This is 50 items Practice Examinations set 1 in Board Examination in Mathematics composed of previous Board Exams Questions. Read each questions and choices carefully! Choose the best answer. Familiarize each and every questions to increase the chance of passing the Engineering Board Examination.

#### Start the Test Yourself Exam 1

**Choose the letter of the best answer in each questions.**

1) Suppose A = {2, 4, 6, 8, 10, 12}, B = {1, 4, 9, 16} and C = {2, 10}

a) A ∪ B = { 1, 2, 4, 6, 8, 9, 10, 12, 16}

b) A ∪ B = {4}

c) A ∪ B = { 1, 2, 6, 8, 9, 10, 12, 16)

d) A ∪ B = { 1, 4, 9, 16}

Answer: **Option A**

Explanation:

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

a) 6 and 15

b) 2 and 12

c) 7 and 14

d) 8 and 13

Answer: **Option C**

Solution:

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3) If (x + 3) : 10 = (3x – 2) : 8, find ((2x –1).

a) 1

b) 4

c) 2

d) 3

Answer: **Option D**

Explanation:

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

a) 63 360

b) 126 720

c) 506 880

d) 22 280

Answer: **Option B**

Explanation:

5) Determine x, so that: x, 2x + 4, 10x – 4 will be a geometric progression.

a) 4

b) 6

c) 2

d) 5

Answer: **Option A**

Explanation:

6) If angle Φ = 2, then angle (180° – Φ) = ____.

a) 65.4° or 1.1416 radian

b) 64.5° or 1.1614 radian

c) 45.6° or 1.6141 radian

d) 54.6° or 1.4161 radian

Answer: **Option A**

Explanation:

7) Suppose A = {2, 4, 6, 8, 10, 12}, B = {1, 4, 9, 16} and C = {2, 10}

a) B ∩ C = { 1, 2, 4, 9, 10, 16}

b) B ∩ C = {0}

c) B ∩ C = ∅

d) B ∩ C = {2, 10}

Answer: **Option C**

Explanation:

8) The hypotenuse of a right triangle is 34 cm. Find the length of the two legs, if one leg is 14 cm longer than the other.

a) 18 and 32 cm

b) 15 and 29 cm

c) 17 and 31 cm

d) 16 and 30 cm

Answer: **Option D**

Solution:

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9) Find the value of x in the equation: csc x + cot x = 3.

a) π/4

b) π/2

c) π/3

d) π/5

Answer: **Option D**

Explanation:

10) Solve for A in the equation: cos^{2} A = 1 – cos^{2} A

a) 15°, 125°, 225°, 335°

b) 45°, 125°, 225°, 315°

c) 45°, 135°, 225°, 315°

d) 45°, 150°, 220°, 315°

Answer: **Option C**

Explanation:

11) a < b if and only if b – a is _____.

a) negative

b) positive

c) zero

d) none of these

Answer: **Option B**

Explanation:

12) A circle with radius 6 has half its area removed by cutting off a border of uniform width. Find the width of the border

a) 2.2

b) 1.35

c) 3.75

d) 1.76

Answer: **Option D**

Explanation:

13) If the radius of the circle is decreased by 20%, by how much is its area decreased?

a) 46%

b) 36%

c) 56%

d) 26%

Answer: **Option B**

Explanation:

14) Exact angle of the dodecagon is equal to ___ deg.

a) 135

b) 100

c) 125

d) 150

Answer: **Option D**

Explanation:

15) A 50-meter cable is divided into two parts and formed into two squares. If the sum of the areas is 100 sq. meters, find the difference in length?

a) 21.5

b) 20.5

c) 24.5

d) 0

Answer: **Option C**

Explanation:

16) a > b if and only if ______.

a) b is more than 1

b) a is more than 1

c) b is zero

d) b is less than a

Answer: **Option D**

Explanation:

17) The volume of a cube is reduced to ___ if all the sides are halved.

a) ½

b) ¼

c) 1/8

d) 1/16

Answer: **Option C**

Explanation:

18) A reservoir is shaped like a square prism. If the area of its base is 225 sq. cm., how many liters of water will it hold if its length is 1.5 meters?

a) 337.5

b) 33.75

c) 3375

d) 3.375

Answer: **Option B**

Solution:

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19) Find the volume of the sphere whose circumference of a great circle is 18π.

a) 3984.43

b) 3053.63

c) 3291.68

d) 3643.03

Answer: **Option B**

Solution:

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20) When the radius of a sphere is increased by 16%, what percent is the increase in the volume of the sphere?

a) 16%

b) 32%

c) 64%

d) 56%

Answer: **Option D**

Explanation:

21) a ≤ b if and only if either a < b or

a) a = 0

b) b = 1

c) a = b

d) none of these

Answer: **Option C**

Explanation:

22) Find the equation of the directrix of the parabola y^{2} = 16x.

a) x = – 4

b) x = – 8

c) x = 4

d) x = 8

Answer: **Option A**

Solution:

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23) The diameter of a circle described by 9x^{2} + 9y^{2} + 2 = 16 is ___.

a) 4/3

b) 16/9

c) 8/3

d) 4

Answer: **Option C**

Explanation:

24) If the points (-2, 3), (x, y) and (-3, 5) lie on a straight line, then the equation of the line is _____.

a) x – 2y – 1 = 0

b) 2x + y – 1 = 0

c) x + 2y – 1 = 0

d) 2x + y + 1 = 0

Answer: **Option D**

Explanation:

