BCA- Mathematics Multiple Choice Questions

1. Any measure indicating the center of a set of data, arranged in an increasing or decreasing order of magnitude, is called a measure of
A. Skewness

B. Symmetry

C. Central tendency

D. Dispersion

2. Scores that differ greatly from the measures of central tendency are called:
A. Raw scores

B. The best scores

C. Extreme scores

D. Z-scores

3. The measure of central tendency listed below is:
A. The raw score

B. The mean

C. The range

D. Standard deviation

4. The total of all the observations divided by the number of observations is called:
A. Arithmetic mean

B. Geometric mean

C. Median

D. Harmonic mean

5. While computing the arithmetic mean of a frequency distribution, the each value of a class is considered equal to:
A. Class mark

B. Lower limit

C. Upper limit

D. Lower class boundary

6. The sum of the squares fo the deviations about mean is:
A. Zero

B. Maximum

C. Minimum

D. All of the above

7. For a certain distribution, if ∑(X -20) = 25, ∑(X- 25) =0, and ∑(X-35) = -25, then is equal to:
A. 20

B. 25

C. -25

D. 35

8. The sum of the squares of the deviations of the values of a variable is least when the deviations are measured from
A. Harmonic mean

B. Geometric mean

C. Median

D. Arithmetic mean

9. If X1, X2, X3, … Xn, be n observations having arithmetic mean and if Y =4X± 2, then is equal to:
A. 4X

B. 4

C. 4 ± 2

D. 4 ± 2

10. If =100 and Y=2X – 200, then mean of Y values will be:
A. 0

B. 2

C. 100

D. 200

11. If the arithmetic mean of 20 values is 10, then sum of these 20 values is:
A. 10

B. 20

C. 200

D. 20 + 10

12. Ten families have an average of 2 boys. How many boys do they have together?
A. 2

B. 10

C. 12

D. 20

13. If the arithmetic mean of the two numbers X1 and X2 is 5 if X1=3, then X2 is:
A. 3

B. 5

C. 7

D. 10

14. We must arrange the data before calculating:
A. Mean

B. Median

C. Mode

D. Geometric mean

15. The lower and upper quartiles of a symmetrical distribution are 40 and 60 respectively. The value of median is:
A. 40

B. 50

C. 60

D. (60 – 40) / 2

16. If in a discrete series 75% values are greater than 50, then:
A. Q1 = 50

B. Q1 < 50 C. Q1 > 50

D. Q1 ≠ 50

17. Suitable average for averaging the shoe sizes for children is
A. Mean

B. Mode

C. Median

D. Geometric mean

18. A measurement that corresponds to largest frequency in a set of data is called:
A. Mean

B. Median

C. Mode

D. Percentile

19. Which of the following average cannot be calculated for the observations 2, 2, 4, 4, 6, 6, 8, 8, 10, 10 ?
A. Mean

B. Median

C. Mode

D. All of the above

20. What have been constructed from OR problems and methods for solving the models that are available in many cases?
A. Scientific models

B. Algorithms

C. Mathematical models

D. None of these

21. Which of the following is not the phase of OR methodology?
A. Formulating a problem

B. Constructing a model

C. Establishing controls

D. Controlling the environment

22. Operations research is the application of methods to arrive at the optimal solutions to the problems.
A. Economical

B. Scientific

C. Both A and B

D. Artistic

23. In operations research, the are prepared for situations.
A. Mathematical models

B. Physical models diagrammatic

C. Diagrammatic models

D. Both B and C

24. OR can evaluate only the effects of .
A. Personnel factors

B. Financial factors

C. Numeric and quantifiable factors

D. Both A and B

25. Which technique is used in finding a solution for optimizing a given objective, such as profit maximization or cost reduction under certain constraints?
A. Qualing theory

B. Waiting Line

C. Both A and B

D. Linear Programming

26. By constructing models, the problems in libraries increase and cannot be solved.
A. TRUE

B. FALSE

27. A solution can be extracted from a model either by
A. Conducting experiments on it

B. Mathematical analysis

C. Both A and B

D. Diversified Technique

28. The main limitation of operations research is that it often ignores the human element in the production process.
A. TRUE

