**Questions:-**

** Business Mathematics (OBB 104) - Semester I**

**Section A**

**QUESTION**

**1.** Write the formula of sum an A.P. When first term, last term and 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 above information answer the following questions.

**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?

**Section C**

**QUESTION 1**

"If a rubber ball consistently bounces back? of the height from which it is dropped, what fraction of its original height will the ball bounce after being dropped and bounced four times without being stopped?"

- 42974
- 16/27
- 16/81
- 81/16

**QUESTION 2**

"What is the sum of the following series? -64, -66, -68, ..... , -100

- -1558
- 1558
- -1458
- -1658

**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?

- 0.25
- 0.5
- 0.6666
- 1

**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%?"

- 25
- 30
- 20
- 15

**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?

- 5
- 4
- 6
- 12

**QUESTION 6**

f(x)= (x³/4)+2x² -6x. Find f(-2)

- 18
- -18
- 4
- -4

**QUESTION 7**

y=3x3 + 7x5; then dy/dx at x =7 is

- 84467
- 84476
- 84477
- 84478

**QUESTION 8**

What will be the amount of Rs1000 for 20 years at 5% per annum compound interst

- Rs 2500
- Rs 2600
- Rs 2655
- Rs 2665

**QUESTION 9**

What is the present value of an annuity of Rs 300 per annum for 5 years at 4% ?

- Rs 1500
- Rs 1335.30
- Rs 1200
- Rs 1333.50

**QUESTION 10**

Given that X²+5X+5 = -Z° then the value of x is:

- "(-2,-3)"
- "(2,3)"
- "2,-3"
- "3,-2"

**QUESTION 11**

"Find the 10th term in the series 8, 16, 24........"

- 72
- 80
- 88
- 90

**QUESTION 12**

"Find the 7th term in the series 5, 25, 125......."

- 78125
- 15625
- 3125
- 390625

**QUESTION 13**

dy/dx of x(x-10) is

- 2x+10
- 2x-10
- x-10
- 2x

**QUESTION 14**

(256)0.16 x (256)0.09 = ?

- 16
- 32
- 256
- 4

**QUESTION 15**

"If 3(x y) = 27 and 3(x + y) = 243, then x is equal to"

- 0
- 2
- 4
- 3

**QUESTION 16**

(18)3.5 ÷ (27)3.5 x 63.5 = 2? :

- 3.5
- 7
- 10.5
- 4

**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?

- m*n
- m*p
- n*m
- p*n

**QUESTION 18**

The matrix

[ 9 0]

[ 0 9]

is a ?

- scalar matrix
- identity matrix
- even matrix
- odd matrix

**QUESTION 19**

Find lim x?? ( 5x + sin x ) /x

- 5
- 5+sinx
- 5/x
- sinx/x

**QUESTION 20**

The sum of three numbers in A.P. is 3 and 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

- 2
- 10
- 5
- 2.5

**QUESTION 22**

A man sold 20 articles for Rs. 60 and gained 20%.How many articles did he buy for Rs.60?

- 24
- 25
- 26
- 20

**QUESTION 23**

"If book bought at prices ranging from Rs. 200 to Rs. 350 are sold a prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling 8 books?"

- Rs 400
- Rs 600
- can´t be determined
- none of these

**QUESTION 24**

"A plot is sold for Rs. 18,700 with a loss of 15%. At what price it should be sold to get profit of 15%."

- Rs 25300
- Rs 22000
- Rs 25000
- Rs 18700

**QUESTION 25**

"By selling a book for Rs. 10, the publisher loses (1/11) of what it costs him. His cost price is:

- Rs 11
- Rs 10
- Rs 9
- Rs 10.50

**QUESTION 26**

"The smallest set A such that A? {1, 2} = {1, 2, 3, 5, 9} is"

- "{2,3,5}"
- "{3,5,9}"
- "{1,2,3,.5.9}"
- none of these

**QUESTION 27**

A set consisting of a definite number of elements is called a

- Finite set
- Infinite set
- Null set
- Singleton set

**QUESTION 28**

"The number of proper subsets of the set {1, 2, 3} is"

- 8
- 9
- 6
- 7

**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

- "6,4"
- "7,4"
- "8,6"
- "7,6"

**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
- 0.24
- 0.39
- 0.5

**QUESTION 31**

"If n (A) = 115, n (B) = 326, n (A-B) = 47, then n (A U B) is equal to"

- 370
- 373
- 441
- none of these

**QUESTION 32**

Every set is a ___________ of itself

- Proper subset
- Compliment
- Improper subset
- None of these

**QUESTION 33**

"In the following question, one term in series is wrong. Find out the wrong term? 2, 5, 10, 50, 500, 5000"

- 500
- 50
- 10
- 5000

**QUESTION 34 **

"If 92x 1 = 27x + 4, then x is equal to"

- 14
- 6
- 10
- 12

**QUESTION 35**

(2m)0 + 5(m)0 simplifies to

- 6m
- 5m
- 6
- 2

**QUESTION 36**

"Find the value of x, if 5x 3 * 32x 8 = 225."

- 4
- 3
- 5
- 6

**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 375
- Rs 365
- Rs 325
- Rs 300

**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 years
- 4.5 years
- 4 years
- 5.5 years

**QUESTION 39**

Find dy/dx of x2+ex+2x when x=3

- 3 + e3
- 5 + e3
- 9 + e3
- 8 + e3

**QUESTION 40**

When we find maxima or minima then derivative of first order is equal to

- 1
- -1
- 0
- can not say