# Algebra 2015-2016 SSC (Marathi Semi-English) 10th Standard [इयत्ता १० वी] Question Paper Solution

Algebra
Date: July 2016

[5] 1 | Solve any five of the following subquestion:
[1] 1.1

If 3x + 2y = 10 and 2x + 3y = 15, then find the value of x + y.

Concept: Pair of Linear Equations in Two Variables
Chapter: [0.01] Linear equations in two variables
[1] 1.2

Find the common difference of the A.P 3, 5, 7, ..........

Concept: Arithmetic Mean - Raw Data
Chapter: [0.03] Arithmetic Progression
[1] 1.3

Two coins are tossed simultaneously. Write the sample space 'S'.

Concept: Sample Space
Chapter: [0.05] Probability
[1] 1.4

Write the following quadratic equation in standard form ax2 + bx + c = 0 : x (x + 3) = 7

[1] 1.5

If Σfi = 25 and Σfixi = 100, then find the mean (bar"x")

Concept: Mean of Grouped Data
Chapter: [0.06] Statistics
[1] 1.6

Find the value of a, b, c in the following quadratic equation: 2x2 + 18 = 6x

[8] 2 | Attempt any four of the following subquestions:
[2] 2.1

Find the eighteenth term of the A.P: 1, 7, 13, 19, ............

Concept: Arithmetic Progressions Examples and Solutions
Chapter: [0.03] Arithmetic Progression
[2] 2.2

Form the quadratic equation if the roots are 3 and 8.

Concept: Roots of a Quadratic Equation
[2] 2.3

Solve the following simultaneous equation using Cramer's rule

4x + 3y = 4
6x + 5y = 8

Concept: Determinants - Cramer’s Rule
Chapter: [0.01] Linear equations in two variables
[2] 2.4

In the following experiment write the sample space S, Number of sample points n(S), write the event P in set form and find n(P):

Form two-digit numbers using the digit 0, 1, 2, 3, 4, without repeating the digits, P is the event, that the number so formed is even.

Concept: Sample Space
Chapter: [0.05] Probability
[2] 2.5

Find a certain frequency distribution, the value of mean and mode are 54.6 and 54 respectively. Find the value of median.

Concept: Median of Grouped Data
Chapter: [0.06] Statistics
[2] 2.6

Subjective marks obtained by a student in an examination are given below:

 Subject Marks Marathi 85 English 90 Science 85 Mathematics 100 Total 360

Draw a pie diagram to represent the above data.

Concept: Concept of Pie Graph (Or a Circle-graph)
Chapter: [0.06] Statistics
[9] 3 | Attempt any three of the following subquestions:
[3] 3.1

Represent the following data by histogram:

 Price of sugar Per kg (in Rs) Number of weeks 28-30 4 30-32 8 32-34 22 34-36 12 36-38 6
Concept: Graphical Representation of Data as Histograms
Chapter: [0.06] Statistics
[3] 3.2

A coin is tossed three time then find the probablity of the following events:

A is an event of getting a head on middle coin.

B is an event of getting exactly one tail.

Concept: Type of Event - Elementry
Chapter: [0.05] Probability
[3] 3.3

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.

Concept: Median of Grouped Data
Chapter: [0.06] Statistics
[3] 3.4

Solve the following quadratic equation by using formula method :

7y2 - 5y - 2 = 0

[3] 3.5

Draw histogram and hence the frequency polygon for the following frequency distribution:

 Rainfall (in cm) No. of years 20-25 2 25-30 5 30-35 8 35-40 12 40-45 10 45-50 7
Concept: Graphical Representation of Data as Histograms
Chapter: [0.06] Statistics
[8] 4 | Attempt any two of the following subquestions:
[4] 4.1

The 11th term and the 21st term of an A.P are 16 and 29 respectively, then find the first term, common difference and the 34th term.

Concept: Sum of First n Terms of an A.P.
Chapter: [0.03] Arithmetic Progression
[4] 4.2

If the point of intersection of ax + by = 7 and bx + ay = 5 is (3,1), then find the value of a and b.

Concept: Pair of Linear Equations in Two Variables
Chapter: [0.01] Linear equations in two variables
[4] 4.3

In a certain race there are three boys A, B, C. The winning probability of A is twice than B and the winning probability of B is twice than C. If P(A) + P(B) + P(C) = 1, then find the probabilities of their winning.

Concept: Basic Ideas of Probability
Chapter: [0.05] Probability
[10] 5 | Attempt any two of the following subquestion:
[5] 5.1

Find the sum of all members from 50 to 250 which divisible by 6 and find t13.

Concept: Sum of First n Terms of an A.P.
Chapter: [0.03] Arithmetic Progression
[5] 5.2

Solve 9("x"^2 + 1/"x"^2) -3("x" - 1/"x") - 20 = 0

[5] 5.3

A three digit number is equal to 17 times the sum of its digits. If 198 is added to the number, the digits are interchanged. The addition of first and third digit is 1 less than middle digit. Find the number.

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method
Chapter: [0.01] Linear equations in two variables

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