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Algebra Balbharati Model Question Paper Set 3 2018-2019 SSC (Marathi Semi-English) 10th Question Paper Solution

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Algebra
Balbharati Model Question Paper Set 3
2018-2019 March
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. 

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

Solve any four of the following. 

`|8|+|-3|=?` 

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

Solve any four of the following. 

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

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

Solve any four of the following. 

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

 

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

Solve any four of the following. 

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

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

Concept: Arithmetic Mean
Chapter: [1] Arithmetic Progression
[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` 

 

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

Solve any two of the following. 

Solve : `3x+y=14 ; x-y=2` 

Concept: Quadratic Equations Examples and Solutions
Chapter: [2] Quadratic Equations
[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
Chapter: [2] Quadratic Equations
[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`

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

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

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

Concept: Probability Examples and Solutions
Chapter: [4] Probability
[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
Concept: Arithmetic Mean
Chapter: [1] Arithmetic Progression
[2]2.2.3

Solve any two of the following.  

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

Concept: Quadratic Equations
Chapter: [2] Quadratic Equations
[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)=________=_________

Concept: Probability Examples and Solutions
Chapter: [4] Probability
[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`

=_________ 

 

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

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

x ________ -1
y 1 _______
(x,y) ________ _______
Concept: Graphical Method of Solution of a Pair of Linear Equations
Chapter: [3] Linear equations in two variables
[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 ? 

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

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

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

Solve the following simultaneous equations by Cramer's method. 

`x+y=7,2x-3y=9` 

 

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

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

 

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

Concept: Simple Situational Problems
Chapter: [3] Linear equations in two variables
[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
Chapter: [2] Quadratic Equations
[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

 

Concept: Histograms
Chapter: [5] Statistics
[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 ?

Concept: Random Experiments
Chapter: [4] Probability
[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%.
Read the table and answer the questions below it.  

Dealer GST
collected
on the sale
GST paid at the time of
purchase
ITC Tax paid
to the
Govt.
Taxbalance
with the
Govt.
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 ? 

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

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