B.com. 2 Sem Mathematics

B.com. 2 Sem Mathematics

Q1. Find three numbers in A.P. such that their sum is 27 and the sum of their squares is 341.
Q2. A firm invests Rs.10, 000 in a business which has a net return of Rs.500 per year. An investment of Rs.20, 000 would yield a net return of Rs.2000 per year. What is the linear relationship between investment and net return? What would be the annual return on an investment of Rs.12, 000?
Q3. The ratio of income of two persons is 9:7 and the ratio of their expenditures is 4:3.If each of them manages to save Rs 2000 per month, find their monthly incomes.
Q4.Discuss about logarithmtic from x
Q5. Discuss the nature of roots
Q6.Integrate followig w.r.t. x
Q7. Relation gives fundamentals of Function, how? Provide example to show that every function is a relation but converse is not true.
Q8.find the derivative

Case Study
An automobile company uses three types of steel S1, S2 and S3 .For producing three types of cars c1, c2 , c3. Steel Requirements (in tons) for each type of car are given below:
Type of car
C1 C2 C3
S1 2 3 4
S2 1 1 2
S3 3 2 1

Type of steel

Q1. Determine the number of cars of each type which can be produced using 29, 13 and 16 tons of steel of three types respectively.

1. If a merchant offers a discount of 40% on the marked price of his goods and thus ends up selling at cost price, what was the % mark up?
2. One year payment to the servant is Rs. 200 plus one shirt. The servant leaves after 9 months and receives Rs. 120 and a shirt. Then find the price of the shirt.
3. A father left a will of Rs.35 lakhs between his two daughters aged 8.5 and 16 such that they may get equal amounts when each of them reach the age of 21 years. The original amount of Rs.35 lakhs has been instructed to be invested at 10% p.a. simple interest. How much did the elder daughter get at the time of the will?
4. What will be Rs.1500 amount in three years if it is invested in 20% p.a. compound interest, interest being compounded annually?
5. In an election contested by two parties, Party D secured 12% of the total votes more than Party R. If party R got 132,000 votes, by how many votes did it lose the election?
6. If the cost price of 20 articles is equal to the selling price of 16 articles, What is the percentage of profit or loss that the merchant makes?
7. (17)3.5 x (17)? = 178
8. The average weight of a class of 24 students is 36 kgs . When the weight of the teacher is also included, the average weight increases by 1kg. What is the weight of the teacher?
9. If 3(x – y) = 27 and 3(x + y) = 243, then x is equal to:
10. The value of [(10)150 ÷ (10)146]
11. (0.04)-1.5 =
12. A circuit in a connected graph, which includes every vertex of the graph is known as
13. Which of the following statements is not correct?
14. If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:
15. log 10 (-1) =?
16. If log10 2 = 0.3010, then log2 10 is equal to:
17. Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit’s age. After further 8 years, how many times would he be of Ronit’s age?
18. In ax2+bx+c = 0, there are—
19. In mathematical theory 0/0 is—
20. The sum of all terms of the arithmetic progression having ten terms except for the first term is 99 and except for the sixth term 89. Find the third term of the progression if the sum of the first term and the fifth term is equal to 10.
21. Sum of first n terms of a series is 5n2 + 2n, and then its second term is—
22. Sum of first n terms of a series is 5n2 + 2n, and then its second term is—
23. Sum of infinite number of terms in G.P. with first term ‘a’ and common ratio ‘r’ is –
24. If a, b, c….in A.P. then a2, b2, c2 will be in –
25. If f(x) = 1/x then f-1 =
26. In the relation of f(x), f-1 is—
27. First Derivative of 5 wrto x is –
28. If f(x) = g(u) and u = u(x) then –
29. Derivative of x-1 wrto x is—
30. Derivative of (x+1)2 wrto x is-
31. Integration of 1wrto x is-
32. ∫ [f(x)+g(x) ]dx
33. ∫ xn dx = xn+1 + C,
34. ∫ dx =
35. Order of a matrix is –
36. Null matrix contains
37. Null matrix contains
38. If A & B are two matrix then A+B =
39. To find the inverse of matrix A,
40. Singular matrix has its determinant value-

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