# Question Paper - Algebra 2013 - 2014-S.S.C-Board Exam Maharashtra State Board (MSBSHSE)

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SubjectAlgebra
Year2013 - 2014 (March)

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Topics
Marks

Marks: 40
Q: 1 | Attempt any five question from the following:[5]
Q: 1.1[1]

For an A.P. t3 = 8 and t4 =12, find the common difference d.

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Q: 1.2[1]

(x + 5)(x - 2) = 0, find the roots of this quadratic equation

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Q: 1.3[1]
Q: 1.4[1]

‘A coin is tossed’. Write the sample space ‘S’.

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Q: 1.5[1]

If sumf_ix_i=75 and sumfi=15 , then find the mean x .

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Q: 1.6[1]

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

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Q: 2 | Attempt any four sub questions from the following:[8]
Q: 2.1[2]

State whether the following sequence is an AP or not:
1, 3, 6, 10………

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Q: 2.2[2]

Solve the following quadratic equation by factorization method:
9x2-25 = 0

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Q: 2.3[2]

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

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Q: 2.4[2]

If 12x +13y =29 and 13x +12y=21, find x + y.

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Q: 2.5[2]

A die is thrown. Write the sample space (S) and number of sample points n(S) and also write event A of getting even number on the upper surface and write n(A).

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Q: 2.6[2]

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

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Q: 3 | Attempt any three of the following sub questions:[9]
Q: 3.1[3]

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

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Q: 3.2[3]

Solve the following simultaneous equations by using Cramers’s rule:
3x-y =7
x +4y =11

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Q: 3.3[3]

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 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

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Q: 3.4[3]

The following table gives the frequency distribution of trees planted by different Housing Societies in a particular locality:

 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 Means Method’

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Q: 3.5[3]

Represent the following data by Histogram:

 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
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Q: 4 | Attempt any two sub-questions from the following:[8]
Q: 4.1[4]

A farmer borrows Rs.1,000 and agrees to repay with a total interest of Rs. 140 in 12 installments, each installment being less that the preceding installment by Rs. 10. What should be his first installment?

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Q: 4.2[4]

There are three boys and two girls. A committee of two is to be formed. Find the probability of events that the committee contains:
a) At least one girl.
b) One boy and one girl
c) Only boys

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Q: 4.3[4]
Q: 5 | Attempt any two of the following sub questions:[10]
Q: 5.1[5]

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

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Q: 5.2[5]
Q: 5.3[5]

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 triangle formed by these lines and the X-axis.

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