Business Mathematics 

Section A

QUESTION

1. Write the formula of sum an A.P. When first term, last term and a number of terms are given. Also find 11th term of A.P.   90, 80, 70, 60........ 

2. "Solve the system of equations by matrix method.   
   x + y + z =62,     y + 5z =-4,        2x + 5y - z = 27" 

                          
3. Find derivative of     e^x/x^2    

4. Integrate       ∫x^5 dx 

5. Simple interest on a certain sum is 9 /16 of the sum. Find the rate percent and time, if both are equal. 

6. A dishonest dealer professes to sell his goods at cost price, but he uses a weight of 960 gm for a kg. Find his gain percent. 

7. Y =2x^3+ 5x^2+4x. Find maxima and minima. 

8. Find the difference between the simple interest and the compound interest on $ 5000 for 2 years at 6% per annum.

Section B

CASE STUDY

Of the 400 candidates who were interviewed for a position at a call center, 200 had a laptop, 140 had a calculator and 280 had a mobile phone. 80 of them had both, a laptop and a calculator, 60 had both, a calculator and a mobile phone and 120 had both, a laptop and mobile phone and 20 had all three. On the basis of the above information answer the following questions.   
    
                                         400
Laptop=200                                                   Calculator = 140
                               a    d   b
                               f    g    e 
                                     c
            Mobile =280     n=20
d+g = 80
80 both laptop & calculator
e+g = 60  had a both a calculator & a monitor phone 
f+g= 120 & 120 had a both a laptop & mobile phones
20 had all them
d+g = 80    ------1
g = 20 --------2
d = 60 -------3
f+g=120  

f = 100     --------4 
e = 40 -------5
a = 200 -(60+20+100)
a = 20  ------6
b = 140 -(120) = 20 ------7
c = 280 - (120+40) = 120 ----8
n = 400 - (a+b+c+d+e+f+g)
n = 400-380
n = 20 ----9

QUESTION 1
How many candidates who attended the interview had at least one of the three gadgets?

QUESTION 2
How many candidates had none of the three? 

    
QUESTION 3
How many candidates have only laptops?

Case Study 

A monopolist's demand function is p = 300 - 5x, answer the questions associated with this information.

1. Find the marginal revenue function.

2. Find the relationship between the slope MR and AR.

3. At what price is the marginal revenue zero?

Section- C    
 
Question 1
Abscissa of any point on the Y-axis is _______ 
   does not exist 
  -1 
  0 
  1 

Question 2
"What is the sum of the following series?   -64, -66, -68, ..... , -100"
  -1558 
  -1458 
  -1658 
  1558 
 
Question 3
A merchant marks his goods in such a way that the profit on sale of 50 articles is equal to the selling price of 25 articles. What is his profit margin
  0.6666 
  0.25 
  1 
  0.5 
 
Question 4
"If apples are bought at the rate of 30 for a rupee, how many apples must be sold for a Rupee so as to gain 20%?"
  20 
  30 
  15 
  25 
 
Question 5
Rs.1000 doubled in 6 years when compounded annually. How many more years will it take to get another Rs.2000 compound interest?
  12 
  5 
  6 
  4 
 
Question 6
f(x)= (x³/4)+2x² -6x. Find f(-2)
  -18 
  4 
  14 
  -4 
 
Question 7
  y=3x^3 + 7x^5;    then dy/dx at x =7 is
  84467 
  84478 
  84476 
  84477 
 
Question 8
What will be the amount of Rs1000 for 20 years at 5% per annum compound interst?
  Rs 2665 
  Rs 2600 (Wrong Ans)
  Rs 2655 
  Rs 2500 (Wrong Ans)
 
Question 9
What is the present value of an annuity of Rs 300 per annum for 5 years at 4%?
  Rs 1500 (Wrong Ans)
  Rs 1200 
  Rs 1335.30 (Wrong Ans)
  Rs 1333.50 
 
Question 10
Given that X²+5X+5 = -Z° then the value of x is:
"(-2,-3)"
"(2,3)"
"3,-2"
"2,-3"
 
Question 11
"Find the 10th term in the series 8, 16, 24........"
  88 
  80 
  90 
  72 
 
Question 12
"Find the 7th term in the series 5, 25, 125......."
  78125 
  15625 
  390625 
  3125 
 
Question 13
dy/dx of   x(x-10) is
  2x 
  2x+10 
  2x-10 
  x-10 
 
Question 14
How many terms of the following series may be taken so that their sum is 66?

