SSC (Marathi Semi-English) 10thMaharashtra State Board
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# Algebra Shaalaa.com Model Set 4 2019-2020 SSC (Marathi Semi-English) 10th Question Paper Solution

Algebra [Shaalaa.com Model Set 4]
Marks: 40Date: 2019-2020 March
Duration: 2h

1
1.A | MCQs
1.A.i

Choose correct alternative for the following question.
Find the value of $\begin{vmatrix}5 & 3 \\ - 7 & - 4\end{vmatrix}$

–1

–41

41

1

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

Choose the correct answer for the following question.
Out of the following equations which one is not a quadratic equation?

x^2+4x=11+x^2

x^2=4x

5x^2=90+5

2x-x^2=x^2

Concept: Quadratic Equations Examples and Solutions
1.A.iii

Write the correct alternative for the following.

The tax levied by the central government for trading within state is ...

IGST

CGST

SGST

UTGST

Concept: GST - Introduction
Chapter:  Financial Planning
1.A.iv

Choose the correct alternative answer for the following question.
Which number cannot represent a probability ?

2/3

1.5

15%

0.7

Concept: Probability Examples and Solutions
Chapter:  Probability
1.B
1.B.i

For the following experiment write sample space ‘S’ and number of sample points n(S).

One coin and one die are thrown simultaneously.

Concept: Sample Space
Chapter:  Probability
1.B.ii

Draw a histogram of the following data.

 Height of student (cm) 135 - 140 140 - 145 145 - 150 150 - 155 No. of students 4 12 16 8
Concept: Graphical Representation of Histograms
Chapter:  Statistics
1.B.iii

Which of the following sequences are A.P. ? If they are A.P. find the common difference .

0, –4, –8, –12,...

Concept: Arithmetic Progression Examples and Solutions
Chapter:  Arithmetic Progression
1.B.iv

‘Tiptop Electronics’ supplied an AC of 1.5 ton to a company. Cost of the AC supplied is Rs 51,200 (with GST). Rate of CGST on AC is 14%. Then find the following amounts as shown in the tax invoice of Tiptop Electronics.

(3) Taxable value of AC

Concept: GST - Tax Invoice
Chapter:  Financial Planning
2
2.A | Solve any 2 of the following
2.A.i

Solve the following word problem.
To find number of notes that Anushka had, complete the following activity. Concept: Simple Situational Problems
Chapter:  Linear equations in two variables
2.A.ii

Determine whether the values given against the quadratic equation are the roots of the equation.

x2 + 4x – 5 = 0 , x = 1, –1

Concept: Solutions of Quadratic Equations by Factorization
2.A.iii

In an A.P. 17th term is 7 more than its 10th term. Find the common difference.

Concept: Sum of First n Terms of an AP
Chapter:  Arithmetic Progression
2.B | Solve any 4 of the following
2.B.i

Solve the following simultaneous equation.
x + 7y = 10; 3x – 2y = 7

Concept: Introduction of System of Linear Equations in Two Variables
Chapter:  Linear equations in two variables
2.B.ii

Determine whether the values given against the quadratic equation are the roots of the equation.

2m2 – 5m = 0, m = 2, 5/2

Concept: Solutions of Quadratic Equations by Factorization
2.B.iii
Find the sum of all even numbers from 1 to 350.
Concept: Sum of First n Terms of an AP
Chapter:  Arithmetic Progression
2.B.iv

The production of electric bulbs in different factories is shown in the following table. Find the median of the productions.

 No. of bulbs produced (Thousands) 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 No. of factories 12 35 20 15 8 7 8
Concept: Tabulation of Data
Chapter:  Statistics
2.B.v

Consider the following distribution of daily wages of 50 worker of a factory.

 Daily wages (in Rs) 500 - 520 520 -540 540 - 560 560 - 580 580 -600 Number of workers 12 14 8 6 10

Find the mean daily wages of the workers of the factory by using an appropriate method.

Concept: Mean of Grouped Data
Chapter:  Statistics
3
3.A | Solve any 1 of the following
3.A.i

Solve the following simultaneous equations.

$\frac{1}{2\left( 3x + 4y \right)} + \frac{1}{5\left( 2x - 3y \right)} = \frac{1}{4} ; \frac{5}{\left( 3x + 4y \right)} - \frac{2}{\left( 2x - 3y \right)} = - \frac{3}{2}$
Concept: Graphical Method of Solution of a Pair of Linear Equations
Chapter:  Linear equations in two variables
3.A.ii

The sum of squares of two consecutive natural numbers is 244; find the numbers.

Concept: Quadratic Equations Examples and Solutions
3.B | Solve any 2 of the following
3.B.i

There are 37 terms in an A.P., the sum of three terms placed exactly at the middle is 225 and the sum of last three terms is 429. Write the A.P.

Concept: Sum of First n Terms of an AP
Chapter:  Arithmetic Progression
3.B.ii

Smt. Anagha Doshi purchased 22 shares of FV Rs 100 for Market Value of Rs 660. Find the sum invested. After taking 20% dividend, she sold all the shares when market value was Rs 650. She paid 0.1% brokerage for each trading done. Find the percent of profit or loss in the share trading.

Concept: GST on Brokerage Services
Chapter:  Financial Planning
3.B.iii

A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets, a red balloon.

Concept: Probability Examples and Solutions
Chapter:  Probability
3.B.iv

The annual investments of a family are shown in the adjacent pie diagram. Answer the following questions based on it.
(1) If the investment in shares is Rs 2000/, find the total investment.
(2) How much amount is deposited in bank ?
(3) How much more money is invested in immovable property than in mutual fund ?
(4) How much amount is invested in post ? Concept: Pie Diagram
Chapter:  Statistics
4 | Solve any 2 of the following
4.A

The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 3 more balls of the same kind for Rs 1300. Represent this situation algebraically and geometrically.

Concept: Pair of Linear Equations in Two Variables
Chapter:  Linear equations in two variables
4.B

An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11km/h more than that of the passenger train, find the average speed of the two trains.

Concept: Solutions of Quadratic Equations by Factorization
4.C

100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:

 Number of letters Number of surnames 1 - 4 6 4 − 7 30 7 - 10 40 10 - 13 6 13 - 16 4 16 − 19 4

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.

Concept: Median of Grouped Data
Chapter:  Statistics
5 | Solve any 1 of the following
5.A

Smt. Mita Agrawal invested Rs 10,200 when MV of the share is Rs 100. She sold 60 shares when the MV was Rs 125 and sold remaining shares when the MV was Rs 90. She paid 0.1% brokerage for each trading. Find whether she made profit or loss ? and how much

Concept: Comparison of FV and MV
Chapter:  Financial Planning
5.B

In a hockey team there are 6 defenders , 4 offenders and 1 goalee. Out of these, one player is to be selected randomly as a captain. Find the probability of the selection that –
The goalee will be selected.

Concept: Probability Examples and Solutions
Chapter:  Probability

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