2 = 41$

a)

y = 4, x = ±1, and y = -4, x = ±1

b)

y = +2, x = ±1, and y = -2, x = ±1

c)

x = 2, y = 3, and x = -2, y = -3

d)

x = 2, y = -2, and x = 2, y = -2

82.

Solve for ω from the following equations: 3x - 2y + ω = 11, x + 5y - 2ω = -9, 2x + y - 3ω = -6

a)

1

b)

2

c)

3

d)

4

83.

When (x + 3)(x - 4) + 4 is divided by x - k, the remainder is k. Find the value of k.

a)

4 or 2

b)

2 or -4

c)

4 or -2

d)

-4 or 2

84.

Find the value of k in the equation $4x^2 + kx + 1 = 0$ so that it will only have one real root.

a)

k = 4

b)

k = 2

c)

k = 1

d)

k = 0

85.

Find the remainder when $(x^{12} + 2)$ is divided by $(x - \sqrt{3})$ .

a)

652

b)

731

c)

231

d)

851

86.

If $3x^3 4x^2y + 5xy^2 + 6y^3$ is divided by $(x^2 - 2xy + 3y^2)$ , the remainder is:

a)

0

b)

1

c)

2

d)

3

87.

If (4y^3 + 8y + 18y^2 - 4) is divided by (2y + 3), the remainder is:

a)

10

b)

11

c)

12

d)

13

88.

Given: f(x) = (x + 3)(x - 4) + 4 when divided by (x - k), the remainder is k. Find the k.

a)

A. 2

b)

B. 3

c)

C. 4

d)

D. -3

89.

The polynomial $x^3 + 4x^2 - 3x + 8$ is divided by $x - 5$ . What is the remainder?

a)

281

b)

812

c)

218

d)

182

90.

Find the quotient of $3x^5 - 4x^3 + 2x^2 + 36x + 48$ divided by $x^3 - 2x^2 + 6$ .

a)

$-3x^2 - 4x + 8$

b)

$3x^2 + 4x + 8$

c)

$3x^2 - 4x - 8$

d)

$3x^2 + 6x + 8$

91.

If 1/x = a + b and 1/y = a - b then x - y is equal to:

a)

1/2a

b)

1/2b

c)

$\frac{2a}{a^2 - b^2}$

d)

$\frac{2b}{a^2 - b^2}$

92.

If x - \frac{1}{x} = 1, find the value of $x^3 - \frac{1}{x^3}$ .

a)

1

b)

2

c)

3

d)

4

93.

If 1/x + 1/y = 3 and 2x - 1/y = 1, then x is equal to:

a)

1/2

b)

2/3

c)

3/4

d)

4/3

94.

Simplify the following expressions: $5x/(2x^2+7x+3)$ - $(x+3)/(2x^2-3x-2)$ + $(2x+1)/(x^2+x-6)$

a)

2/(x-3)

b)

(x-3)/5

c)

(x+3)/(x-1)

d)

4/(x+3)

95.

If 3x = 4y then $3x^2/4y^2$ is equal to:

a)

3/4

b)

4/3

c)

2/3

d)

3/2

96.

Simplify: $(a + 1/a^2)^2 - (a - 1/a)^2$ .

a)

-4

b)

0

c)

4

d)

$-2/a^2$

97.

The quotient of (x^5 + 32) by (x + 2) is:

a)

$x^4 - x^3 + 8$

b)

$x^3 + 2x^2 + 8x + 4$

c)

$x^4 - 2x^3 + 4x^2 - 8x + 16$

d)

$x^4 + 2x^3 + x^2 + 16x + 8$

98.

Solve the simultaneous equations: $y - 3x + 4 = 0$ $y + \frac{x^2}{y} = \frac{24}{y}$

a)

A. x = (–6 + 2√14)/5 or (–6 – 2√14)/5 y = (2 + 6√14)/5 or (–2 + 6√14)/5

b)

B. x = (6 + 2√15)/5 or (6 – 2√15)/5 y = (–2 + 6√14)/5 or (–2 – 6√14)/5

c)

C. x = (6 + 2√14)/5 or (6 – 2√14)/5 y = (–2 + 6√14)/5 or (–2 – 6√14)/5

d)

D. x = (6 + 2√14)/5 or (6 – 2√14)/5 y = (–6 – 2√14)/5 or (–6 + 2√14)/5

99.

Find the value of A in the equation $\frac{x^2 + 4x + 10}{x^3 + 2x^2 + 5x}$ = $\frac{A}{x}$ + $\frac{B(2x+2)}{x^2 + 2x + 5}$ + $\frac{C}{x^2 + 2x + 5}$

a)

2

b)

-2

c)

-1/2

d)

½

100.

Find A and B such that $\frac{x^2 + 10}{x^2 - 4}$ = $A/(x - 2)$ + $B/(x + 2)$

a)

A = –3; B = 2

b)

A = 3; B = –2

c)

𝐴 = −3; 𝐵 = −2

d)

𝐴 = 3; 𝐵 = 2

BSME SET#1

Total questions: 100

Worksheet time: 33mins

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