ALGEBRA BOARD PAPER 2014 WITH SOLUTION

Q.P. SET CODE		SEAT NO.
A	N 217 – w		ALGEBRA PAPER – I
	NEW COURSE
2014	MATHEMATICS (71)		MAX MARKS:	40	(E)
	BOARD PAPER

Note : - (i) All question are compulsory.

(ii) Use of calculator is not allowed.

1. Attempt any five sub – questions from the following: [5]

(i) For an A.P.  t₃ = 8 and t₄ = 12, find the common difference d. [ANS]  
[VIDEO]

ii. (x + 5) (x – 2) = 0, find the roots of this quadratic equation. [ANS]

iii. The following data give the number students using different modes of transport: [ANS]

Modes of Transport	Number of Students
Bicycle	140
Bus	100
Walk	70
Train	40
Car	10

From this table, find the central angle (θ ) for the Mode of Transport 'Bus'.

iv. A coin is tossed. Write the sample space S. [ANS]

v. If Σ f_ix_i = 75 and Σ f_i = 15, then find the mean x̅. [ANS]

vi. Write the following quadratic equation in a standard form: 3x² = 10x + 7. [ANS]

Q2. Attempt any four sub questions from the following: [8]

i. State whether the following sequence is an A.P. or not: 1, 3, 6, 10, ……… [Ans]

ii. Solve the following quadratic equation by factorization method: 9x² – 25 = 0. [Ans]

iii. If the point (3,2) lies on the graph of the equation 5x + ay = 19, then find a. [Ans]

iv. If 12x + 13y = 29 and 13x + 12y = 21, find x + y. [Ans]

v. A die is thrown then write the sample space (S) and number of sample points n(S) and also write events A of getting even umber on the upper surface and write n(A). [Ans.]

vi. For a certain frequency distribution, the value of mean is 20 and mode is 11. Find the value of median. [Ans]


3. Attempt any three of the following sub questions: [9]

i. Solve the equation: 3y2 + 7y + 4 = 0, by using formula method.

ii. Solve the following simultaneous equations by using Cramer's rule: 3x – y = 7 & x + 4y = 11

iii. Two coins are tossed simultaneously. Write the sample space 'S' and the number of sample points n(S). Write the following events using set notation and mention the total number of elements in each of them:

a. A is the event of getting at least one head.

b. B is the event of getting exactly one head. 

iv. The following table gives frequency distribution of trees planted by different Housing Societies in a particular locality: [Ans]

No. of Trees	No. of Housing Societies
10 – 15	2
15 – 20	7
20 – 25	9
25 – 30	8
30 – 35	6
35 – 40	4

Find the mean number of trees planted by Housing Societies by using 'Assumed Mean Method'. 

v. Represent the following data by Histogram: [Ans] 

Price of Sugar Per kg. (in Rs.)	Number of Weeks
18 – 20	4
20 – 22	8
22 – 24	22
24 – 26	12
26 – 28	8
28 – 30	6

Q4. Attempt any two sub questions form the following: [ 8 Marks ]

i. A farmer borrows Rs. 1000 and agrees to repay with a total interest of Rs. 140 in 12 instalments, each instalment being less than the preceding instalment by Rs. 10. What should be his first instalment? [Ans]

(ii). There are three boys and two girls. A committee of two is to be formed, find the probability of events that the committee contains: [Ans]

a. at least one girl.

b. one boy and one girl.

c. only boys. 

(iii) The sales of salesmen in a week are given in the pie diagram. Study the diagram and answer the following questions. If the total sale due to salesman A is Rs. 18,000, then: [Ans.]

a. Find the total sale.

b. Find the sale of each salesman.

c. Find the salesman with the highest sale.

d. Find the difference between the highest sale and the lowest sale. 

5. Attempt any two of the following sub questions: [10]

i. If m times the mth term of an A. P. is equal to n times its nth term then show that the (m + n)th term of the A. P. is zero. [Ans.]

(ii) The product of four consecutive natural numbers which are multiples of five is 15,000. Find these natural numbers. [Ans.]

(iii) Draw the graphs representing the equations 4x + 3y = 24 and 3y = 4x + 24 on the same graph paper. Write the co – ordinates of the point of intersection of these lines and find the area of the triangle formed by these lines and the x – axis. [Ans.]