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

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Algebra
Balbharati Model Question Paper Set 1
2018-2019 March
Marks: 40

[8]1
[4]1.1 | Solve any four of the following.
[1]1.1.1

Observe the adjacent Venn diagram and write the complement of A. 

Concept: Arithmetic Progression Examples and Solutions
Chapter: [1] Arithmetic Progression
[1]1.1.2

Multiply : 2`sqrt(12) × sqrt(3)`

Concept: Arithmetic Progression Examples and Solutions
Chapter: [1] Arithmetic Progression
[1]1.1.3

Find the geometric mean of 4 and 25.

Concept: Geometric Mean
Chapter: [1] Arithmetic Progression
[1]1.1.4

Find x if x + y = 5, and x - y = 7

Concept: Arithmetic Progression Examples and Solutions
Chapter: [1] Arithmetic Progression
[1]1.1.5

The estimated tax on the income of Shreemati Hinduja is Rs. 8000. How much education cess has she to pay at 3% ?

Concept: Arithmetic Progression Examples and Solutions
Chapter: [1] Arithmetic Progression
[1]1.1.6

Find the class-mark of 80-90.

Concept: Arithmetic Progression Examples and Solutions
Chapter: [1] Arithmetic Progression
[4]1.2 | Solve any two of the following
[1]1.2.1

Factorise : m2 + 5m + 6.

Concept: Solutions of Quadratic Equations by Factorization
Chapter: [2] Quadratic Equations
[1]1.2.2

The sum of two natural numbers is 20 while their difference is 4. Find the numbers.

Concept: Solutions of Quadratic Equations by Factorization
Chapter: [2] Quadratic Equations
[1]1.2.3

In PQRS, ∠ R = 60°. Find the ratio ∠ R : ∠ Q

Concept: Linear Equations in Two Variables Applications
Chapter: [3] Linear equations in two variables
[8]2
[4]2.1 | Choose the correct alternative answer and write.
[1]2.1.1

(1) For a simultaneous equation in x and y, if Dx = 25, Dy = 50 and
D = 5, What is the value of x ?
 

(A) -5

(B) `1/ 5` 

    (C) 10

   (D) 5

Concept: Linear Equations in Two Variables Applications
Chapter: [3] Linear equations in two variables
[1]2.1.2

Which of the following is a quadratic equation ?
     
    

(A) 6x2 = 20 - x3

  (B) `x^2(1/x-2) = 72`

(C)` 3/x - 3 = 4x^2`   

     (D) 5x + 7 = 3x

Concept: Quadratic Equations Examples and Solutions
Chapter: [2] Quadratic Equations
[1]2.1.3

If in an A. P., d = 10, find t6 - t2.

(A) 10

(B) 20

(c) 30

(D) 40

Concept: Quadratic Equations Examples and Solutions
Chapter: [2] Quadratic Equations
[1]2.1.4

The rate of GST on stainless steel is 18%, of which the share of a state government is ...............

(A) 18%

(B) 9%

(C) 36%

Concept: Shares
Chapter: [6] Financial Planning
[4]2.2 | Solve any two of the following.
[1]2.2.1

Two coins are tossed simultaneously. Find the probability of getting at least one head.

Concept: Probability Examples and Solutions
Chapter: [4] Probability
[1]2.2.2

If the roots of 2x2 - 6x + k = 0 are real and equal, find k.

Concept: Roots of a Quadratic Equation
Chapter: [2] Quadratic Equations
[1]2.2.3

Solve the following simultaneous equations.
101x + 99y = 501, 99x + 101y = 499

Concept: Introduction of System of Linear Equations in Two Variables
Chapter: [3] Linear equations in two variables
[8]3
[4]3.1 | Solve any two of the following.
[2]3.1.1

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]3.1.2

Complete the following activity to solve the simultaneous equations
3x + 2y = 6 and 2x + 4y = 12 by cramer's method.

