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# Question Paper Solutions for Algebra Balbharati Model Question Paper Set 3 2018-2019 SSC (English Medium) Class 10th Board Exam

Marks: 40
[8]1
[4]1.1 | Solve any four of the following.
[1]1.1.1

Solve any four of the following.

Write the set Q of rational numbers in the property form.

Chapter: [1] Arithmetic Progression
Concept: Introduction to Sequence
[1]1.1.2

Solve any four of the following.

|8|+|-3|=?

Chapter: [1] Arithmetic Progression
Concept: Introduction to Sequence
[1]1.1.3

Solve any four of the following.

Find the value of x^4-x^3+5 When x=-1

Chapter: [1] Arithmetic Progression
Concept: Introduction to Sequence
[1]1.1.4

Solve any four of the following.

If x is the geometric mean of 16 and 9, find x.

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

Solve any four of the following.

Find the value of y in the equation x + y = 12, when x = 5

Concept: Quadratic Equations Examples and Solutions
[1]1.1.6

Solve any four of the following.

Write the dates of start and end of a financial year in our country.

Chapter: [6] Financial Planning
Concept: GST - Introduction
[4]1.2 | Solve any two of the following.
[2]1.2.1

Solve any two of the following.

In some families in a colony the daily purchase of milk in litre is 1, 3, 2, 2, 4, 1, 2, 2, 1. Find the mean, median and mode of daily purchase of milk.

Chapter: [1] Arithmetic Progression
Concept: Arithmetic Mean
[2]1.2.2

Solve any two of the following.

If a : b = 7 : 2, find the ratios  (i) b : a  (ii) (a+b)/b

Chapter: [1] Arithmetic Progression
Concept: Introduction to Sequence
[2]1.2.3

Solve any two of the following.

Solve : 3x+y=14 ; x-y=2

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

Select the correct alternative and write it.

What is the solution of the quadratic equation 2x^2-7x+6=0

(A) -3/2,2

(B) 3/2,2

(C) -2,3/2

(d) 2,2/3

Concept: Quadratic Equations Examples and Solutions
[1]2.1.2

Select the correct alternative and write it.

What is the sum of first n natural numbers ?

(A) (n(n-1))/2

(B)n/2(n-2)

(c) n(n+1)/2

(D) (n(n+2))/2

Chapter: [1] Arithmetic Progression
Concept: General Term of an Arithmetic Progression
[1]2.1.3

Select the correct alternative and write it.

If a share is at premium, then -

(A) Market value > Face value

(B) Market value = Face value

(C) Market value < Face value

(D) Market value ≤ Face value

Chapter: [1] Arithmetic Progression
Concept: General Term of an Arithmetic Progression
[1]2.1.4

Select the correct alternative and write it.

What is the degree of the determinant |[a ,b],[c,d]|

(A) 1

(B) 3

(C) 4

(D) 2

Chapter: [3] Linear equations in two variables
Concept: Determinant of Order Two
[4]2.2 | Solve any two of the following.
[2]2.2.1

Solve any two of the following.

If two coins are tossed simultaneously, find the probability of getting a head on both the coins.

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

Solve any two of the following.

Find the mean of the data given in the following table.

 Class 0-20 20-40 40-60 60-80 80-100 Frequency 6 4 5 7 3
Chapter: [1] Arithmetic Progression
Concept: Arithmetic Mean
[2]2.2.3

Solve any two of the following.

Form a quadratic equation whose roots are 4 and -12.

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

The following table shows the blood-groups of employees in a bank.
Event C is : ‘the blood-group of an employee is AB.’

 Blood - group A B AB 0 No. of employees 20 40 15 25

If an employee is chosen at random, what is the probability that his blood-group is AB ?
Fill in the following boxes and find the answer
n(S)=  ______

n(C)= ______

p(C)=________=_________

Chapter: [4] Probability
Concept: Probability Examples and Solutions
[2]3.1.2

The first term and the common difference of an A.P. is 10 and 5 respectively. Complete the following activity to find the sum of first 30 terms of the A. P.

