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Question Paper Solutions - Algebra 2014 - 2015-S.S.C-10th Maharashtra State Board (MSBSHSE)


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

State whether the following sequence is an A.P. or not?

1, 4, 7, 10, ………………..

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

A card is drawn from the pack of 25 cards labeled with numbers 1 to 25. Write the sample space for this random experiment.

Chapter: [7] Probability
Concept: Sample Space
[1]1.3

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
[1]1.4

For a sequence if n `S_n=n/(n+1)` then find the value of S10.

Chapter: [1] Arithmetic Progression
Concept: Introduction to Sequence
[1]1.5

Verify whether 1 is the root of the quadratic equation : `x^2+3x-4=0`

Chapter: [2.02] Quadratic Equations
Concept: Quadratic Equations
[1]1.6

If x + y = 5 and x = 3, then find the value of y.

Chapter: [3] Linear equations in two variables
Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method
[8]2 | Attempt any four sub-questions from the following:
[2]2.1

Solve the following quadratic equation by factorization method : `x^2-5x+6=0`

Chapter: [2.03] Quadratic Equations
Concept: Solutions of Quadratic Equations by Factorization
[2]2.2

Find the term t15 of an A.P. : 4, 9, 14, …………..

Chapter: [2.04] Arithmetic Progressions
Concept: General Term of an Arithmetic Progression
[2]2.3

If the point A(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

A die is thrown. If A is the event that the number on upper face is less than 5, then write sample space and event A in set notation.

Chapter: [7] Probability
Concept: Sample Space
[2]2.5

For a certain frequency distribution, the value of Mean is 101 and Median is 100. Find the value of Mode.

Chapter: [5] Statistics
Concept: Median of Grouped Data
[2]2.6

If one root of the quadratic equation kx2 – 7x + 12 = 0 is 3, then find the value of k.

Chapter: [2.02] Quadratic Equations
Concept: Quadratic Equations
[9]3 | Attempt any three of the following sub questions:
[3]3.1

Area under different crops in a certain village is given below. Represent it by a pie diagram :

Corps  Area (in Hectares)
Jowar 80
Wheat 20
Sugarcane 60
Vegetables 20
Chapter: [5] Statistics
Concept: Pie Diagram
[3]3.2

If two coins are tossed, then find the probability of the event that at least one head turns up.

Chapter: [4] Probability
Concept: Probability Examples and Solutions
[3]3.3

Solve the following simultaneous equations by using graphical method : x + y = 6;  x – y = 4.

Chapter: [3] Linear equations in two variables
Concept: Graphical Method of Solution of a Pair of Linear Equations
[3]3.4

There is an auditorium with 35 rows of seats. There are 20 seats in the first row, 22 seats in the second row, 24 seats in the third row and so on. Find the number of seats in the twenty-fifth row.

Chapter: [1] Arithmetic Progression
Concept: Arithmetic Progression
[3]3.5

Solve the following quadratic equation by completing square method : x2 + 10x + 21 = 0. 

Chapter: [2] Quadratic Equations
Concept: Solutions of Quadratic Equations by Completing the Square
[8]4 | Attempt any two sub-questions from the following:
[4]4.1

Two digit numbers are formed using the digits 0, 1, 2, 3, 4, 5 where digits are not repeated.


P is the event that the number so formed is even.
Q is the event that the number so formed is greater than 50.
R is the event that the number so formed is divisible by 3.
Then write the sample space S and events P, Q, R using set notation.

Chapter: [4] Probability
Concept: Probability Examples and Solutions
[4]4.2

The following table shows ages of 3000 patients getting medical treatment in a hospital on a particular day : 

Age (in years) No. of Patients
10-20 60
20-30 42
30-40 55
40-50 70
50-60 53
60-70 20

Find the median age of the patients.

Chapter: [5] Statistics
Concept: Median of Grouped Data
[4]4.3

If α + β = 5 and α33 = 35, find the quadratic equation whose roots are α and β.

Chapter: [2.02] Quadratic Equations
Concept: Quadratic Equations
[10]5 | Attempt any two of the following sub questions:
[5]5.1

Babubhai borrows Rs. 4,000 and agrees to repay with a total interest of Rs. 500 in 10 instlments, each instalment being less than the preceding instalment by Rs. 10. What should be the first and the last instalments?

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

On the first day of the sale of tickets of a drama, in all 35 tickets were sold. If the rates tickets were Rs. 20 and Rs. 40 per ticket and the total collection was Rs, 900, find the number of tickets sold of each rate.

Chapter: [2.02] Pair of Linear Equations in Two Variables
Concept: Simple Situational Problems
[5]5.3

Given below is the frequency distribution of driving speeds (in km/hour) of the vehicles of 400 college students:

Speed (in km/hr) No. of Students
20-30 6
30-40 80
40-50 156
50-60 98

60-70
60

Draw Histogram and hence the frequency polygon for the above data.

Chapter: [6] Statistics
Concept: Histograms, Frequency Polygon and Frequency Curve

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