Q.1. Attempt any five of the following sub - questions. [5]
(i) For the given A.P. 5, 10, 15, 20, ........ find the common difference (d)
(ii) In linear equation x + y = 5, if x = 3, then find the value of y.
(iii) The number of notebooks (n) and the cost of notebooks (P) have direct variation between them. Write it symbolically.
(iv) Find the sale price when the marked price is Rs. 80 and discount is Rs. 20.
(v) The marked price of goods is Rs. 500 and the discount rate is 10%. Find the discount.
(vi) If y ∝ 1/x and x = 7 when y = 9, find the constant of variation (k).
Q. 2. Attempt any four of the following sub - questions. [8]
(i) If tn = 3n + 5, then find the first two terms of an A.P.
(ii) If a = 2, b = 6, c = 3, then find the value of b2 - 4ac.
(iii) Determine whether (1,4) is the solution of linear equation x + y = 5.
(iv) An agent sold an article for Rs. 4,000 by taking 6% commission. Find the commission of the agent.
(v) Mr. Somnath purchased a mobile for Rs. 5,000. The rate of Central sales Tax (C.S.T) is 2%. Find the C.S.T. on the mobile.
(vi) Express the following information in mathematical form using two variables x and y:
(a) The sum of the two numbers is 57.
(b) The difference of the two number is 40.
Q. 3. Attempt any three of the following sub - questions:
(i) Solve the given quadratic equation by factorization method: x2 + 10x + 24 = 0.
(ii) Solve the following simultaneous equations by the method of elimination by substitution. X + y = 3 and x - y = 1.
(iii) Complete the following table if n ∝ m.
n
|
3
|
4
|
5
|
............
|
7
|
m
|
12
|
16
|
.............
|
24
|
........
|
(iv) A shopkeeper makes his goods 30% above the cost price, but allows 20% discount for each purchase. What percent profit does he make?
(v) Sunder Enterprises purchases cosmetics for Rs. 6,000 and sold it to customer for Rs. 10,000. Find M - VAT paid at the rate of 10% by invoice method.
Q. 4. Attempt any two of the following sub - questions: [8]
(i) Find the sum of all odd natural numbers from 1 to 100.
(ii) If 10 workers can build a wall in 50 hours, how many workers will be required to do the same work in 25 hours?
(iii) Mr. Kale (52 years old) having taxable income of Rs. 3,25,000 in the financial year 2012 - 13. Calculate the net income tax payable.
Q. 5. Attempt any two of the following sub - questions: [5]
(i) A farmer borrowed Rs. 8,000 and agreed to repay with a total interest of Rs. 1,360 in 12 monthly instalments, each instalment - being less than the preceding by Rs. 40. Find the amount of the first and the last instalment.
(ii) Solve the following quadratic equation by completing square method. 5y2 - 4y - 1 = 0.
(iii) A bicycle is sold for Rs. 3,000 cash or for Rs. 1,000 cash down payment followed by two monthly instalment of Rs. 1,024 each. Compute the rate of interest charged under the instalment scheme.