S_n=n/2[ ____+(n-1)d ]

∴ s_30=30/2[20+(30-1)xx _____ ]

=15[20+________]

=15xx165

=_________

Chapter: [1] Arithmetic Progression
Concept: Sum of the First 'N' Terms of an Geometric Progression
[2]3.1.3

Complete the following table to draw the graph of 3x - y = 2

 x ________ -1 y 1 _______ (x,y) ________ _______
Chapter: [3] Linear equations in two variables
Concept: Graphical Method of Solution of a Pair of Linear Equations
[4]3.2 | Solve any two of the following.
[2]3.2.1

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 ?

Chapter: [6] Financial Planning
Concept: Shares
[2]3.2.2

The "n"^(th) term of the A. P. 3, 8, 13, 18, ............ is 148. Find n

Chapter: [1] Arithmetic Progression
Concept: Arithmetic Mean
[2]3.2.3

Solve the following simultaneous equations by Cramer's method.

x+y=7,2x-3y=9

Chapter: [3] Linear equations in two variables
Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method
[9]4 | Solve any three of the following.
[3]4.1

If α and β are the roots of the quadratic equation x^2 - 4x - 6 = 0, find  the values of (i) α^2+β^2 (ii) α^3+β^3

Concept: Roots of a Quadratic Equation
[3]4.2

The sum of third and seventh term of an A. P. is 6 and their product is 8. Find the first term and the common difference of the A. P.

Chapter: [1] Arithmetic Progression
Concept: Sum of First n Terms of an AP
[3]4.3

A survey was conducted in Aadarsh Vidyalaya to know the inclication of students towards different subjects. The data obtained is presented by the adjacent pie diagram. If the total number of students was 500, answer the following questions.

(i) How many students show inclination towards mathematics ?

(ii) How many students are inclined towards social sciences ?

(iii) How many more students are inclined towards languages than
science ?

Chapter: [1] Arithmetic Progression
Concept: Sum of the First 'N' Terms of an Geometric Progression
[3]4.4

The sum of a two digit number and the number obtained by reversing its digits is 121. Find the number if its units place digit is greater than the tens place digit by 7.

Chapter: [3] Linear equations in two variables
Concept: Simple Situational Problems
[4]5 | Solve any one of the following.
[4]5.1

The distance between Akola and Bhusawal is 168 km. An express train takes 1 hour less than a passenger train to cover the distance. Find the average speed of each train if the average speed of the express train is more by 14 km/hr than the speed of the passenger train.

Concept: Solutions of Quadratic Equations by Factorization
[4]5.2

The following table is based on the marks of the first term examination of 10th class students. Show the information by a histogram. Also, draw  a frequency polygon with the help of the histogram.

 Class-mark of marks 325 375 425 475 525 575 No. of students 25 35 45 40 32 20

Chapter: [5] Statistics
Concept: Histograms
[4]6 | Solve any one of the following.
[4]6.1

A bag contains in all 50 balls. Some of them are white, some are blue and some are red. The number of white balls is 11 times the number of blue balls. The number of red balls is less than the number of white balls. Also, the number of red balls is more than the number of blue balls. If one of the balls is selected at random from the bag, what is the probability that it is red ?

Chapter: [4] Probability
Concept: Random Experiments
[4]6.2

There are three dealers A, B and C in Maharashtra. Suppose, the trade of each of them in september 2018 was as shown in the following table.
The rate of GST on each transaction was 5%.

 Dealer GSTcollectedon the sale GST paid at the time ofpurchase ITC Tax paidto theGovt. Taxbalancewith theGovt. A Rs.5000 Rs. 6000 Rs. 5000 Rs. 0 Rs. 1000 B Rs 5000 Rs. 4000 Rs. 4000 Rs. 1000 Rs. 0 C Rs.5000 Rs. 5000 Rs. 5000 Rs. 0 Rs. 0

(i) How much amount did the dealer A get by sale ?
(ii) For how much amount did the dealer B buy the articles ?
(iii) How much is the balance of CGST and SGST left with the government that was paid by A ?

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

## Maharashtra State Board previous year question papers Class 10th Board Exam Algebra with solutions 2018 - 2019

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