`D = [[ 3,2] ,[2, 4  ]] = 8  Dx = [[6,2],[12,4]] = square , Dy = [[3,6],[2,12]] = square  x= square   y = square`

 

Concept: Cramer'S Rule
Chapter: [3] Linear equations in two variables
[2]3.1.3

The six faces of a die are marked
The event M is getting a vowel on the upper face of the die when it is tossed. Complete the following activity and find the probability of the event.

`  S = {square}`
 `n(S) =square`
` M = {square}`
`n(M) =square`
`P(M) = square/square=square`

Concept: Probability of an Event
Chapter: [4] Probability
[4]3.2 | Solve any two of the following.
[2]3.2.1

The following table shows the percentages of vehicles passing a signal. Find out the measures of central angle to show the information by a pie diagram and hence draw the pie diagram.

Type of Vehicle Bicycle Two wheeler Car Bus Rickshaw
Percentage 10 30 20 20 20
Concept: Pie Diagram
Chapter: [5] Statistics
[2]3.2.2

Mr. Mahajan purchased 100 shares, each of face value Rs. 100, when the market price was Rs. 45 per share, paying 2% brokerage. If the rate of GST on the brokerage is 18%, find the total amount he spent.

Concept: Brokerage and taxes on share tradin
Chapter: [6] Financial Planning
[2]3.2.3

There are 25 rows of seats in an auditorium. The first row is of 20 seats, the second of 22 seats, the third of 24 seats, and so on. How many chairs are there in the 21st row ?

Concept: Sum of First n Terms of an AP
Chapter: [1] Arithmetic Progression
[9]4 | Solve any three of the following.
[3]4.1

Solve : 7y = -3y2 - 4 

Concept: Roots of a Quadratic Equation
Chapter: [2] Quadratic Equations
[3]4.2

In a game of chance, the spinning arrow rests at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8. All these are equally likely outcomes. Find the probabilities of the following events.
(A) The arrow rests at an odd number.
(B) It rests at a prime
number.
(C) It rests at a multiple
of 2.

Concept: Equally Likely Outcomes
Chapter: [4] Probability
[3]4.3

Find out the sum of all natural numbers between 1 and 145 which are divisible by 4.

Concept: Sum of First n Terms of an AP
Chapter: [1] Arithmetic Progression
[3]4.4

The following frequency distribution table shows the number of mango trees in a grove and their yield of mangoes, and also the cumulative frequencies. Find the median of the data.

Class
(No. of mangoes)
Frequency
(No. of trees)
Cumulative frequency (less than)
50-100 33 33
100-150 30 63
150-200 90 153
200-250 80 233
250-300 17 250
Concept: Median of Grouped Data
Chapter: [5] Statistics
[4]5 | Solve any one of the following.
[4]5.1

Six year before, the age of mother was equal to the square of her son's age. Three year hence, her age will be thrice the age of her son then. Find the present ages of the mother and son.

Concept: General Term of an Arithmetic Progression
Chapter: [1] Arithmetic Progression
[4]5.2

Draw a frequency polygon from the information given in the following table.

Age of blood donar (Years) No. of blood donars
Less than 20 0
Less than 25 30
75Less than 30 75
165Less than 35 127
Less than 40 165
Less than 45 185
Less than 50 197
Concept: Frequency Polygon
Chapter: [5] Statistics
[3]6 | Solve any one of the following.
[3]6.1

Draw the graph of x + y = 6 which intersects the X-axis and the Y-axis at A and B respectively. Find the length of seg AB. Also, find the area of Δ AOB where point O is the origin.

Concept: Graphical Method of Solution of a Pair of Linear Equations
Chapter: [3] Linear equations in two variables
[3]6.2

The market value of a mutual fund is 400 crore rupees. Which is divided into 8 crore units.

(a) Suppose you invest Rs. 10,000 in the units, how many units will you
get ?
(b) While selling the units if their market value is increased by 10%,
how much amount will you get by selling them ?

Concept: Mutual Fund - MF
Chapter: [6] Financial Planning

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