July 2016 Algebra Board Paper SSC
Q. 1. Attempt any five of the following sub - questions: [5]
(i) If 3x + 2y = 10 and 2x + 3y = 15, then find the value of x + y.
(ii) Find the common difference of the A.P. : 3, 5, 7, ......
(iii) Two coins are tossed simultaneously. Write the sample space S.
(iv) Write the following quadratic equation in the standard form ax2 + bx + c = 0.
x(x + 3) = 7
(v) If Σf = 25 and Σfx = 100, then find the mean (x)
(vi) Find the value of a, b and c in the following quadratic equation:
2x2 + 18 = 6x.
Q. 2. Attempt any four of the following sub - questions. [8]
(i) Find the eighteenth term of the A.P. : 1, 7, 13, 19, .....
(ii) Form the quadratic equation if the roots are 3 and 8.
(iii) Solve the following simultaneous equations using Cramer’s rule:
4x + 3y = 4; 6x + 5y = 8
(iv) In the following experiment, write the sample space S, number of sample points n(S) , write the event P in set form and find n(P):
Form two - digit numbers using the digits 0, 1, 2, 3, 4 without repeating the digits, P is the event, that the number so formed is even.
(v) For a certain frequency distribution, the value of mean and mode are 54.6 and 54 respectively. Find the value of median.
(vi) Subject Wise marks obtained by a student in an examination are given below:
Subject
|
Marathi
|
English
|
Science
|
Mathematics
|
Total
|
Marks
|
85
|
90
|
85
|
100
|
360
|
Draw a pie diagram to represent the above data.
Q. 3. Attempt any three of the following sub - questions: [9]
(i) Represent the following data by a histogram.
Price of Sugar per kg (in Rs. )
|
28 - 30
|
30 - 32
|
32 - 34
|
34 - 36
|
36 - 38
|
Number of Weeks
|
4
|
8
|
22
|
12
|
6
|
(ii) A coin is tossed three times, then find the probability of the following events:
A is an event of getting a head on the middle coin.
B is an event of getting exactly one tail.
(iii) The following table shows ages of 300 patients getting medical treatment in a hospital on a particular day:
Age (in years)
|
10 - 20
|
20 - 30
|
30 - 40
|
40 - 50
|
50 - 60
|
60 - 70
|
No of Patients
|
60
|
42
|
55
|
70
|
53
|
20
|
Find the median age of patients.
(iv) Solve the following quadratic equation by using formula method.
7y2 - 5y - 2 = 0
(v) Draw a histogram and hence the frequency polygon for the following frequency distribution:
Rainfall (in cm)
|
20 - 25
|
25 - 30
|
30 - 35
|
35 - 40
|
40 - 45
|
45 - 50
|
No. of Years
|
2
|
5
|
8
|
12
|
10
|
7
|
Q. 4. Attempt any two of the following sub - questions: [8]
(i) The 11th term and the 21st term of an A.P. are 16 and 29 respectively, then find the first term, common difference and the 34th term.
(ii) If the point of intersection of ax + by = 7 and bx + ay = 5 is (3, 1) then find the value of a a and b.
(iii) In a certain race, there are three boys A, B and C. The winning probability of A is twice that of B and the winning probability of B is twice that of C. If P(A) + P(B) + P(C) = 1, then find the probabilities of their winning.
Q. 5. Attempt any two fo the following sub - questions: [10]
(i) Find the sum of all numbers from 50 to 250 which are divisible by 6 and find t13.
(ii) Solve: 9 (x2 + 1/x2) - 3 (x - 1/x) - 20 = 0 .
(iii) A three - digit numbers is equal to 17 times the sum of its digits. If 198 us added to the number, the extreme digits get interchanged. The sum of first and third digit is 1 less than middle digit. Find the number.