-9,-6,3,…

  14 
  10 
  11 
  12 
 
Question 15
"If 3(x - y) = 27 and 3(x + y) = 243, then x is equal to"
  0 
  2 
  4 
  3 
 
Question 16
Perimeter of a triangle with vertices (0,0),(0,4) and (3,0) is _______

  13 (Wrong Ans)
  12 
  11 (Wrong Ans)
  14 
 
Question 17
If the order of matrix A is m * p. And the order of B is p*n. Then the order of AB is?
  n*m 
  p*n 
  m*n 
  m*p 
 
Question 18
The matrix
  

 [ 9    0]            

 [  0    9]

 is a ?  

  even matrix 
   odd matrix
   scalar matrix
   identity matrix
 
Question 19
If m and n are whole numbers such that m^n =121, the value of (m-1)^ (n+1) is  _______

  10 
  500 
  100 
  1000 
 
Question 20
The sum of three numbers in A.P. is 3 and the sum of their square is 3. The numbers are..
"1,0,1"
"2,-1,0"
"1,1,1"
"2,1,0"
 
Question 21
 (0.04)2.5 + x = (0.04)5   find value of x
  5 
  2.5 
  10 (Wrong Ans)
  2 (Wrong Ans)
 
Question 22
A man sold 20 articles for Rs. 60 and gained 20%. How many articles did he buy for Rs.60?
  25 
  26 
  24 
  20 
 
Question 23
"If book bought at prices ranging from Rs. 200 to Rs. 350 are sold prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling 8 books?"
  Rs 600 
  none of these 
can't be determined
  Rs 400 
 
Question 24
"A plot is sold for Rs. 18,700 with a loss of 15%. At what price it should be sold to get a profit of 15%."
  Rs 18700 
  Rs 25000 
  Rs 25300 
  Rs 22000 
 
Question 25
"By selling a book for Rs. 10, the publisher loses (1/11) of what it costs him. His cost price is:"
  Rs 10.50 
  Rs 9 
  Rs 11 
  Rs 10 
 
Question 26
The sum of first n terms of two Arithmetic Progressions are 3n+8 and 7n+15. The ratio of their 12th term is _____

  2/13 
  4/19 
  7/16 
  1 
 
Question 27
A set consisting of a definite number of elements is called a
  Infinite set 
  Null set 
  Singleton set 
  Finite set 
 
Question 28
"The number of proper subsets of the set {1, 2, 3} is"
  7 
  6 
  9 
  8 
 
Question 29
Two finite sets have n and m elements. The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second set. Then the values of m and n are
"7,6" (Wrong Ans)
"6,4"
"8,6" (Wrong Ans)
"7,4"
 
Question 30
"A survey showed that 63 % of the Americans like cheese whereas 76 % like apples. If x % of Americans like both cheese and apples, then find the maximum value of x?"
  0.37 
  0.5 
  0.39 
  0.24 
 
Question 31
"If n (A) = 115, n (B) = 326, n (A-B) = 47, then n (A U B) is equal to"
  441 
  373 
  none of these  
  370 
 
Question 32
Every set is a ___________ of itself
  Compliment 
  Proper subset 
  None of these 
  Improper subset 
 
Question 33
"In the following question, one term in series is wrong.  Find out the wrong term.

2, 5, 10, 50, 500, 5000"

  50 
  500 
  5000 
  10 
 
Question 34
The sum of all numbers between 200 and 400 which are divisible by 7 is _______
  8729 
  8965 
  8500 
  4537 
 
Question 35
 (2m)^0 x 5(m)^0 simplifies to
  6m (Wrong Ans)
  1 
  2 
  5m 
 
Question 36
A committee consisting of 5 members is to be formed out of 6 men and 4 women. How many committees can be formed so that at least one woman is always there in the committee?
  232 
  523 
  246 
  none of these (Wrong Ans)
 
Question 37
"If the difference between the simple interest and compound interests on some principal amount at 20% for 3 years is Rs. 48, then the principal amount is"
  Rs 325 
  Rs 375 
  Rs 300 
  Rs 365 
 
Question 38
How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
  5.5 years 
  4.5 years 
  4 years 
  5 years 
 
