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Algebra 2014-2015 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

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Algebra
Marks: 40Academic Year: 2014-2015
Date: July 2015

All questions are compulsory. 


[5]1 | Attempt any five of the following sub questions:
[1]1.i

Find the first two terms of the following sequence: 

tn = n +2 . 

Concept: Terms in a sequence
Chapter: [0.03] Arithmetic Progression
[1]1.ii

Write the quadratic equation 3y2 = 10y +7 in the standard form ax2 + bx + c = 0 .

Concept: Quadratic Equations
Chapter: [0.02] Quadratic Equations
[1]1.iii

find the value of the following determinant: `|[4,3],[2,7]|` 

Concept: Determinant of Order Two
Chapter: [0.01] Linear equations in two variables
[1]1.iv

Write the sample space if two coins are tossed.

Concept: Sample Space
Chapter: [0.05] Probability
[1]1.v

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

1,3,6,10,...... 

Concept: Terms in a sequence
Chapter: [0.03] Arithmetic Progression
[1]1.vi

The perimeter of a rectangle is 36 cm. Write the equation for this statement using two variables.  

Concept: Linear Equations in Two Variables
Chapter: [0.01] Linear equations in two variables
[8]2 | Attempt any four of the following sub questions:
[2]2.i

If one root of the quadratic, x2 - 7x + k = 0 is 4. then find the value of k.

Concept: Roots of a Quadratic Equation
Chapter: [0.02] Quadratic Equations
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[2]2.ii

Find the eighteenth term of the A.P.7.13,19,25,....

Concept: Arithmetic Progression Examples and Solutions
Chapter: [0.03] Arithmetic Progression
[2]2.iii

A die is thrown. Write the sample space. If P is the event of getting an odd number, then write the event P using set notation.

Concept: Sample Space
Chapter: [0.05] Probability
[2]2.iv

If D= 18, Dy = 15 and D = 3 are the values of the determinants for certain simultaneous equations in x and y, then find the values of x and y. 

Concept: Cramer'S Rule
Chapter: [0.01] Linear equations in two variables
[2]2.v

Form the quadratic equation if its roots are 5 and 7. 

Concept: Roots of a Quadratic Equation
Chapter: [0.02] Quadratic Equations
[2]2.vi

If for certain frequency distribution, Median = 156 and Mode = 180, Find the value of the Mean. 

Concept: Mean of Grouped Data
Chapter: [0.06] Statistics
[9]3 | Attempt any three of the following sub questions :
[3]3.i

Solve the quadratic equation 2x2 + 5x + 2= 0 using formula method.

Concept: Formula for Solving a Quadratic Equation
Chapter: [0.02] Quadratic Equations
[3]3.ii

There are 30 tickets numbered from 1 to 30 in the box and a ticket is drawn at random. If A is the event that the number on the ticket is a perfect square, then write the sample space S, n(S), the event A and n(A).

Concept: Random Experiments
Chapter: [0.05] Probability
[3]3.iii

Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.

Concept: Sum of First n Terms of an AP
Chapter: [0.03] Arithmetic Progression
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[3]3.iv

Draw the graph of the equation 3x - y =-6 and write the points of intersection of the graph with the X-axis and Y-axis. 

Concept: Graphical Method of Solution of a Pair of Linear Equations
Chapter: [0.01] Linear equations in two variables
[3]3.v

Electricity used by farmers during different parts of a day for irrigation is as follows:

Party of the day  Morning  Afternoon  Evening Night 
percentage of Electricity Used 30 40 20 10

Draw a pie diagram to represent this information. 

Concept: Concept of Pie Graph (Or a Circle-graph)
Chapter: [0.06] Statistics [0.06] Statistics
[8]4 | Attempt any two of the following sub questions :
[4]4.i

A card is drawn at random from a well-shuffled pack of 52 playing cards. Find the probability of the events that the card drawn is :

(a) a king (b) a face card.

Concept: Random Experiments
Chapter: [0.05] Probability
[4]4.ii

Solve the quadratic equation : 3x4 - 13x2 +10 = 0.

Concept: Roots of a Quadratic Equation
Chapter: [0.02] Quadratic Equations
[4]4.iii

The maximum bowing speed (km/hour) or 33 players at a cricket coaching centre is given below:

Bowling Speed(km/hour) 85-100 100-115 115-130 130-145
Numbers of players  9 11 8 5

find the modal bowling speed of players. 

Concept: Frequency Polygon
Chapter: [0.06] Statistics
[10]5 | Attempt any two of the following sub questions:
[5]5.i

Students of a school were made to stand in rows for drill. If 3 students less were standing in each row, 10 more rows would be required and if 5 students more were standing in each row, then the number of rows would be reduced by 10. Find the number of students participating in the drill.

Concept: Basic Ideas of Probability
Chapter: [0.05] Probability [0.05] Probability
[5]5.ii

in winter, the temperatures at a hill station from Monday to Friday are in A.P. The sum of the temperatures of Monday, Tuesday and Wednesday is 0° C and the sum of the temperatures of  Thursday and Friday is 15° C. Find the temperature of each of the five days.  

Concept: Basic Ideas of Probability
Chapter: [0.05] Probability [0.05] Probability
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[5]5.iii

Draw the Histogram and hence, the frequency polygon for the following frequency distribution: 

House Rent (In ₹ per month) 400-600 600-800 800-1000 1000-1200
Number of families  200 240 300 50
Concept: Graphical Representation of Data as Histograms
Chapter: [0.06] Statistics [0.06] Statistics
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