MBSE HSSLC Sample Question Paper Business Maths

Total number of printed pages – 4 HSS/027

BUSINESS MATHEMATICS
SAMPLE QUESTION PAPER
Full Marks – 80
Time – 3 hours

General Instructions :
(v) The question paper has three parts – A, B and C. All the parts are compulsory.
(vi) Write the number of the question before attempting it.
(vii) Marks for each question are indicated against it.

PART-A
(COMMERCIAL ARITHMETIC – 24 MARKS)

1. Choose the correct answer from the options given below. 3x1=3
(a) The method of solving a problem by forming a compound proportion is
called_______
(i) The Compound Rule of three (ii) Rule of three
(iii) Ratio and proportion method (iv) None of these
(b) If a:b=2:3 and b:c=4:3, then a:b:c will be
(i) 8:12:9 (ii) 2:3:9
(iii) 2:3:12 (iv) 2:3:8
(c) In a ratio which is equal to 3:8, if the antecedent is 51. Then, the consequent
is________
(i) 136 (ii) 24
(iii) 11 (iv) 146
2. Two partners A and B start a business. A contributes Rs.12, 000 and B Rs.18, 000. B was to
have 15 % of the profit for his salary as manager. At the end of 7 months, A withdrew one
third of his capital, and two months later B withdrew one half of his. The profit for the year
amounted to Rs.3130. What sum of money ought each to receive? 2
3. If 10 men, 40 women, 80 boys can do a piece of work in 60 days working 6 hours a day,in
how many days will 5 men,5 women and 10 boys do the same working 9 hours a
day.(men:women:boy=1:2:4) 3
4. A contractor undertook to build a house in 21 days and engaged 15 men for that purpose.
After 15 days, he put in 9 more men on the work and he had it finished one day too soon.
How many days would he have taken without the additional men? 3

5. (a) Two pipes A and B can fill a cistern in 20 and 30 minutes respectively. The pipe B
opened first, after how many minutes the pipe A must also be opened so that the
cistern may be filled in 10 more minutes? 3
OR
(b) Divide Rs. 600 among A, B, and C so that B may get Rs.40 less than A and C may
get half of what B gets. 3

59

6. A, B and C have Rs 50,000, Rs 35,000 and Rs 25,000 respectively in Health care scheme. A
and B receives respectively 20 and 10 per cent of the annual profit as benefit. The remainder
of the profit is divided among them in proportion to their capital. If at the end of the year A
receives altogether Rs 1200 more than B, what does each receive? 5
7. (a) A and B enter into a partnership with Rs 40,000 and Rs 50,000 respectively. It is
agreed that A will draw salary of Rs. 300 per month for supervising the business and
B is to receive a commission of 2 % on the turnover as a salesman and the profit will
be shared in the proportion 2:3. In 1953,the sales amount to Rs 1,47,300 and the
profit amount to Rs 32,436 before charging salary and commission. Calculate the
returns that the income of A and B represent on their respective capitals. 5
OR
(b) A, B and C start a Partnership. A contributing Rs1440 and they agree to share profit
and losses prorate. A withdrew his capital after 4 months, B after 6 months and C
after 8 months. At the end of the year A got as his share 1/8 of the total profit, B got
1/3 and C the balance. Find how much B and C contribute to the business. 5

PART B
(ALGEBRA – 40 MARKS)
8. Choose the correct answer from the options given below: 9x1=9
(a) If >'„ = >'L .Then,. =
(i) 0 (ii) 14
(iii) 48 (iv) 1
(b) The LCM of 2!, 3! and 4! is
(i) 12! (ii) 4!
(iii) 2! (iv) 3!
(c) The 16th term of √2, 3√2, 5√2, 7√2, … is
(i) 16√2 (ii) 32√2
(iii) 31√2 (iv) 30√2
(d) The arithmetic mean between 2 and -18 is
(i) 10 (ii) -10
(iii) 8 (iv) -8

