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9TH MAHARASHTRA: MATHS I MATHS II 2019 BOARD PAPER SOLUTION

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Q.1. Attempt any five of the following sub - questions. [5]

(i) Find the next two terms of the following sequence: 1, 3, 5, 7, ......

(ii) If tn = 4n, find t1.

(iii) Compare the quadratic equation x2 + 3x - 1 = 0 with the general form ax2 + bx + c = 0 and write the value of ‘a’ and ‘b’.

(iv) Write any one linear equation using the variables ‘x’ and ‘y’.

(v) Find the discount when the marked price is Rs. 25 and the selling price is Rs. 23.

(vi) Mohan paid tax Rs. 1,000 on purchase value and collected Rs. 1,200 tax on sale value. Find the M - VAT payable by Mohan.

Q. 2. Attempt any four of the following sub - questions. [8]

(i) Find the 10th term of an A.P: 2, 5, 8, 11, ......

(ii) Check whether m = - 1 is the root of the quadratic equation: m2 + 4m + 3 = 0.

(iii) Find (x + y) for the following simultaneous equations: 2x + 3y = 4 and 3x + 2y = 6.

(iv) If x ∝ y and x = 20 when y = 5, find the constant of variation (k).

(v) Vishwasrao purchased Khadi shirt and trousers having printed price Rs. 900 together, getting 15% rebate on printed price. Find the amount of rebate.

(vi) Mr. Kadam (below 60 years) has a gross annual income of Rs. 2,40,000 from all sources for the financial year 2012 - 13. Calculate his taxable income for the current year.

Q. 3. Attempt any three of the following sub - questions:

(i) Find S25 of an A.P.: 4, 8, 12, 16, .......

(ii) Solve the quadratic equation by factorization method: m2 + 10m + 24 = 0.

(iii) If ‘x’ varies inversely as ‘y’ and x = 10, when y = 8.

(a) Find the constant of variation (k)

(b) Write the equation of variation.

(c) Find ‘y’ when x = 4.

(iv) Sheshrao Patil purchased 2 towels for Rs. 90 each. 3 shirts for Rs. 220 each and 4 trousers for Rs. 290 each from Swarajya Khadi Bhandar, Wardha. The Bhandar gave 20% rebate. Find the amount Sheshrao Patil paid.

(v) Ashwini purchased a set of cooking range with the list price of Rs. 50,000. If 5% discount was given and 2% CST was paid, then find the amount paid by Ashwini.

Q. 4. Attempt any two of the following sub - questions: [8]

(i) The product of two consecutive odd natural numbers is 99. Find the numbers.

(ii) The electric current (I) flowing through circuit is directly proportional to the potential difference (V) in it. When the potential difference is 60 volts, the electric current is 1.5 amperes. Find the electric current flowing through the circuit when the potential difference is 100 volts.

(iii) A wholesaler purchased electric material for Rs. 1,50,000. He sold it to a retailer for Rs. 1,80,000. The retailer sold the same material to a customer for Rs. 2,20,000. Find the M - VAT payable at every stage of trading at the rate of 12.5 %.

Q. 5. Attempt any two of the following sub - questions: [5]

(i) Devendra invested in a National Saving Certificate Scheme. In the first year he invested Rs. 1,000, in second year Rs. 1,400, in the third year Rs. 1,800 and so on. Find the total amount that he invested in 12 years.

(ii) The sum of the present ages of Reshma and her mother is 60 years. Five years ago, her mother’s age was 4 times the age of Reshma. Find their present ages.

(iii) An artificial jewellery item is available for Rs. 850 cash or Rs. 600 cash - down payment and Rs. 270 to be paid in one instalment after 6 months. Find the rate of interest charged under instalment scheme.

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