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Question Paper Solutions - Algebra 2017 - 2018-S.S.C-10th Maharashtra State Board (MSBSHSE)


Marks: 40
[5]1 | Attempt any FIVE of the following sub-questions :
[1]1.1

Find next two terms of an A.P. 

4, 9, 14, ......

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

State whether the given equation is quadratic or not. Give reason.

`5/4m^2 - 7 = 0`

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

if `D_x = 25`, D = 5 are the values of the determinants for certain simultaneous equations in x and y, find x

Chapter: [3] Linear equations in two variables
Concept: Cramer'S Rule
[1]1.4

If S = {2, 4, 6, 8, 10, 12} and A = {4, 8, 12}, find A'

Chapter: [5.02] Probability
Concept: Probability - A Theoretical Approach
[1]1.5

Write any one solution of equation x + 2y = 7.

Chapter: [3] Linear equations in two variables
Concept: Linear Equations in Two Variables Applications
[1]1.6

If `S_5 = 15` and `S_6 = 21`, Find `t_6`.

Chapter: [1] Arithmetic Progression
Concept: Arithmetic Progression
[8]2 | Attempt any FOUR of the following subquestions
[2]2.1

Find n if the nth term of the following A.P. is 68

5, 8, 11, 14, ..........

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

If one of the roots of the quadratic equation x2 - 11x  + k = 0 is 9, then find the value of k

Chapter: [2] Quadratic Equations
Concept: Quadratic Equations Examples and Solutions
[2]2.3

A box contains 20 cards marked with numbers 1 to 20. One card is drawn at random. Event A is the number of the card which is multiple of 5. Write S, n(S), A and n(A).

Chapter: [5.02] Probability
Concept: Concept Or Properties of Probability
[2]2.4

Find the value of x- y  if 4x + 3y = 25, 3x + 4y = 24

Chapter: [3] Linear equations in two variables
Concept: Linear Equations in Two Variables Applications
[2]2.5

Form the quadratic equation if its roots are –3 and 4.

Chapter: [2.03] Quadratic Equations
Concept: Nature of Roots
[2]2.6

For a certain frequency distribution, the values of mean and median are 72 and 78 respectively. Find the value of mode.

Chapter: [5] Statistics
Concept: Median of Grouped Data
[9]3 | Attempt any THREE of the following subquestions
[3]3.1

For an A.P., find S7 if a = 5 and d = 4.

Chapter: [1] Arithmetic Progression
Concept: Arithmetic Progression
[3]3.2

Solve the following quadratic equation by using formula method :

2x2 - 3x = 2

Chapter: [2.03] Quadratic Equations
Concept: Quadratic Equations
[3]3.3

Solve the following simultaneous equations using Cramer’s rule :

3x - 2y = 3

2x + y = 16

Chapter: [3] Linear equations in two variables
Concept: Cramer'S Rule
[3]3.4

A die is thrown, find the probability of the event of getting a number less than 3.

Chapter: [7] Probability
Concept: Sample Space
[3]3.5

The marks obtained by a student in an examination out of 100 are given below. The total marks obtained in various subjects are as follows:

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

Represent the above data using pie diagram

Chapter: [5] Statistics
Concept: Pie Diagram
[8]4 | Attempt any TWO of the following subquestions :
[4]4.1

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

Chapter: [2.03] Quadratic Equations
Concept: Quadratic Equations
[4]4.2

Two dice are thrown. Find the probability of getting :

1) The sum of the numbers on their upper faces is at least 9.

2) The sum of the numbers on their upper faces is 15.

3) The number on the upper face of the second die is greater than the number on the upper face of the first die.

Chapter: [4] Probability
Concept: Probability Examples and Solutions
[4]4.3

Frequency distribution of daily commission received by 100 salesmen is given below :

Daily Commission

(in Rs.)

No. of Salesmen
100-120 20
120-140 45
140-160 22
160-180 09
180-200 04

Find mean daily commission received by salesmen, by the assumed mean method.

Chapter: [5.01] Statistics
Concept: Mean of Grouped Data
[10]5 | Attempt any TWO of the following subquestions :
[5]5.1

A boat takes 10 hours to travel 30 km upstream and 44 km downstream, but it takes 13 hours to travel 40 km upstream and 55 km downstream. Find the speed of the boat in still water and the speed of the stream.

Chapter: [3] Linear equations in two variables
Concept: Linear Equations in Two Variables Applications
[5]5.2

If the 9th term of an A.P. is zero, then prove that 29th term is double of 19th term.

Chapter: [1] Arithmetic Progression
Concept: General Term of an Arithmetic Progression
[5]5.3

Draw histogram and frequency polygon on the same graph paper for the following frequency distribution

Class Frequency
15-20 20
20-25 30
25-30 50
30-35 40
35-40 25
40-45 10

 

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