Q.1. Attempt any five of the following sub - questions. [5]
(i) Find the next two terms of the sequence : 2, 4, 6, 8, .........
(ii) Write the quadratic equation x2 - 3x = - 5 in the form of ax2 + bx + c = 0..
(iii) Write the linear equation in two variables using x and y to represent the following information. “The sum of two numbers is 30”.
(iv) Find the selling price when the marked price is Rs. 65 and discount is Rs. 15.
(v) A person has a gross annual income of Rs. 3,00,000 for the F.Y. 2012 - 13. Under section 80C, Rs. 1,00,000 is deducted from the gross annual income. Find his taxable income for the F.Y. 2012-13.
(vi) For the given A.P. 10, 15, 20, 25, ... find the common difference ‘d’.
Q. 2. Attempt any four of the following sub - questions. [8]
(i) Write any two Arithmetic Progression with common difference 3.
(ii) Solve the quadratic equation n2 - 36 = 0.
(iii) Find x + y for the following simultaneous equations.
(iv) If y ∝ x and x = 7 and y = 21, find the constant of variation (k) .
(v) The marked price of a machine is Rs. 2400. It is sold at a discount of 8%. Find the discount allowed on the machine.
(vi) Robin, the wholesaler paid Rs. 6,500 tax at the time of purchase and collected Rs. 8,000 tax at the time of sale. Find the M - VAT payable by Robin.
Q. 3. Attempt any three of the following sub - questions:
(i) Surendra saves Rs. 1 on the first day, Rs. 2 on the second day, Rs. 3 on the third day and so on. What will be his total savings after 20 days?
(ii) The product of two consecutive natural numbers is 56. Find the numbers.
(iii) If a ∝ 1/b, complete the following table.
a
|
20
|
8
|
............
|
............
|
b
|
4
|
............
|
5
|
40
|
(iv) A small scale industry gives 9% commission and 5% del - credere to his agent. If the agent sells the goods of Rs. 95,000, find the total earnings of the agent.
(v) The printed price of an article is Rs. 300. The rate of C.S.T. is 2%. Find the selling price, if discount is not given.
Q. 4. Attempt any two of the following sub - questions: [8]
(i) Solve the quadratic equation by formula method: 3x2 + 7x + 2 = 0.
(ii) The length of a piece of cloth varies directly as its cost. The cost of cloth having length 24m is Rs. 840. Find the length of a cloth having cost Rs. 525.
(iii) Mr. Albert’s gross annual income is Rs. 5,00,000 for the F.Y. 2012 - 13. His annual savings in this year are as follows.
(a) L.I.C. premium = Rs. 70,000.
(b) Contribution towards P.F. = Rs. 12,000.
(c) P.P.F. = Rs. 30,000
(d) N.S.C. = Rs. 10,000.
Find the taxable income and income tax for F.Y. 2012 - 13.
Q. 5. Attempt any two of the following sub - questions: [5]
(i) Find the sum of all natural numbers from 1 to 200 which are divisible by 4.
(ii) 5 pens and 6 pencils together cost Rs. 37 and 3 pens and 3 pencils together cost Rs. 21. Find the cost of a pen and a pencil.
(iii) A dinner set is sold for Rs. 1,500 cash or Rs. 1,000 cash down payment and Rs. 545 to be paid in one instalment after 6 months. Find the rate of interest charged under instalment scheme.