Q.1. Attempt any five of the following sub - questions. [5]
(i) Write any two arithmetic progressions with common difference 3.
(ii) Write the following quadratic equation in the standard form.
ax2 + bx + c = 0.
x2 = 3x - 5.
(iii) Write the following equation in the general form of a linear equation in two variables. 7x = 3y + 23.
(iv) If y varies directly as x and y = 40 when x = 15, find the constant of variation.
(v) If the printed price is Rs. 50 and discount is Rs. 10, then find the selling price.
(vi) If the cost price is Rs. 100 and selling price is Rs. 120, then find the profit.
Q. 2. Attempt any four of the following sub - questions. [8]
(i) If tn = 2n + 3, then find the first two terms of a given sequence.
(ii) Solve the following quadratic equation by factorization method. n2 + n - 42 = 0.
(iii) If tn = 3n + 5, then find the A.P.
(iv) Write the following quadratic equation in the form of ax2 + bx + c = 0 and write the values of a, b and c. 3(m2 - m + 2) = 0.
(v) An agent sold an article for Rs. 4,000 at 6% commission. Find the commission of the agent.
(vi) If the rate of C.S.T. is 2%, then find C.S.T. for the printed price Rs. 800.
Q. 3. Attempt any three of the following sub - questions: [9]
(i) Find the sum of all even natural numbers which are less than 75.
(ii) If x = 2 and y = 5 are the roots of the equation 7x + by = 54, then find the value of b.
(iii) Complete the following table in which x ∝ y.
x
|
4
|
5
|
2
|
.............
|
3
|
y
|
12
|
15
|
..........
|
21
|
...........
|
(iv) A salesman is offered 4% discount. Still he gets 20% profit. If the printed price of an article is Rs. 850, then find the cost price of the article.
(v) The printed price of an article is Rs. 500. If the rate of C.S.T. is 2%, then find the actual selling price if discount is not given.
Q. 4. Attempt any two of the following sub - questions: [8]
(i) Find S23 of an A.P.: 4, 8, 12, 16, .....
(ii) Solve the following simultaneous equations.
12x + 13y = 62 and 13x + 12y = 63.
(iii) A salesman is paid 7% commission on the total sales and an additional incentive at 4/5 on excess sales over Rs. 50,000. Find his total earnings on a total sales of Rs. 75,000.
Q. 5. Attempt any two of the following sub - questions: [10]
(i) The sum of two squares of two consecutive natural numbers is 85. Find the numbers.
(ii) y ∝ 1/√x and y = 10 when x = 6.25. Find y when x = 100.
(iii) The taxable income of Smt. Rekha (Age 45 years) is Rs. 6,50,000 for the financial year 2012 - 13. Complete the income tax she will have to pay for F.Y. 2012 - 13.