B. FALSE

29. Feasible solution satisfies
A. Only constraints

B. only non- negative

C. Both A and B

D. A, B and optimal solution

30. What is the objective function in linear programming problems?
A. A constraint for available resource

B. An objective for research and development of a company

C. A linear function in an optimization problem

D. A set of non- negativity conditions

Answer: C.A linear function in an optimization problem

31. The area of the region bounded by the curves y = |x – 2|, x = 1, x = 3 and the x-axis is

A. 1
B. 2
C. 3
D. 4

32. Let A (2, –3) and B(–2, 1) be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is the line

A. 2x + 3y = 9
B. 2x – 3y = 7
C. 3x + 2y = 5
D. 3x – 2y = 3

Answer: A. 2x + 3y = 9

33. The equation of the straight line passing through the point (4, 3) and making intercepts on the co-ordinate axes whose sum is –1 is

A. x/2 + y/3 = -1 and x/-2 + y/1 = -1
B. x/2 – y/3 = -1 and x/-2 + y/1 = -1
C. x/2 + y/3 = 1 and x/2 + y/1 = 1
D. x/2 – y/3 = 1 and x/-2 + y/1 = 1

Answer: D. x/2 – y/3 = 1 and x/-2 + y/1 = 1

34. Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

A. 3/2
B. 5/2
C. 7/2
D. 9/2

35. A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates of each of the point of intersection are given by

A. (3a, 3a, 3a), (a, a, a)
B. (3a, 2a, 3a), (a, a, a)
C. (3a, 2a, 3a), (a, a, 2a)
D. (2a, 3a, 3a), (2a, a, a)

Answer: B. (3a, 2a, 3a), (a, a, a)

36. Consider the following statements:
(1) Mode can be computed from histogram
(2) Median is not independent of change of scale
(3) Variance is independent of change of origin and scale. Which of these is/are correct?

A. only (1)
B. only (2)
C. only (1) and (2)
D. (1), (2) and (3)

Answer: C. only (1) and (2)

37. If the straight lines x = 1 + s, y = –3 – Ks, z = 1 + ls and x = , y = 1 + t, z = 2 – t with parameters s and t respectively, are co-planar then K equals

A. –2
B. –1
C. – 1/2
D. 0

38. The probability that A speaks truth is , while this probability for B is . The probability that they contradict each other when asked to speak on a fact is

A. 3/20
B. 1/5
C. 7/20
D. 4/5

39. The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

A. 37/256
B. 219/256
C. 128/256
D. 28/256

40. A particle moves towards east from a point A to a point B at the rate of 4 km/h and then towards north from B to C at the rate of 5 km/h. If AB = 12 km and BC = 5 km, then its average speed for its journey from A to C and resultant average velocity direct from A to C are respectively

A. 17/4 km/h and 13/4 km/h
B. 13/4 km/h and 17/4 km/h
C. 17/9 km/h and 13/9 km/h
D. 13/9 km/h and 17/9 km/h

Answer: A. 17/4 km/h and 13/4 km/h

41. If A2 – A + I = 0, then the inverse of A is

A. A + I
B. A
C. A – I
D. I – A

42. Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12} be a relation on the set A = {3, 6, 9, 12}. The relation is

A. reflexive and transitive only
B. reflexive only
C. an equivalence relation
D. reflexive and symmetric only

Answer: A. reflexive and transitive only

43. If in a frequently distribution, the mean and median are 21 and 22 respectively, then its mode is approximately

A. 22.0
B. 20.5
C. 25.5
D. 24.0

44. Let P be the point (1, 0) and Q a point on the locus y2 = 8x. The locus of mid point of PQ is

A. y2 – 4x + 2 = 0
B. y2 + 4x + 2 = 0
C. x2 + 4y + 2 = 0
D. x2 – 4y + 2 = 0
Here 2 is read as square

Answer: A. y2 – 4x + 2 = 0

45. The system of equations
αx + y + z = α – 1,
x + αy + z = α – 1,
x + y + αz = α – 1
has no solution, if α is

A. -2
B. either – 2 or 1
C. not -2
D. 1

46. The value of α for which the sum of the squares of the roots of the equation
x2 – (a – 2)x – a – 1 = 0 assume the least value is

A. 1
B. 0
C. 3
D. 2

47. If roots of the equation x2 – bx + c = 0 be two consectutive integers, then b2 – 4c equals

A. – 2
B. 3
C. 2
D. 1

48. If the letters of word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number

A. 601
B. 600
C. 603
D. 602

49. Let f be differentiable for all x. If f(1) = – 2 and f′(x) ≥ 2 for x ∈ [1, 6] , then

A. f(6) ≥ 8
B. f(6) < size=”2″>

50. If in a triangle ABC, the altitudes from the vertices A, B, C on opposite sides are in H.P., then sin A, sin B, sin C are in

