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# Question Paper Solutions - Algebra 2013 - 2014-S.S.C-10th Maharashtra State Board (MSBSHSE)

SubjectAlgebra
Year2013 - 2014 (March)

Marks: 40
[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.

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

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

Chapter: [2.02] Quadratic Equations
Concept: 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’.

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

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

Chapter: [7] Probability
Concept: Sample Space
[1]1.5

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

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

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

Chapter: [2.02] Quadratic Equations
Concept: 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………

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

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

Chapter: [2.03] Quadratic Equations
Concept: Solutions of Quadratic Equations by Factorization
[2]2.3

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

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

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

Chapter: [3] Linear equations in two variables
Concept: Linear Equations in Two Variables Applications
[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).

Chapter: [7] Probability
Concept: Sample Space
[2]2.6

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

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

Chapter: [2.02] Quadratic Equations
Concept: Nature of Roots
[3]3.2

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

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

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

Chapter: [5.01] Statistics
Concept: Mean of Grouped Data
[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
Chapter: [6] Statistics
Concept: Histograms, Frequency Polygon and Frequency Curve
[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?

Chapter: [1] Arithmetic Progression
Concept: 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

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

Chapter: [5] Statistics
Concept: Pie Diagram
[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.

Chapter: [1] Arithmetic Progression
Concept: 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.

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

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

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