SSC (Marathi Semi-English) 10thMaharashtra State Board
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Algebra Shaalaa.com Model Set 2 2019-2020 SSC (Marathi Semi-English) 10th Question Paper Solution

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Algebra [Shaalaa.com Model Set 2]
Marks: 40Date: 2019-2020 March
Duration: 2h

[8]1
[4]1.A | MCQs
[1]1.A.i

Choose correct alternative for the following question.
To draw graph of 4x + 5y = 19, Find y when x = 1.

4

3

2

-3

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

Choose the correct answer for the following question.
Which one is the quadratic equation?

\[\frac{5}{x} - 3 = x^2\]

x ( x+5 ) = 2

n - 1 = 2n

`1/x^2(x+2)=x`

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

Choose the correct alternative answer for the following question.

If n(A) = 2, P(A) =`1/5` , then n(S) = ?

10

` 5/2`

`2/5`

`1/3`

Concept: Probability Examples and Solutions
Chapter: [4] Probability
[1]1.A.iv
No. of trees planted by each student 1 - 3 4 - 6 7 - 9 10 - 12
No. of students 7 8 6 4

The above data is to be shown by a frequency polygon. The coordinates of the points to show number of students in the class 4-6 are . . . .

(A) (4, 8) (B) (3, 5) (C) (5, 8) (D) (8, 4)
Concept: Histograms
Chapter: [5] Statistics
[4]1.B
[1]1.B.i

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

Concept: Arithmetic Progression
Chapter: [1] Arithmetic Progression
[1]1.B.ii

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

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

Concept: Quadratic Equations
Chapter: [2] Quadratic Equations
[1]1.B.iii

Factorise : m2 + 5m + 6.

Concept: Solutions of Quadratic Equations by Factorization
Chapter: [2] Quadratic Equations
[1]1.B.iv

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

Concept: Probability Examples and Solutions
Chapter: [4] Probability
[12]2
[4]2.A | Solve any 2 of the following
[2]2.A.i

If the point A(3, 2) lies on the graph of the equation 5x + ay = 19, then find a.

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method
Chapter: [3] Linear equations in two variables
[2]2.A.ii

Represent the following data by Histogram:

Price of Sugar per kg

         (in Rs.)

       Number of Weeks
18-20 4
20-22 8
22-24 22
24-26 12
26-28 8
28-30 6
Concept: Histograms
Chapter: [5] Statistics
[2]2.A.iii

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

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

Concept: Arithmetic Progression
Chapter: [1] Arithmetic Progression
[8]2.B | Solve any 4 of the following
[2]2.B.i

Write the equation of X-axis. Hence, find the point of intersection of the graph of the equation x + y = 5 with the X-axis.

Concept: Graphical Method of Solution of a Pair of Linear Equations
Chapter: [3] Linear equations in two variables
[2]2.B.ii

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: [2] Quadratic Equations
[2]2.B.iii

The first term of an A. P. is 5 and the common difference is 4. Complete the following activity and find the sum of the first 12 terms of the A. P.

a = 5, d = 4, s12 = ?
`s_n = n/2 [ square ]`
`s_12 = 12/2 [10 +square]`
         `= 6 × square  `
         ` =square`

Concept: Sum of First n Terms of an AP
Chapter: [1] Arithmetic Progression
[2]2.B.iv

For a certain frequency distribution, the value of Mean is 101 and Median is 100. Find the value of Mode.

Concept: Median of Grouped Data
Chapter: [5] Statistics
[2]2.B.v

The market price of share is Rs. 200 and the rate of brokerage is 0.3%.
Find the cost of one such share.

Concept: Shares
Chapter: [6] Financial Planning
[9]3
[3]3.A | Solve any 1 of the following
[3]3.A.i

A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

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

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

Concept: Nature of Roots
Chapter: [2] Quadratic Equations
[6]3.B | Solve any 2 of the following
[3]3.B.i

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

Concept: Arithmetic Progression
Chapter: [1] Arithmetic Progression
[3]3.B.ii

Prasad purchased a share of face value Rs. 100 when its market price was Rs. 150. Company declared a dividend of 12% on the share. What was the rate of return on the investment Prasad made ? 

Concept: Shares
Chapter: [6] Financial Planning
[3]3.B.iii

Two coins are tossed simultaneously. Write the sample space ‘S’ and the number of sample points n(S). Write the following events using set notation and mention the number of elements in each of them:-

(a) A is the event of getting at least one head.

(b) B is the event of getting exactly one head

Concept: Probability Examples and Solutions
Chapter: [4] Probability
[3]3.B.iv

The sales of salesmen in a week are given in the pie diagram. Study the diagram and answer the following questions. If the total sale due to salesmen A is Rs. 18,000, then

a) Find the total sale.
b) Find the sale of each salesman.
c) Find the salesman with the highest sale.
d) Find the difference between the highest sale and the lowest sale.

Concept: Pie Diagram
Chapter: [5] Statistics
[8]4 | Solve any 2 of the following
[4]4.A

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: [3] Linear equations in two variables
[4]4.B

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

Concept: Quadratic Equations
Chapter: [2] Quadratic Equations
[4]4.C

Given below is the frequency distribution of driving speeds (in km/hour) of the vehicles of 400 college students:

Speed (in km/hr) No. of Students
20-30 6
30-40 80
40-50 156
50-60 98

60-70
60

Draw Histogram and hence the frequency polygon for the above data.

Concept: Histograms
Chapter: [5] Statistics
[3]5 | Solve any 1 of the following
[3]5.A

Market value of shares and dividend declared by the two companies is given below. Face Value is same and it is Rs 100 for both the shares. Investment in which company is more profitable ?
(1) Company A - Rs 132 , 12%
(2) Company B - Rs 144 , 16%

Concept: Comparison of FV and MV
Chapter: [6] Financial Planning
[3]5.B

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: Probability Examples and Solutions
Chapter: [4] Probability

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