A. G.P.
B. A.P.
C. Arithmetic − Geometric Progression
D. H.P.

51. The area enclosed between the curve y = loge (x + e) and the coordinate axes is

A. 1
B. 2
C. 3
D. 4

52. If x dy/dx = y (log y − log x + 1), then the solution of the equation is

A. y log(x/y) = cx
B. x log(y/x) = cy
C. log(y/x) = cx
D. log(x/y) = cy

53. The line parallel to the x−axis and passing through the intersection of the lines ax + 2by + 3b = 0 and bx − 2ay − 3a = 0, where (a, b) ≠ (0, 0) is

A. below the x−axis at a distance of 3/2 from it
B. below the x−axis at a distance of 2/3 from it
C. above the x−axis at a distance of 3/2 from it
D. above the x−axis at a distance of 2/3 from it

Answer: A. below the x−axis at a distance of 3/2 from it

54. ∫ cosx

A. tanx
B. secx
C. sinx
D. -sinx

55. The angle between the lines 2x = 3y = − z and 6x = − y = − 4z is

A. 0 Degree
B. 90 Degree
C. 45 Degree
D. 30 Degree

56. If the plane 2ax − 3ay + 4az + 6 = 0 passes through the midpoint of the line joining the centres of the spheres
x2 + y2 + z2 + 6x − 8y − 2z = 13 and
x2 + y2 + z2 − 10x + 4y − 2z = 8, then a equals
Here 2 is read as Square

A. − 1
B. 1
C. − 2
D. 2

57. If non-zero numbers a, b, c are in H.P., then the straight line x/a + y/b + z/c always passes through a fixed point. That point is

A. (-1, 2)
B. (-1, -2)
C. (1, -2)
D. (1, -1/2)

58. If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is

A. (-1, 7/3)
B. (-1/3, 7/3)
C. (1, 7/3)
D. (1/3, 7/3)

59. If the circles x2 + y2 + 2ax + cy + a = 0 and x2 + y2 – 3ax + dy – 1 = 0 intersect in two distinct points P and Q then the line 5x + by – a = 0 passes through P and Q for

A. exactly one value of a
B. no value of a
C. infinitely many values of a
D. exactly two values of a
Here 2 is read as Square

Answer: B. no value of a

60. A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is

A. an ellipse
B. a circle
C. a hyperbola
D. a parabola

61. Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is

A. 5/9
B. 1/9
C. 8/9
D. 4/9

62. A lizard, at an initial distance of 21 cm behind an insect, moves from rest with an acceleration of 2 cm/s2 and pursues the insect which is crawling uniformly along a straight line at a speed of 20 cm/s. Then the lizard will catch the insect after

A. 19 s
B. 1 s
C. 21 s
D. 25 s

63. If both the roots of the quadratic equation x2 – 2kx + k2 + k – 5 = 0 are less than 5, then k lies in the interval

A. (5, 6]
B. (6, ∞)
C. (-∞, 4)
D. [4, 5]

64. A plane passes through (1, − 2, 1) and is perpendicular to two planes 2x − 2y + z = 0 and x − y + 2z = 4. The distance of the plane from the point (1, 2, 2) is

A. 0
B. 2
C. Square Root of 3
D. 2 Square Root of 2

Answer: D. 2 Square Root of 2

65. A tangent drawn to the curve y = f(x) at P(x, y) cuts the x-axis and y-axis at A and B respectively such that BP : AP = 3 : 1, given that f(1) = 1, then

A. equation of curve is x dy/dx – 3y = 0
B. normal at (1, 1) is x + 3y = 4
C. curve passes through (2, 1/8)
D. equation of curve is x dy/dx + 3y = 0

Answer: C. curve passes through (2, 1/8)

66. Suppose a population A has 100 observations 101, 102, … , 200, and another population B has 100 observations 151, 152, … , 250. If VA and VB represent the variances of the two populations, respectively, then VA/VB is

A. 1
B. 9/4
C. 4/9
D. 2/3

67. The number of values of x in the interval [0, 3π] satisfying the equation 2sin2x + 5sinx − 3 = 0 is

A. 4
B. 6
C. 1
D. 2

68. Let W denote the words in the English dictionary. Define the relation R by : R = {(x, y) ∈ W × W | the words x and y have at least one letter in common}. Then R is

A. not reflexive, symmetric and transitive
B. reflexive, symmetric and not transitive
C. reflexive, symmetric and transitive
D. reflexive, not symmetric and transitive

