General Maths Algebra July 2016 Board Paper.

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

(i) Find the next two terms of the following sequence: 3, 6, 9, 12, .....

(ii) Write the equation 3x - 7y + 12 in “general form” of linear equation in two variables.

(iii) ‘x varies inversely as y’ - write it symbolically.

(iv) If a α b and a = 20, b = 5, then find the constant of variation (k).

(v) A marked price of goods is Rs. 1880 and selling price is Rs. 1504. Find the discount

(vi) Find the Central Sales Tax (CST) on selling price Rs. 800; if the rate of CST is 2%.

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

(i) If tn = a + (n - 1)d and a = 8, d = 4; then find the value of t4.

(ii) Write the following quadratic equation in the form of ax2 + bx + c = 0.
(x + 4) (x + 1) = 0

(iii) In linear equation 2x + 5y = 25, if x = 5, then find the value of y.

(iv) Express the following information in mathematical form using two variables x and y.

(a) Total cost of 5 pens and 6 pencils is is Rs. 37.
(b) Total cost of 3 pens and 3 pencils is Rs. 21.

(v) Find the selling price, when marked price of goods is Rs. 900 and discount is 10%.

(vi) Purchase value of goods is Rs. 1,000 and the sale value  is Rs. 1,200. M-VAT rate is 10%. Calculate the M - VAT by subtraction method.

Q. 3. Attempt any  three sub - questions from the following. (9)

(i) Check whether the given values of the variables are the roots of the given quadratic equation:
X2 - 4x + 3 = 0, x = 1 and x = 2.

(ii) Solve the following simultaneous equations by the method of elimination by substitution.
X + y = 15; x - y = 5.

(iii) If y α x and x = 5 when y = 20, then find
(a) The constant of variation (k)
(b) The value of x, when y = 8
(c) The value of y, when x = 3.

(iv) A small scale industrialist gives 10% commission and 5% del credre, to his agent. If the agent sells the goods of Rs. 50,000, find the total earnings of the agent.

(v) Mr. Khare is serving in  a company and earns Rs. 30,000 per month as a salary. His annual investments are as follows.
(1) L.I.C. annual premium Rs. 60,000.
(2) P.P.F. Rs. 20,000.
(3) P.F. Rs. 15,000
(a) Calculate gross annual income of Mr. Khare.
(b) Find total annual investment of Mr. Khare.
(c) Find the total taxable income of Mr. Khare.

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

(i) Find the sum of all even natural numbers from 1 to 100.

(ii) The wavelength of a sound and its frequency are inversely proportional to each other. If the frequency is 280 Hz, then the wavelength is 60 cm. Find the frequency, when the wavelength is 100 cm.

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

Q. 5 . Attempt any two sub - questions from the following. [10]

(i) A man borrows Rs. 4000 and agrees to repay with a total interest of Rs. 680 in 12 monthly instalments. Each instalment is being less than the preceding one by Rs. 20. Find the amount of the first and the last instalment.

(ii) In a mango grove, each vertical lines has 4 more trees than the horizontal row. If the total number of trees in the grove is 480, then find the number of trees in each horizontal row.

(iii) Shyam works at 4% commission, on the total sales, and incentive at 2% on excess of sales over Rs. 25,000. If he earns Rs. 2,350 as only a commission, find his total earnings.