/ s ‰
(e) If T = 66, T S = 66 and T ∩ S = 66, then T ZŠ[ =
/ s
(i) (ii)
(iii) (iv)
s /

(f) A coin is tossed and a die is thrown. Then, the probability of obtaining a 6, given that
a head came up is
6 6
(i) (ii)
! M
6 6
(iii) (iv)
L

(g) A die is thrown and the outcome is odd, what is the probability that it is prime.
! 6
(i) (ii)
M M
M 6
(iii) (iv)
L

60

(h) A matrix is invertible if it is
(i) Singular (ii) Non-Singular
(iii) Skew-symmetric (iv) Symmetric
(i) If is an . × . square matrix. Then × ‹> =
(i) 0 (ii) ‹>
(iii) (iv) No value
9. If >TΠ= 840, >'Π= 35, find the value of N. 2
10. Find the value of . if >$6TM : >^6TM = 5: 12. 2
11. In a class, 40% of students study mathematics; 25% study Economics and 15% study both.
One student is selected at random. Find the probability that
(i) he studies Mathematics if it is known that he studies Economics
(ii) he studies Economics if it is known that he studies Mathematics 2

1 2 3 1
12. If |1 1 } •4 5 6Ž • −2 Ž = 0, find the value of . 2
3 2 5 3

13. Find the matrix • such that 2 − S + • = 0, 2
3 1 −2 1
where = and S =
0 2 0 3

14. Find the sum of all integers between 101 and 500 which are divisible by 9. 3
15. (a) Using property of determinant prove that 3
4+ 2 2
• 2 4+ 2 •= 5 +4 −4 !
2 2 4+
OR
9 7 3
(b) Express = •5 −1 4Ž as sum of Symmetric and Skew- Symmetric. 3
6 8 2

16. Divide 32 into four parts which are in AP such that the product of extremes is to the product of
means is 7:15. 5
17. Using matrix method solve 5
(a) 4 + 3 + 2‘ = 60;
+ 2 + 3‘ = 45;
6 + 2 + 3‘ = 70.
OR
(b) 3 − 4 + 2‘ = −1
2 + 3 + 5‘ = 7
+‘ =2

61

18. (a) Using graphical method, Maximize ’ = 4 + 3 subject to the constraints 5
≥ 0, ≥ 0, ≤ 400, ≤ 700, + ≤ 800 and 2 + ≤ 1000.

OR

(b) Maximize and Minimize ’ = 50 + 15 subject to the constraints 5
+ ≤ 16, 5 + ≤ 100, ≥ 0, ≥ 0.

PART-C
(BASIC CALCULUS – 16 MARKS)

19. Choose the correct answer from the options given below: 4x1=4
3x
e −1
(a) lim = ___
x →0 x
(i) 1/3 (ii) 3 (iii) 2 (iv) 1
dy
(b) if y = cos x 3 , then =_____
dx
(i) −3 x sin x 3 (ii) − x 2 sin x 3 (iii) −3 x 2 sin x3 (iv) − x 3 sin x 3

(c) ∫ 3x dx =_________
3x 3x 3x
(i) +c (ii) +c (iii) +c (iv) 3x log 3 + c
log 3 3log 3 log 3x

dy
(d) y = sin x , =_______
dx
cos x cos x cos x cos x
(i) (ii) − (iii) (iv)
sin x 2 sin x 2 sin x 2sin x

3 x − 2 when, x ≤ 0 
20. Show that the function f ( x) =   is discontinuous at x = 0 2
 x + 1 when, x > 0 

x+h − x
21. Evaluate lim 2
h→0 h

22. Differentiate ( x − 1)( x − 2)( x − 3) w.r.t x 2

23. (a) Find dy/dx y = (tan x)cot x + (cotx) tan x 3
OR
x2
(b) Evaluate: ∫ dx
1 + x6

<=>!
24. Evaluate: ∫tan-1Z [ 3
6^m”<!

_____________________
62