Maharashtra State BoardSSC (Marathi Semi-English) 10th
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Algebra 2013-2014 SSC (Marathi Semi-English) 10th Question Paper Solution

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Algebra
Marks: 40Date: 2013-2014 March

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

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

Concept: Arithmetic Progression
Chapter: [1] Arithmetic Progression
[1]1.2

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

Concept: Quadratic Equations
Chapter: [2] Quadratic Equations
[1]1.3

The following data shows the number of students using different modes of transport:

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’.

Concept: Tabulation of Data
Chapter: [5] Statistics
[1]1.4

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

Concept: Sample Space
Chapter: [4] Probability
[1]1.5

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

Concept: Median of Grouped Data
Chapter: [5] Statistics
[1]1.6

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

Concept: Quadratic Equations
Chapter: [2] Quadratic Equations
[8]2 | Attempt any four sub questions from the following:
[2]2.1

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

Concept: Arithmetic Progression
Chapter: [1] Arithmetic Progression
[2]2.2

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

Concept: Solutions of Quadratic Equations by Factorization
Chapter: [2] Quadratic Equations
[2]2.3

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

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method
Chapter: [3] Linear equations in two variables
[2]2.4

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

Concept: Linear Equations in Two Variables Applications
Chapter: [3] Linear equations in two variables
[2]2.5

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).

Concept: Sample Space
Chapter: [4] Probability
[2]2.6

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

Concept: Median of Grouped Data
Chapter: [5] Statistics
[9]3 | Attempt any three of the following sub questions:
[3]3.1

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

Concept: Nature of Roots
Chapter: [2] Quadratic Equations
[3]3.2

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

Concept: Cramer'S Rule
Chapter: [3] Linear equations in two variables
[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

Concept: Probability Examples and Solutions
Chapter: [4] Probability
[3]3.4

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’

Concept: Mean of Grouped Data
Chapter: [5] Statistics
[3]3.5

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
Concept: Histograms
Chapter: [5] Statistics
[8]4 | Attempt any two sub-questions from the following:
[4]4.1

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?

Concept: Arithmetic Progression
Chapter: [1] Arithmetic Progression
[4]4.2

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

Concept: Probability Examples and Solutions
Chapter: [4] Probability
[4]4.3

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 salesmen A is Rs. 18,000, then

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.

Concept: Pie Diagram
Chapter: [5] Statistics
[10]5 | Attempt any two of the following sub questions:
[5]5.1

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.

Concept: Arithmetic Progression
Chapter: [1] Arithmetic Progression
[5]5.2

The product of four consecutive natural numbers, which are multiples of fives, is Rs. 15,000. Find those natural numbers.

Concept: Linear Equations in Two Variables Applications
Chapter: [3] Linear equations in two variables
[5]5.3

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.

Concept: Graphical Method of Solution of a Pair of Linear Equations
Chapter: [3] Linear equations in two variables

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