BASIC MATHEMATICS & ELEMENTS
1.
2.
3.
4.
5.
In mathematical number system, π is considered ?
a.) Radical
b.) Non – Radical
c) Rational
d) none of the above
In mathematical number system, e is considered ?
a.) Radical
b.) Non – Radical
c) Rational
d) non of the above
In mathematical number system, √3 is considered ?
a.) Radical
b.) Non – Radical
c) Rational
d) non of the above
In mathematical number system, √25 is considered ?
a.) Radical
b.) Non – Radical
c) Rational
d) non of the above
In mathematical number system, 1/3 is considered ?
a.) Radical
b.) Non – Radical
c) Rational
d) non of the above
6.
Evaluate and solve for x . 3x + 9x = 27x ---- Ans : 0.438
7.
Evaluate and solve for x . ex + e-x = 5 ---- Ans : 1.57
8.
Evaluate and solve for x . log7x + log7(x-2) = (log315)/(log37) ---- Ans : 5
9.
The equation x2-4Kx+10-6K = 0 will have two equal roots if the value of K is ---- Ans : -5/2
10. If x , y, and 5x are three consecutive term of an arithmetic progression whose sum is 81, find x ? ---- Ans : 9
11. What is the sum of the first 100-positive odd integers ? ---- Ans : 10,000
12. In how many ways can a poster colored if there are 5 different colors available ? --- Ans : 31
13. In how many ways can a panel of 5-judges make a majority decision ? ---- Ans : 16
14. How many ways can four girls and four boys be seated alternately in a row of eight chairs ? ---- Ans : 1152
15. What is the value of “ x “ in the expression : x – 1/x = 0 ---- Ans : x = 1 , -1
16. What is the value of A : A-6/8 = 0.001. ----- Ans : 10000
17. How many 4-digits number can be made using the digits from 1 to 9 if no digit is repeated in each number ? ---- Ans :
3024
18. How many arrangements can be made from the letters of the word “ RESISTORS” when all are taken all at a time ? ---Ans : 40,320
19. In how many ways can 8-students be divided into 4-groups of 2 ? ---- Ans : 2520
20. In how many ways can be 3-men be selected out of 15 men if 2 of the men are to be excluded from every selection ? ---Ans : 286
21. How many possible mathematical methods we can solve a linear equation ? --- 5 (by elimination, by substitution, by
determinants, by graphical, & by comparison)
22. Is cologarithm of a number is equal to the reciprocal of the logarithm of that number ? (no)
23. Is the greater angle is opposite the squares of the other angles complementary to each other ? ( no )
24. The total surface area of the cube is twice the square of its diagonal. Derive the solution.





Where D = is the diagonal & x = is the side
D2 = X 2 + X 2 + X 2 = 3 X 2
Surface Area = 6 (area of each face) = 6 X2 = 2 (3 X2)
Where 3 X2 = D
Then Surface Area = 2 D2
25. Vector components are called _____________________ (rectangular components)
26. How many times the volume of a sphere increases if the radius of the sphere is doubled ? (8 times)
27. Is the function of a reference angle is the function of any angle A which is equal to plus or minus. (no)
28. The term _____________ refers to describe another mathematical expression and appears most frequently in column
formulas. (radius of gyration).
29. State the quadrant in which the coordinate (15,-2) lies : (quadrant IV)
30. Add the given vectors (-4 , 7) + (5,-9) : (1 , -2)
31. The straight lines : 4x-y+3 = 0 & 8x-2y+6 = 0 . They intersect at __________________ : (coincident , parallel, infinity,
origin)
32. If a circle of radius b rolls without slipping on the inside of a circle of radius a, any point of the 1 st Circle traces a roulette
known as _____________ : (hypocycloid , cycloid, strophoid, epicycloid)
33. The equation x3 + y3 – 3axy = 0 represents a curve called ______________ (stropoid, cardioid , lemniscate, folium of
descartes)
34. The cotangent function is negative in what quadrant _____. (III only, II & IV , IV only , I & III)
35. What curve is represented by the equation r = a ? (spiral of Archimedes, four leaved rose, cardiod, three leaved rose)
36. If n is large & positive the it is _______ . (large, irrational, negative, none of these insufficient data)
37. The inflection point of the function f (x) = 3x (5/3) is ______ : (0, -1, infinity, non-existent)
38. The acute angle between the two straight lines y=3x+2 & y=4x+7 is close to ____. ( 0deg , 90deg, 4.399 deg, & 28.305
deg)
39. The earliest recorded std. of length was ___________ . (palm, digitus, cubit, uncia)
40. King Henry I of England invented the ____________. (yard, pace, cubit, foot)
41. Mile is equal to _________ paces. (1000, 590, 5000, 1130)
42. The std. cubit was made of a stable material available during those days, which is ________ . (stainless steel, alloy,
platinum, granite)
43. The _____is also called the Iron Ulna . (yard, pace, cubit, foot)
44. The metre is equal to 1,650,763.73 wavelengths in vacuum of the orange-red radiation emitted from the atom of _______
( krypton 86)
45. An equation that is true for all values of the variable is called ______________ (identity, like terms, expression,
coefficient)
46. _______ is an equation that contains letters, in addition to variable & numbers (literal eqn., simple eqn, linear eqn., none
of these)
47. _______________ is the values obtained by equal subdivisions of a set of values. (quantiles, quartiles, percentiles, none
of these)
48. It is a measure of dispersion which depends only on two scores in the entire distribution. (mean deviation, quartile
deviation, variance, range)
49. The most numerous or most common value in a series of values is called the ________. (range, mode, mean, median)
50. An arrangement of raw numerical data in ascending or descending order of magnitude is called _______. (data, array,
frequency, category)
51. The probability of an impossible event is ______. (zero, unity, infinity, undefined)
52. It is a variable that can only assume designated values . (continuous variable, parameter, discrete variable, variate)
53. If two events have no outcomes in common, then they are said to be _______. (dependent, independent, mutually
exclusive, mutually inclusive)
54. The class interval 50-52 theoretically includes all measurements from 49.5 to 52.5 and these end points are called the
__________ . (class limits, class boundaries, class marks, none of these).
55. The total area under a probability curve is always _________. (equal to unity, between zero & one, greater than one, less
than one)
56. The range is a measure of ___________________. (variability, deviation, central tendency, distribution)
57. If A & B are two events and p(A & B) = p(A) p(B), then the two events are said to be _______. (complementary, disjoint,
independent, dependent)
58. The highest score in a distribution minus the lowest score is called the ____________. (class mark, median, range,
standard score)
59. The most widely used measure of dispersion is the __________. (mean deviation, std. deviation, quartile deviation,
average deviation)
60. The sum of the squared deviations about the mean is called ____________. (variate, variable, variance, value)