Answer: B. reflexive, symmetric and not transitive

69. A particle has two velocities of equal magnitude inclined to each other at an angle θ. If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. Then θ is

A. 90°
B. 120°
C. 45°
D. 60°

70. A body falling from rest under gravity passes a certain point P. It was at a distance of 400 m from P, 4s prior to passing through P. If g = 10 m/s2, then the height above the point P from where the body began to fall is

A. 720 m
B. 900 m
C. 320 m
D. 680 m

71. A straight line through the point A(3, 4) is such that its intercept between the axes is bisected at A. Its equation is

A. x + y = 7
B. 3x − 4y + 7 = 0
C. 4x + 3y = 24
D. 3x + 4y = 25

Answer: C. 4x + 3y = 24

72. In an ellipse, the distance between its foci is 6 and minor axis is 8. Then its eccentricity is

A. 3/5
B. 1/2
C. 4/5
D. 7

73. The function f(x) = x/2 + 2/x has a local minimum at

A. x = 2
B. x = −2
C. x = 0
D. x = 1

74. The set of points where f(x) = x / 1+|x| is differentiable is

A. (−∞, 0) ∪ (0, ∞)
B. (−∞, −1) ∪ (−1, ∞)
C. (−∞, ∞)
D. (0, ∞)

75. At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote is

A. 5040
B. 6210
C. 385
D. 1110

76. Differentiation of logx.sinx

A. sinx.1/x
B. cosx.sinx + logx
C. sinx.1/x + logx.cosx
D. cosx.(-1/x) + 1/logx

77. y = sinx then evaluate dy/dx = ? then what is Integration of ?

A. sinx
B. cosx
C. -sinx
D. -cosx

78. What is the value of factorial Zero (0!)

A. 10
B. 0
C. 1
D. -1

79. y = sinx + cosx – 5a what is dy/dx

A. cosx – sinx
B. cosx + sinx -5
C. sinx – secx
D. sinx + cosx + 5

80. If the system of linear equations
x + 2ay + az = 0
x + 3by + bz = 0
x + 4cy + cz = 0
has a non-zero solution, then a, b, c

A. are in A. P.
B. are in G. P.
C. are in H.P.
D. satisfy a + 2b + 3c = 0

81. If the sum of the roots of the quadratic equation ax2 + bx + c = 0 is equal to the sum of the squares of their reciprocals, then a/c, b/a, and c/b are in

A. arithmetic progression
B. geometric progression
C. harmonic progression
D. arithmetic-geometric-progression

82. A student is to Discussion 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is

A. 140
B. 196
C. 280
D. 346

83. The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by

A. 6! * 5!
B. 50
C. 5! * 4!
D. 7! * 5!

84. Let f (x) be a polynomial function of second degree. If f (1) = f (- 1) and a, b, c are in A. P., then f’ A., f’ B. and f’ C. are in

A. A.P.
B. G.P.
C. H. P.
D. arithmetic-geometric progression

85. If x1, x2, x3 and y1, y2, y3 are both in G.P. with the same common ratio, then the points (x1, y1) (x2, y2) and (x3, y3)

A. lie on a straight line
B. lie on an ellipse
C. lie on a circle
D. are vertices of a triangle

Answer: A. lie on a straight line

86. The real number x when added to its inverse gives the minimum value of the sum at x equal to

A. 2
B. 1
C. – 1
D. – 2

87. The area of the region bounded by the curves y = |x – 1| and y = 3 – |x| is

A. 2 sq units
B. 3 sq units
C. 4 sq units
D. 6 sq units

88. The degree and order of the differential equation of the family of all parabolas whose axis is x-axis, are respectively

A. 2, 1
B. 1, 2
C. 3, 2
D. 2, 3

89. Locus of centroid of the triangle whose vertices are (a cos t, a sin t), (b sin t, – b cos t) and (1, 0), where t is a parameter, is

A. (3x – 1)2 + (3y)2 = a2 – b2
B. (3x – 1)2 + (3y)2 = a2 + b2
C. (3x + 1)2 + (3y)2 = a2 + b2
D. (3x + 1)2 + (3y)2 = a2 – b2
Here 2 is read as Square

