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# Algebra Set A 2017-2018 SSC (Marathi Semi-English) 10th Standard [इयत्ता १० वी] Question Paper Solution

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Algebra [Set A]
Marks: 40Academic Year: 2017-2018
Date & Time: 10th March 2018, 11:00 am
Duration: 2h

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

Find next two terms of an A.P.

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

Concept: Arithmetic Progression
Chapter: [0.03] Arithmetic Progression
[1]1.2

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

5/4m^2 - 7 = 0

Concept: Quadratic Equations
Chapter: [0.02] 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

Concept: Cramer'S Rule
Chapter: [0.01] Linear equations in two variables
[1]1.4

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

Concept: Probability - A Theoretical Approach
Chapter: [0.05] Probability
[1]1.5

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

Concept: Linear Equations in Two Variables Applications
Chapter: [0.01] Linear equations in two variables
[1]1.6

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

Concept: Arithmetic Progression
Chapter: [0.03] 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, ..........

Concept: Arithmetic Progression
Chapter: [0.03] Arithmetic Progression
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[2]2.2

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

Concept: Quadratic Equations Examples and Solutions
Chapter: [0.02] Quadratic Equations
[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).

Concept: Concept Or Properties of Probability
Chapter: [0.05] Probability
[2]2.4

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

Concept: Linear Equations in Two Variables Applications
Chapter: [0.01] Linear equations in two variables
[2]2.5

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

Concept: Nature of Roots
Chapter: [0.02] Quadratic Equations
[2]2.6

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

Concept: Median of Grouped Data
Chapter: [0.06] Statistics
[9]3 | Attempt any THREE of the following subquestions
[3]3.1

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

Concept: Arithmetic Progression
Chapter: [0.03] Arithmetic Progression
[3]3.2

Solve the following quadratic equation by using formula method :

2x2 - 3x = 2

Concept: Quadratic Equations
Chapter: [0.02] Quadratic Equations
[3]3.3

Solve the following simultaneous equations using Cramer’s rule :

3x - 2y = 3

2x + y = 16

Concept: Cramer'S Rule
Chapter: [0.01] Linear equations in two variables
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[3]3.4

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

Concept: Sample Space
Chapter: [0.05] Probability
[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

Concept: Concept of Pie Graph (Or a Circle-graph)
Chapter: [0.06] Statistics [0.06] Statistics
[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.

Concept: Quadratic Equations
Chapter: [0.02] 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.

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

Concept: Mean of Grouped Data
Chapter: [0.06] Statistics
[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.

Concept: Linear Equations in Two Variables Applications
Chapter: [0.01] Linear equations in two variables
[5]5.2

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

Concept: General Term of an Arithmetic Progression
Chapter: [0.03] Arithmetic Progression
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[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

Concept: Graphical Representation of Data as Histograms
Chapter: [0.06] Statistics [0.06] Statistics
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## Maharashtra State Board previous year question papers 10th Standard [इयत्ता १० वी] Algebra with solutions 2017 - 2018

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