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Algebra Set 1 2018-2019 SSC (Marathi Semi-English) 10th Question Paper Solution

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Algebra
Set 1
2018-2019 March
Marks: 40

1) All questions are compulsory.
2) Use of calculator is not allowed.
3i) Figures to the right of questions indicate full marks.


[8]1 | Attempt any four.
[4]1.A | Solve the following questions
[1]1.A.i

Find the median of :
66, 98, 54, 92, 87, 63, 72.

Concept: Median of Grouped Data
Chapter: [5] Statistics
[1]1.A.ii

Multiply and write the answer in the simplest form :
`5sqrt7  xx 2sqrt7`

Concept: Introduction to Sequence
Chapter: [1] Arithmetic Progression
[1]1.A.iii

If 3x + 5y = 9 and 5x +3y = 7, Then Find the Value of X + Y

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

Write the ratio of second quantity of first quantity in the reduced form :
5 dozen pens, 120 pens

Concept: GST - Introduction
Chapter: [6] Financial Planning
[1]1.A.v

Write the following polynomial in coefficient form :
2x3 + x2 - 3x +4

Concept: Introduction of System of Linear Equations in Two Variables
Chapter: [3] Linear equations in two variables
[1]1.A.vi

For computation of income tax which is the assessment year of financial year 01-04-2016 to 31-03-2017 ?

Concept: GST - Introduction
Chapter: [6] Financial Planning
[4]1.B | Attempt any two.
[2]1.B.i

Find the value of the polynomial 2x3 + 2x , when x = -1

Concept: Introduction of System of Linear Equations in Two Variables
Chapter: [3] Linear equations in two variables
[2]1.B.ii

If A = {11, 21, 31, 41}, B = {12, 22, 31, 32}, then find :
(1) A ∪ B
(2) A ∩ B

Concept: Terms in a sequence
Chapter: [1] Arithmetic Progression
[2]1.B.iii

Sangeeta’s monthly income is Rs. 25,000. She spent 90% of her income and donated 3% for socially useful causes. How much money did she save ?

Concept: Comparison of FV and MV
Chapter: [6] Financial Planning
[8]2
[4]2.A | Choose the correct alternative
[1]2.A.i

In the A.P. 2, –2, –6, –10, ..... common difference (d) is :

–4

–2

4

Concept: Arithmetic Progression Examples and Solutions
Chapter: [1] Arithmetic Progression
[1]2.A.ii

For the quadratic equation x2 + 10x -7 =0 , the value of a ,b,c are :

a = –1, b = 10, c = 7 

a = 1, b = –10, c = –7

a = 1, b = 10, c = –7

a = 1, b = 10, c = 7

Concept: Quadratic Equations Examples and Solutions
Chapter: [2] Quadratic Equations
[1]2.A.iii

The tax levied by Central Government for trading within a state is :

IGST 

CGST

SGST

UTGST

Concept: GST - Introduction
Chapter: [6] Financial Planning
[1]2.A.iv

If a die is rolled, what is the probability that number appearing on upper face is less than 2 ?

`1/3`

`1/2`

1

`1/6`

Concept: Introduction to Probability
Chapter: [4] Probability
[4]2.B | Attempt any two
[2]2.B.i

First term and common difference of an A.P. are 12 and 4 respectively. If tn = 96 find n.

Concept: Arithmetic Progression Examples and Solutions
Chapter: [1] Arithmetic Progression
[2]2.B.ii

If  `|( 4,5), (m , 3)| = 22, "then find the value of m."`

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method
Chapter: [3] Linear equations in two variables
[2]2.B.iii

Solve the following quadratic equation :
x2 +8x + 15 = 0

Concept: Quadratic Equations Examples and Solutions
Chapter: [2] Quadratic Equations
[8]3 | Attempt any two.
[4]3.A | Complete the following activities
[2]3.A.i

Smita has invested Rs. 12,000 to purchase shares of FV Rs.10 at a premium of Rs.2. Find the number of shares she purchased. Complete the given activity to get the answer.
Activity : FV = Rs. 10, Premium = Rs. 2
∴ MV = FV +   = + 2 = 12
`therefore  "No. of .shares" ="total investment"/"MV" = square/12 = square "shares"`

Concept: GST - Computation and ITC
Chapter: [6] Financial Planning
[2]3.A.ii

The following table shows the daily supply of electricity to different places in a town. To show the information by a pie diagram, measures of central angles of sectors are to be decided.
Complete the following activity to find the measure :