Answer: B. (3x – 1)2 + (3y)2 = a2 + b2

90. Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is

A. a function
B. reflexive
C. not symmetric
D. transitive

91. Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

A. x2 + 18x + 16 = 0
B. x2 – 18x – 16 = 0
C. x2 + 18x – 16 = 0
D. x2 – 18x + 16 = 0
Here x2 read as x Square

Answer: D. x2 – 18x + 16 = 0

92. If (1 – p) is a root of quadratic equation x2 + px + (1-p) = 0 , then its roots are

A. 0, 1
B. -1, 2
C. 0, -1
D. -1, 1

93. How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?

A. 120
B. 480
C. 360
D. 240

94. If one root of the equation x2 + px + 12 = 0 is 4, while the equation x2 + px + q = 0 has equal roots, then the value of ‘q’ is

A. 49/4
B. 4
C. 3
D. 12

95. A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is and when he retires 40 meter away from the tree the angle of elevation becomes . The breadth of the river is

A. 20 m
B. 30 m
C. 40 m
D. 60 m

96. The graph of the function y = f(x) is symmetrical about the line x = 2, then

A. f(x + 2)= f(x – 2)
B. f(2 + x) = f(2 – x)
C. f(x) = f(-x)
D. f(x) = – f(-x)

Answer: B. f(2 + x) = f(2 – x)

97. A point on the parabola y2 = 18x at which the ordinate increases at twice the rate of the abscissa is

A. (2, 4)
B. (2, -4)
C. (-9/8, 9/2)
D. (9/8, 9/2)

98. The normal to the curve x = a(1 + cosq), y = asinq at ‘q’ always passes through the fixed point

A. (a, 0)
B. (0, a)
C. (0, 0)
D. (a, a)

99. If 2a + 3b + 6c =0, then at least one root of the equation ax2 + bx + c lies in the interval

A. (0, 1)
B. (1, 2)
C. (2, 3)
D. (1, 3)

100. A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P (A ∪ B) is

A. 3/5
B. 0
C. 1
D. 5/2

101. The area of the plane region bounded by the curves x + 2y2 = 0 and x + 3y2 = 1 is equal to (y2 = y square)

A. 3/5
B. 4/3
C. 7/3
D. 1

102. A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2. Then the length of the semi−major axis is

A. 4/3
B. 8/3
C. 7/3
D. 5/3

103. A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at

A. (0, 2)
B. (0, 1)
C. (1, 0)
D. (2, 0)

104. The point diametrically opposite to the point P (1, 0) on the circle x2 + y2 + 2x + 4y − 3 = 0 is

A. (− 3, − 4)
B. (-3, 4)
C. (3, 4)
D. (-4, -1)

105. The conjugate of a complex number is 1/i-1. Then the complex number is

A. -1/i-1
B. 1/i+1
C. 1/i-1
D. -1/i+1

106. Let R be the real line. Consider the following subsets of the plane R × R. S = {(x, y) : y = x + 1 and 0 < t =” {(x,”>
A. neither S nor T is an equivalence relation on R
B. both S and T are equivalence relations on R
C. S is an equivalence relation on R but T is not
D. T is an equivalence relation on R but S is not

Answer: D. T is an equivalence relation on R but S is not

107. The perpendicular bisector of the line segment joining P (1, 4) and Q (k, 3) has y−intercept − 4. Then a possible value of k is

A. 1
B. -4
C. 3
D. 2

108. The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?

A. a = 0, b = 7
B. a = 5, b = 2
C. a = 3, b = 4
D. a = 2, b = 4

Answer: C. a = 3, b = 4

109. The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz−plane at the point (0, 17/2, -13/2) Then

A. a = 2, b = 8
B. a = 4, b = 6
C. a = 6, b = 4
D. a = 8, b = 2

Answer: C. a = 6, b = 4

110. Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity matrix. Denote by tr A., the sum of diagonal entries of A. Assume that A2 = I.
Statement −1: If A ≠ I and A ≠ − I, then det A = − 1.
Statement −2: If A ≠ I and A ≠ − I, then tr A. ≠ 0.

A. Statement −1 is false, Statement −2 is true
B. Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1
C. Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.
D. Statement − 1 is true, Statement − 2 is false.

Answer: D. Statement − 1 is true, Statement − 2 is false.

111. The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

A. -2
B. -4
C. -12
D. 8

112. How many real solutions does the equation x7 + 14×5 + 16×3 + 30x – 560 = 0 have?

A. 1
B. 4
C. 7
D. 5

113. The statement p → (q → p) is equivalent to

A. p → (p → q)
B. p → (p ∨ q)
C. p → (p ∧ q)
D. p → (p ↔ q)

Answer: B. p → (p ∨ q)

114. The value of cot(cosec-1 5/3 + tan-1 2/3) is

A. 2/17
B. 6/17
C. 7/17
D. 3/17