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Question Paper Solutions - Algebra 2015 - 2016-S.S.C-10th Maharashtra State Board (MSBSHSE)


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

Write the first two terms of the sequence whose nth term is tn = 3n ‒ 4.

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

Find the value of a, b, c in the following quadratic equation : 2x2 ‒ x ‒ 3 = 0

Chapter: [2.03] Quadratic Equations
Concept: Quadratic Equations
[1]1.3

Write the quadratic equation whose roots are ‒2 and ‒3.

Chapter: [2.03] Quadratic Equations
Concept: Quadratic Equations
[1]1.4

Find the value of determinant: `|[4,-2],[3,1]|`

 

Chapter: [3] Linear equations in two variables
Concept: Determinant of Order Two
[1]1.5

Write the sample space for selecting a day randomly of the week.

Chapter: [7] Probability
Concept: Sample Space
[1]1.6

Find the class mark of the classes 20-30 and 30-40.

Chapter: [4] Probability
Concept: Probability Examples and Solutions
[8]2 | Attempt any four sub-questions from the following:
[2]2.1

Write the first three terms of the A.P. whose common difference is ‒3 and first term is 4.

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

Solve the following quadratic equation by Factorisation method: x2 + 7x + 10 = 0

Chapter: [2.02] Quadratic Equations
Concept: Solutions of Quadratic Equations by Factorization
[2]2.3

If the value of determinant `|[m,2],[-5,7]|`is 31, find the value of m

Chapter: [3] Linear equations in two variables
Concept: Determinant of Order Two
[2]2.4

A die is thrown, then find the probability of the following events:
A is an Event: getting an odd number on the top upper surface of the die.
B is an Event: getting a perfect square on the upper surface of the die.

Chapter: [4] Probability
Concept: Probability Examples and Solutions
[2]2.5

Below is the given frequency distribution of words in an essay

Number of Words Number of Candidates
600 – 800 8
800 – 1000 22
1000 – 1200 40
1200 – 1400 18
1400 - 1600 12

Find the mean number of words written.

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

Subjectwise marks obtained by a student in an examination are given below

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

Draw pie diagram

Chapter: [5] Statistics
Concept: Pie Diagram
[9]3 | Attempt any three of the following sub questions:
[3]3.1

Solve the following quadratic equation by using formula method: 5m2 + 5m – 1 = 0

Chapter: [2.03] Quadratic Equations
Concept: Nature of Roots
[3]3.2

There are three boys and two girls. A committee of two is to be formed. Find the probability of the following events:
Event A: The committee contains at least one girl
Event B: The committee contains one boy and one girl

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

The measurements (in mm) of the diameters of the head of the screws are given below:

Diameter (in mm) No. of Screws
33 — 35 10
36 — 38 19
39 — 41 23
42 — 44 21
45 — 47 27

Calculate mean diameter of head of a screw by ‘Assumed Mean Method’.

Chapter: [5.01] Statistics
Concept: Mean of Grouped Data
[3]3.4

The marks scored by students in Mathematics in a certain Examination are given below:

Marks Scored Number of Students
0 — 20 3
20 — 40 8
40 — 60 19
60 — 80 18
80 — 100 6

Draw histogram for the above data.

Chapter: [6] Statistics
Concept: Histograms, Frequency Polygon and Frequency Curve
[3]3.5

Draw 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
Chapter: [6] Statistics
Concept: Histograms, Frequency Polygon and Frequency Curve
[8]4 | Attempt any two of the following sub questions:
[4]4.1

The 11th term and the 21st term of an A.P. are 16 and 29 respectively, then find:
(a) The first term and common difference
(b) The 34th term
(c) ‘n’ such that tn = 55

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

Solve the following simultaneous equations: `7/(2X+1)+13/(Y+2)=27,13/(2X+1)+7/(Y+2)=33`

 

 
Chapter: [2.02] Pair of Linear Equations in Two Variables
Concept: Equations Reducible to a Pair of 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 probability of win for each boy.

Chapter: [4] Probability
Concept: Probability Examples and Solutions
[10]5 | Attempt any two of the following sub questions:
[5]5.1

The divisor and quotient of the number 6123 are same and the remainder is half the divisor. Find the divisor.

Chapter: [2] Quadratic Equations
Concept: Quadratic Equations Examples and Solutions
[5]5.2

Find the sum of all numbers from 50 to 350 which are divisible by 6. Hence find the 15th term of that A.P.

Chapter: [2.04] Arithmetic Progressions
Concept: Sum of First n Terms of an AP
[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.

Chapter: [2.02] Pair of Linear Equations in Two Variables
Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method
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