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Assignment A

1. Find three numbers in A.P. such that their sum is 27 and the sum of their squares is 341..
2. 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?
3. 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.

1. Discuss about Logarithmic form of   xa = n and Prove that

1. Discuss the nature of roots of a Quadratic Equation. What is the Restriction imposed on ax2+bx+c=0 to be a quadratic also solve

Assignment B

1. Relation gives fundamentals of Function, how? Provide example to show that every function is a relation but converse is not true.
2. Integrate following w.r.t x

3.   Find the derivative of the following with respect to x,

1. 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

Types

of

Steel

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

Assignment C

Tick mark (√) the most appropriate Answers

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?
1. 57%
2. 40%
3. 66%
4. 33%
1. 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.

1. 80
2. 100
3. 120
4. Cannot be determined

1. 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?
1. 17.5 lakhs
2. 21 lakhs
3. 15 lakhs
4. 20

1. What will be Rs.1500 amount in three years if it is invested in 20% p.a. compound interest, interest being compounded annually?

1. 2400
2. 2592
3. 2678
4. 2540
1. 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?

1. 300,000
2. 168000
3. 3600
4. 24000

1. 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?

1. 20% Profit
2. 25% Loss
3. 25% Profit
4. 33% Loss
5. (17)3.5 x (17)? = 178
6. 29
7. 75
8. 25
9. 5

1. 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?

1. 60 kgs
2. 61 kgs
3. 37 kgs
4. None
5. If 3(xy) = 27 and 3(x + y) = 243, then x is equal to:
6. 0
7. 4
8. 2
9. 6

1. The value of [(10)150 ÷ (10)146]
2. 1000
3. 10000
4. 100000
5. 106

1. (0.04)-1.5 =?

1. 25
2. 125
3. 250
4. 625
5. A circuit in a connected graph, which includes every vertex of the graph is known as—

1. a) Euler
2. b) Universal
3. c) Hamilton
4. d) None of these

1. Which of the following statements is not correct?
2. log10 10 = 1
3. log (2 + 3) = log (2 x 3)
4. log10 1 = 0
5. log (1x 2 x 3) = log 1 + log 2 + log 3
6. If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:
7. 870
8. 976
9. 876
10. 912
11. log 10 (-1) =?
12. 0
13. 1
14. 10
15. Not Defined
16. If log10 2 = 0.3010, then log2 10 is equal to:
17. 699/301
18. 1000/301
19. 3010
20. 6990
21. 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?
22. 2 times
23. 5 times
24. 11/4 times
25. 3 times
26. In ax2+bx+c = 0, there are—
27. 2 roots
28. 3 root
29. n roots
30. none

1. a)
2. b)
3. c) g
4. d) none

1. In mathematical theory 0/0 is—
2. 0
3. 1
4. Meaningless
5. None

21.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.

1. 15
2. 8
3. 10
4. 5

1. Sum of first n terms of a series is 5n2 + 2n, and then its second term is—-

1. 15
2. 16
3. 17
4. None

1. Sum of first n terms of a series is 5n2 + 2n, then its second term is—-

1. 15
2. 16
3. 17
4. None

1. Sum of infinite number of terms in G.P. with first term ‘a’ and common ratio ‘r’ is —-
2. a/r
3. r/a
4. a/(1-r)
5. None
6. If a, b, c….in A.P. then a2, b2, c2 will be in —

1. P.
2. P.
3. P. & G.P. both
4. Can not say
5. If f(x) = 1/x then f-1 =
6. x
7. 1/x
8. 1/x2
9. None

1. In the relation of f(x), f-1 is—
2. Inverse Function
3. Reverse Function
4. opposite Function
5. None

1. First Derivative of 5 wrto x is —
2. x
3. 1/x
4. 0
5. None

1. If f(x) = g(u) and u = u(x) then —1. f ‘(x) = g ‘(u)
2. f ‘(x) = g ‘(u) . u ‘(x)
3. f ‘(x) = u ‘(x)
4. None of the above

1. Derivative of x-1 wrto x is—a) -1/x2
b)  1/x2
c)  1
d) None of the above

1. Derivative of (x+1)2 wrto x is—a)  x+1
b)  2(x+1)
c)  1
d) None of the above

1. Integration of 1wrto x is—a) 0
b) 1
c)  x
d) None of the above

1. ∫ [f(x)+g(x) ]dx =a)  ∫f(x)dx +∫g(x)dx
b)  ∫f(x)dx .∫g(x)dx
c)  ∫f(x)dx -∫g(x)dx
d) None of the above

1. ∫ xn dx =  xn+1 + C,a)  for all
b)  for all n = 1
c)  for all n = 0
d) None of the above

1. ∫dx =a)  log x + C
b)  log (1/x) + C
c) 1
d) None of the above

1. Order of a matrix is —a)  No. of rows × No. of column
b) No. of rows + No. of column
c)  No. of rows – No. of column
d) None of the above

1. Null matrix contains—a)  No element
b)  One element
c)  Two element
c) None of the above

1. If A & B are two matrix then A+B =a)  A – B
b)  B+A
c)  B – A
d) None of the above

1. To find the inverse of matrix A,—a)  |A| = 0
b)  |A| = 1
c)  |A| = 2
d) None of the above
2. Singular matrix has its determinant value—
a) 1
b)  2
c)  infinite
d) 0