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Algebra Balbharati Model Question Paper Set 2 2018-2019 SSC (English Medium) Class 10th Board Exam Question Paper Solution

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Algebra
Balbharati Model Question Paper Set 2
2018-2019 March
Marks: 40

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

A = {1, 2, 3,4, 5}, B = {5, 6, 7} write AUB .

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

Simplify `sqrt(50)`

Concept: Sum of First n Terms of an AP
Chapter: [1] Arithmetic Progression
[1]1.1.3

Write a trinomial of degree 7.

Concept: Arithmetic Progression Examples and Solutions
Chapter: [1] Arithmetic Progression
[1]1.1.4

Convert 15 : 20 into percentage.

Concept: Quadratic Equations Examples and Solutions
Chapter: [2] Quadratic Equations
[1]1.1.5

If 3x + 5y = 9 and 5x + 3y = 7 find the value of x + y. 

Concept: Quadratic Equations Examples and Solutions
Chapter: [2] Quadratic Equations
[1]1.1.6

Write the lower and the uppper class limit of 35 to 40

Concept: Arithmetic Progression Examples and Solutions
Chapter: [1] Arithmetic Progression
[4]1.2 | Solve any two of the following.
[2]1.2.1

The yield of soyabean per acre in the farm of Mukund for 7 years was 10,7,5,3,9,6,9 quintal. Find the mean of yield per acre. 

Concept: Mean of Grouped Data
Chapter: [5] Statistics
[2]1.2.2

Alka spends 90 % of the amount sent to her and saves Rs. 120 per
month. Find the amount sent to her per month.

Concept: Inconsistency of Pair of Linear Equations
Chapter: [3] Linear equations in two variables
[2]1.2.3

If P(y) = y² - 2y + 5, find P(2) .

Concept: Quadratic Equations Examples and Solutions
Chapter: [2] Quadratic Equations
[8]2
[4]2.1 | Select the correct alternative answer and write it.
[1]2.1.1

If the roots of x² + kx + k = 0 are real and equal, what is the value of k?

(A) 0

(B) 4

(C) 0 or 4

(D) 2

Concept: Roots of a Quadratic Equation
Chapter: [2] Quadratic Equations
[1]2.1.2

What is the sum of first 10 terms of the A. P. 15,10,5,........?

(A) -75

(B) -125

(C) 75

(D) 125

Concept: Sum of First n Terms of an AP
Chapter: [1] Arithmetic Progression
[1]2.1.3

How many alpha numerals are there in the GSTIN of a registered dealer ?

(A)15

(B) 10

(C) 16

(D) 9

Concept: GST - Introduction
Chapter: [6] Financial Planning
[1]2.1.4

What is the value of D if the equations x + y =3 ; 3x -2y =4 are solved by
Cramer’s method.

(A)5

(B) 1

(C) -5

(D) -1

Concept: Cramer'S Rule
Chapter: [3] Linear equations in two variables
[4]2.2 | Solve any two of the following.
[2]2.2.1

A card is drawn at random from a well shuffled pack of 52 playing cards.
Find the probability that the card drawn is a spade.

Concept: Probability Examples and Solutions
Chapter: [4] Probability
[2]2.2.2

The age groups and the number of persons in the age groups, who donated blood in blood donation camp is given below. Find the measures of central angles to show the information by a pie diagram.

Age group (Years) 20-25 25-30 30-35 35-40
No of persons 80 60 35 25
Concept: Graphical Representation of Histograms
Chapter: [5] Statistics
[2]2.2.3

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
[8]3
[4]3.1 | Carry out any two of the following activities.
[2]3.1.1

Complete the following table to draw the graph of the equation x - y = 1

x 0  
y   0
(x, y)    
Concept: Graphical Method of Solution of a Pair of Linear Equations
Chapter: [3] Linear equations in two variables
[2]3.1.2

Fill up the boxes and find out the number of terms in the A.P.
1,3,5,....,149 .

Here a = 1 , d =b`[    ], t_n = 149`

tn = a + (n-1) d 

∴ 149 =`[  ]     ∴149 = 2n -  [  ]`
∴ n =`[  ]`

 

Concept: Sum of First n Terms of an AP
Chapter: [1] Arithmetic Progression
[2]3.1.3

In a class of 42 students in Model High School, 3 students use spectacles.
Fill in the following boxes to find the probability of a students selected
at random is wearing sepctacles.
The total number of students in the class is 42.
∴n(S) =   ...... ,
Let the event, a student uses spectacles, be A.
∴ n(A) = ...........
∴ P(A) =   ............ ∴ P(A) = ............ 

Concept: Probability Examples and Solutions
Chapter: [4] Probability
[4]3.2 | Solve any two of the following.
[2]3.2.1

Solve : 5m² - 22m-15 = 0

Concept: Arithmetic Progression Examples and Solutions
Chapter: [1] Arithmetic Progression
[2]3.2.2

3x - 4y = 10 , 4x + 3y = 5 find the values of Dx and Dy to solve
the simultaneous equations by Cramer’s method

Concept: Cramer'S Rule
Chapter: [3] Linear equations in two variables
[2]3.2.3

The first term and the common difference of an A. P. is 10,000 and
2000 resectively. Find the sum of first 12 terms of the A.P.

Concept: Arithmetic Progression
Chapter: [1] Arithmetic Progression
[9]4 | Solve any three of the following.
[3]4.1

If α and β are the roots of the quadratice equation x²- 2x - 7= 0, find the
value α² + β²

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

How many three digit natural numbers are divisible by 5?

Concept: Introduction to Sequence
Chapter: [1] Arithmetic Progression
[3]4.3

The following table shows the investment made by some families. Show
the information by a histogran. 

Investment
(Thousand Rupees)
10-15 15-20 20-25 25-30 30-35
No. of families 30 50 60 55 15

 

 

Concept: Histograms
Chapter: [5] Statistics
[3]4.4

A two digit number is to be formed from the digits 0,1,2,3,4,
without repetition of the digits. Find the probability that the number so
formed is a prime number

Concept: Sample Space
Chapter: [4] Probability
[4]5 | Solve any one of the following.
[4]5.1

Yogesh requires 3 days more than Vivek to do a work completely. If both
of them work together, the work can be completed in 2 days. Find the
number of days required for each of them to do the work completely.

Concept: Arithmetic Progression Examples and Solutions
Chapter: [1] Arithmetic Progression
[4]5.2

The following table shows the number of patients of different age groups admitted to a hospital for treatment on a day. Find the median of ages of the patients.

Age- group (Yrs.) 10-20 20-30 30-40 40-50 50-60 60-70
No. of patients 40 32 35 45 33 15

 

Concept: Median of Grouped Data
Chapter: [5] Statistics
[3]6 | Solve any one of the following.
[3]6.1

Krishna Electricals had bought a TV from a wholesaler at Rs 36000.
The marked price on it in Krishna Electricals was Rs. 50000. If it was
sold to Kalyan Deshmukh at 10% discount, calculate the input GST
and output GST for Krishna Electricals if the rate of GST is 18%.

Concept: Types of Taxes Under GST
Chapter: [6] Financial Planning
[3]6.2

Construct a word problem on simultaneous linear equations in two
variables so that the value of one of the variables will be 10 (persons, rupees, metres, years etc.) and solve it.

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

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