Places

Supply of electricity  (Thosand units)

Measure of central angle
Roads 4 `4/30 xx 360 = 48^circ`
Factories 12 `square/square xx 360=144^circ`
shops 6 `6/30xx360 = square`
Houses 8 `square/squarexx360=square`
Total ⇒ 30  
Concept: Pie Diagram
Chapter: [5] Statistics
[2]3.A.iii

Two coins are tossed simultaneously. Complete the following activity of writing of the sample space (S) and expected outcomes of the events :
1) Event A : to get at least one head.
2) Event B : to get no head.
Activity : If two coins are tossed simultaneously
∴ s =  {`square , "HT","TH", square`}
1) Event A : at least getting one head.
∴ A = {`"HH" , square , "TH"`}
2) Event B : to get no head.
∴ B = {`square`}

Concept: Sample Space
Chapter: [4] Probability
[4]3.B | Solve the following questions Attempt any two:
[2]3.B.i

Find the 19th term of the A.P. 7, 13, 19, 25, ............,

Concept: Arithmetic Progression Examples and Solutions
Chapter: [1] Arithmetic Progression
[2]3.B.ii

Obtain a quadratic equation whose roots are –3 and –7.

Concept: Quadratic Equations Examples and Solutions
Chapter: [2] Quadratic Equations
[2]3.B.iii

Two numbers differ by 3. The sum of the greater number and twice the smaller number is 15. Find the smaller number

Concept: Linear Equations in Two Variables Applications
Chapter: [3] Linear equations in two variables
[9]4 | Solve the following questions Attempt any three:
[3]4.A

Amit saves certain amount every month in a specific way. In the first month he saves Rs. 200, in the second month Rs. 250, in the third month Rs.300 and so on. How much will be his total savings in 17 months?

Concept: Arithmetic Progression Examples and Solutions
Chapter: [1] Arithmetic Progression
[3]4.B

A two digit number is to be formed using the digits 0, 1, 2, 3. Repetition of the digits is allowed. Find the probability that a number so formed is a prime number.

Concept: Introduction to Probability
Chapter: [4] Probability
[3]4.C

Smt. Malhotra purchased solar panels for the taxable value of Rs. 85,000. She sold them for Rs. 90,000. The rate of GST is 5%. Find the ITC of Smt. Malhotra. What is the amount of GST payable by her?

Concept: GST - Computation and ITC
Chapter: [6] Financial Planning
[3]4.D

Solve the following simultaneous equations graphically :
x + y = 0; 2x – y = 9

Concept: Linear Equations in Two Variables Applications
Chapter: [3] Linear equations in two variables
[8]5 | Solve the following questions Attempt any one:
[4]5.A

The following frequency distribution table shows marks obtained by 180 students in Mathematics examination

Marks  No .of. students
0 - 10 25
10 - 20  x

 20 - 30

30
30 - 40 2x
40 - 50 65

Find the value of x.
Also draw a histogram representing the above information.

Concept: Histograms
Chapter: [5] Statistics
[4]5.B

Two taps together can fill a tank completely in `(3)1/13` minutes. The smaller tap takes 3 minutes more than the bigger tap to fill the tank. How much time does each tap take to fill the tank completely?

Concept: Linear Equations in Two Variables Applications
Chapter: [3] Linear equations in two variables
[3]6 | Solve the following questions Attempt any one:
[3]6.A

The co-ordinates of the point of intersection of lines ax + by = 9 and bx + ay = 5 is (3, –1). Find the values of a and b.

Concept: Linear Equations in Two Variables Applications
Chapter: [3] Linear equations in two variables
[3]6.B

The following frequency distribution table shows the distances travelled by some rickshaws in a day. Observe the table and answer the following questions

Class (daily distance travelled in km) continuous classes Frequency (no.of. rickshaws) Cumulative frequency less than type
60 - 64 59.5 - 64.5 10 10
65 - 69 64.5 -69.5 34 10+34=44
70 - 74 69.5 - 74.5 58 44+58=102
75 - 79 74.5 - 79.5 82 102+82=184
80 - 84 79.5 - 84.5  10 184+10=194
85 - 89  84.5 - 89.5  6 194+6=200

1) Which is the modal class? Why?
2) Which is the median class and why?
3) Write the cumulative frequency (C.F) of the class preceding the median class.
4) What is the class interval (h) to calculate median?

Concept: Tabulation of Data
Chapter: [5] Statistics

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