25) Find the location of the vertex of the parabola defined by the equation: y =x^{2} – 4x + 1

a) (2, 3)

b) (-2, 3)

c) (2, -3)

d) (-2, -3)

Answer: **Option C**

Explanation:

26) a > 0 if and only if _____

I. a is positive

II. a is negative

III. –a < 0

IV. –a > 0

a) I & III only

b) II & IV only

c) I & II only

d) III & IV only

Answer: **Option A**

Explanation:

27) Evaluate: M = lim (x^{2} –4) / (x – 2)

x→2

a) 3

b) 4

c) 2

d) 5

Answer: **Option B**

Explanation:

28) The derivative of ln cos x is:

a) sec x

b) –tan x

c) –sec x

d) tan x

Answer: **Option B**

Explanation:

29) Find the radius of curvature at any point of the curve y + ln (cosx) = 0.

a) 1

b) 1.5707

c) cos x

d) sec x

Answer: **Option D**

Explanation:

30) Find the equation of the normal to x^{2} + y^{2} = 1 at the point (2, 1)

a) X = 3Y

b) X = 2Y

c) X = Y

d) X = 4Y

Answer: **Option B**

Explanation:

31) If a < b & b < c, then ___

a) a < c

b) c < a

c) a > c

d) c > a

Answer: **Option A**

Explanation:

32) What is the integral of (3t – 1)^{3} dt?

a) (1/12) (3t – 1)^{4} + c

b) (1/12) (3t –4)^{4} + c

c) (1/4) (3t –1)^{4} + c

d) (1/4) (3t – 1)^{3} + c

Answer: **Option A**

Explanation:

33) Find the value of (1 + I)^{5} , where I is an imaginary number.

a) 1 – i

b) 1 + i

c) –4 (1 +i)

d) 4 (1 + i)

Answer: **Option C**

Explanation:

34) If a < b, then a + c < b + c, and a – c < b – c if c is

a) subtracted from a only

b) added to b only

c) subtracted from b only

d) any real number

Answer: **Option D**

Explanation:

35) If a < b & c < d, then

a) a + c < b –d

b) a + b < b + d

c) a + d < b + c

d) none of these

Answer: **Option B**

Explanation:

36) If a < b & if c is any positive number, then ____

a) ac < bc

b) ac > bc

c) ac < bd

d) none of these

Answer: **Option A**

Explanation:

37) If a < b & if c is any negative number, then ___

a) ac < bc

b) ac > bc

c) ac < bd

d) none of these

Answer: **Option B**

Explanation:

38) If 0 < a < b and 0 < c < d, then ___

a) ac < bd

b) ac > bd

c) ab > cd

d) ab < cd

Answer: **Option A**

Explanation:

39) If a > b & b > c, then ___

a) a > c

b) c > a

c) a > b is positive

d) a > b is negative

Answer: **Option A**

Explanation:

40) If a > b, then a + c > b + c, and a – c > b – c if c is

a) subtracted from a only

b) any real number

c) added to b only

d) subtracted form b only

Answer: **Option B**

Explanation:

41) If a > b and c > d, then ___

a) a + d > b + c

b) a + c > b + d

c) a + b > c + d

d) none of these

Answer: **Option B**

Explanation:

42) If a > b & if c is any positive number, then

a) ac < bc

b) ac = bc

c) ab > ac

d) ac > bc

Answer: **Option D**

Explanation:

43) If a > b & c is any negative number, then _____

a) ac < bc

b) ac = bc

c) ab > ac

d) ac > bc

Answer: **Option A**

Explanation:

44) In mathematical logic, there are three traditional laws of thought to exemplify something fundamental on the way, we think. If we say that something cannot be TRUE and FALSE all at the same time, this law is called the Law of __________.

a) Contradiction

b) Excluded Middle

c) Identity

d) Subaltern

Answer: **Option A**

Explanation:

45) Felicito draws three balls in succession (without replacement), from a box containing five (5) Red Balls, Six (6) Yellow Balls, Seven (7) Green Balls. The probability of drawing the balls in the order Red, Yellow and Green is ______

a) 0.2894

b) 0.3894

c) 0.4289

d) 0.3489

Answer: **Option C**

Explanation:

46) A family of curves whose equations are the solutions of a given differential equation, i.e. the family of circles: x^{2} + y^{2} = c^{2}, which is the solution of the differential equation x + y (dy / dx) = 0.

a) Integral Curves

b) Differential Curves

c) Double Points

d) Orthogonals

Answer: **Option A**

Explanation:

47) Find a, b, c which satisfies the hypothesis of Rolle’s theorem for f(x) = x^{2} – 1.

a) a = 0; b = 1; c = 1/2

b) a = -1; b = 1; c = 1/2

c) a = -1; b = 0;c = 1/2

d) a = -1; b = 1; c = 0

Answer: **Option D**

Explanation:

48) A rectangle is inscribed in a square so that each vertex of the rectangle is at the trisection point of different sides of the square. The ratio of the area of the rectangle to that of the square is _____.

a) 7:72

b) 2:7

c) 4:9

d) 5:9

Answer: **Option C**

Explanation:

49) An integer greater than one that has no integral factors except itself and one is called _____ number.

a) Prime

b) Irrational

c) Transcendental

d) Differential

Answer: **Option A**

Explanation:

50) Find a number “c” which satisfies the conclusion of the “Mean Value Theorem” for f(x) = 1/x, a = 2 and b = 4.

a) √5

b) 2 √3

c) 7 √2

d) 2 √2

Answer: **Option D**

Explanation:

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