Question 39
Find dy/dx of   x^2+e^x+2x when x=3
  5 + e^3 (Wrong Ans)
  9 + e^3 (Wrong Ans)
  3 + e^3 
  8 + e^3
 
Question 40
When we find maxima or minima then derivative of first order is equal to
  -1 
  0 
  cannot say 
  1

41. If transpose of a matrix is same as the given matrix, then the matrix is _____________

Null matrix

Diagonal matrix

Skew - Symmetric matrix

None of these

42. In which type of matrix, all entries above the main diagonal are zeros?

Triangular
Upper Triangular
Lower Triangular
All of these

43. Two matrices A and B must be _______ for multiplication to be possible.

Square
Rectangular
Conformable
Null

44. Inverse of any matrix is dependent upon ________

Determinant
Cofactor Matrix
Adjoint Matrix
All of these

45. What will be the amount of Rs1000 for 20 years at 5% per annum compound interest?

Rs 2500
Rs 2600
Rs 2655
Rs 2665

46. Relation between "Domain set - Types of fruits" to “Range set - Colors of fruits" is ________.
one one function
many one function
one to one function
not a function

47. In a linear function, ration of x change to y change is always __________
1:2
constant
2:3
None of these

48. Which of the following methods is used to solve the system of linear equations with the help of determinants only?
Gauss Elimination Method
Cramer's Rule
Matrix Inversion Method
All of these

49. lim x ⟶ 0 ( S i n x /x )

1

2

3

4

50. dy/dx  of   x(x-10) is
2x+10
2x-10
x-10
2x

51. A function is called continuous if at every point of the domain set, the ___________.
limit exists
function value is same as limit value
Both of these
None of these

52. In a linear function, ration of x change to y change is always __________
1:2
constant
2:3
None of these

53. In a function, if limit do not exist at a domain value x= a, then function is _________. 
Discontinuous
Continuous
Uniform
Linear

54. Differentiation of the function f(x) = 4− 5is ___________. 
2
√x/2
2/ 
None of these 

55. According to Product Rule for differentiation, [f(x) . g(x)]'= __________
f'(x) . g'(x)
f(x) . g'(x)
f'(x) . g(x)
None of these

56. 
 
(x+1).e^x
(x-1)e^x
(x+1)/e^x
None of these

57. A function is strictly increasing in a region where ________.

f´(x) > 0

f´(x) < 0

f´(x) ≥ 0

None of these

58. The domain values at which the first prime of the function becomes zero are called _________.
zeros
roots
critical values
mid values

59. Critical values for the function f(x) = 2 x 3 − 3 x 2 − 12 x + 1 are _______.

x=-3 and x=4

x=3 , x=4

x=3 , x=-4

x=-3, x=-4

60. If f′(x)>0  ∀ x<c and f′(x)<0  ∀ x>c , then f(c) is __________ value of f.  

absolute minimum
local maximum
absolute maximum
local minimum

61. Maxima for the function f(x) = x 3 − 6 x 2 + 9 x + 20 is ________.

x = 3

x = 1

x = 2

none of these

62. Which method of integration among the following is derived from product rule of differentiation?

Substitution Method
Partial Fractions Method
Integration by Parts
All of these

63. In LPP, a term ____________ is often used to denote the unutilized capacity of resources.

constraint
decision variable
surplus variable
slack variable

64. As a part of simplex method to solve LPP, the formula used for finding new elements in the Key row = 

(key element)/(old element in key row)
(old element in key row)/(new key element)
(old element in key row)/(key element)
(new element in key row)/(key element)

65. As a part of Simplex method to solve LPP, Key row is selected on the basis of ___________. 

highest entry in Key column
maximum ratio
minimum ratio
None of these

66. As a part of Simplex method to solve the LPP, Key column is selected on the basis of __________.

lowest positive value of Cj - Zj
highest negative value of Cj - Zj
highest positive value of Cj - Zj
lowest negative value of Cj - Zj

67. In simplex method to solve the LPP, constraints needs to be converted from __________ to __________.
equations, inequalities
inequalities, equations
inequalities, sum
none of these

68. Which of the following methods to solve system of linear equations, uses Augmented Matrix form?
Cramer's Rule
Matrix Inversion Method
Gauss Elimination Method
None of these