### ALGEBRA PRELIMINARY PAPER

1. Attempt any five of the following: (5)
1. Find the common difference (d) for the given A.P. 13, 23, 33, 43, .......
2. In the linear equation x + y = 15, if x = 12  then find the value of y.
3. Find the value of discriminant for the following: x2 + 4x + 1 = 0.
4. Check whether it is a quadratic or not: (m - 5) (m + 7) = 0
5. Write the following quadratic equation in a standard form: p(p - 6) = 0.
6. For the given quadratic equation: x2 + x - 5 = 0, find b2 - 4ac.

1. Attempt any four of the following. (8)
1. Show that the nth odd natural number is 2n - 1.
2. Solve the following simultaneous equation using Cramer’s rule: 4x + 3y - 4 = 0; 6x = 8 - 5y.
3. Solve x2 - 7x + 12 = 0 by formula method.
4. Find the value of discriminant: x2 + 4x + 1 = 0.
5. Express the following information in mathematical form using two variables x and y.
1. Sum of two numbers is 30.
2. Difference of the two numbers is 5.

1. Attempt any three of the  following: (9)
1. Solve the quadratic equation by completing square method: 2x2 + 8x + 6 = 0.
2. Mary got a job with a starting salary of Rs. 15,000/- per month. She will get an incentive of Rs. 100/-  per month. What will be her salary after 20 months?
3. Find the value of y from the following equation 6x + 3y = 9. If the value of x =1 .
4. For a certain frequency distribution, the values of Mean and Mode are 54.6 and 54 respectively. Find the value of median.

1. Attempt any two of the following: (8)
1. Find the sum of all even natural numbers from 1000 to 2000.
2. Following is the distribution of the size of certain farms from a taluka (tehasil)

 Size of farm (in Acres) 5 - 15 15 - 25 25 - 35 35 - 45 45 - 55 55 - 65 56 - 75 No. of farms 7 12 17 25 31 5 3
Find median size of farm.

1. Form the quadratic equation whose roots are: 3 and 10.
2. Two coins are tossed. Find the probability of the events that head appears on both the coins.

1. Attempt any two of the following: (10)
1. Draw Histogram and frequency polygon for the following frequency distribution.
 Class 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 Frequency 20 30 50 40 10
1. Solve the following quadratic equation by completing square method: 5y2 - 4y - 1 = 0.
2. Find four consecutive terms in an A.P. whose sum is 12 and the sum of 3rd and 4th term is 14.
3. Following is the componentwise expenditure per article, draw a pie chart.
 Component Expenditure (in Rs.) Raw Material 800 Labour 300 Transportation 100 Packing 100 Taxes 140