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Algebra Shaalaa.com Model Set 3 2019-2020 SSC (English Medium) Class 10th Board Exam Question Paper Solution

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Algebra [Shaalaa.com Model Set 3]
Marks: 40Academic Year: 2019-2020
Date: March 2020
Duration: 2h

[8]1
[4]1.A | MCQs
[1]1.A.i

Choose correct alternative for the following question.
For simultaneous equations in variables x and y, D= 49, Dy = –63, D = 7 then what is x ?

7

-7

`1/7`

`(-1)/7`

Concept: Determinant of Order Two
Chapter: [3] Linear equations in two variables
[1]1.A.ii

Choose the correct alternative answer for  the following question .

 In an A.P. 1st term is 1 and the last term is 20. The sum of all terms is = 399 then n = ....

42

38

21

19

Concept: Sum of First n Terms of an AP
Chapter: [1] Arithmetic Progression
[1]1.A.iii

Write the correct alternative for the following.

When a registered dealer sells goods to another registered dealer under GST, then this trading is termed as ...

BB

B2B

BC

 B2C

Concept: GST - Introduction
Chapter: [6] Financial Planning
[1]1.A.iv

Choose the correct alternative answer for the following question.

There are 40 cards in a bag. Each bears a number from 1 to 40. One card is drawn at random. What is the probability that the card bears a number which is a multiple of 5 ?

`1/5  `

`3/5 `

`4/5`

`1/3`

Concept: Probability Examples and Solutions
Chapter: [4] Probability
[4]1.B
[1]1.B.i

Find the value of discriminant of the following equation.

\[2 y^2 - y + 2 = 0\] 

Concept: Relation Between Roots of the Equation and Coefficient of the Terms in the Equation Equations Reducible to Quadratic Form
Chapter: [2] Quadratic Equations
[1]1.B.ii

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

Concept: Concept Or Properties of Probability
Chapter: [4] Probability
[1]1.B.iii

Find the values of following determinant.

\[\begin{vmatrix}- 1 & 7 \\ 2 & 4\end{vmatrix}\]
Concept: Equations Reducible to a Pair of Linear Equations in Two Variables
Chapter: [3] Linear equations in two variables
[1]1.B.iv

Complete the following activity to solve the simultaneous equations.
5x + 3y = 9 -----(I)
2x + 3y = 12 ----- (II)

Concept: Introduction of System of Linear Equations in Two Variables
Chapter: [3] Linear equations in two variables
[12]2
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[4]2.A | Solve any 2 of the following
[2]2.A.i

In an A.P. the first term is –5 and last term is 45. If sum of all numbers in the A.P. is 120, then how many terms are there ? What is the common difference ?

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

Anna Patil (Thane, Maharashtra) supplied vacuum cleaner to a shopkeeper in Vasai (Mumbai) for the taxable value of Rs 14,000, and GST rate of 28%. Shopkeeper sold it to the customer at the same GST rate for Rs16,800 (taxable value) Find the following – 

Amount of CGST and SGST charged by the shopkeeper in Vasai. 

Concept: GST - Tax Invoice
Chapter: [6] Financial Planning
[2]2.A.iii

Solve using formula.

5m2 – 4m – 2 = 0

Concept: Relation Between Roots of the Equation and Coefficient of the Terms in the Equation Equations Reducible to Quadratic Form
Chapter: [2] Quadratic Equations
[8]2.B | Solve any 4 of the following
[2]2.B.i

On 1st Jan 2016, Sanika decides to save Rs 10, Rs 11 on second day, Rs 12 on third day. If she decides to save like this, then on 31st Dec 2016 what would be her total saving ?

Concept: Arithmetic Progression Examples and Solutions
Chapter: [1] Arithmetic Progression
[2]2.B.ii

A ready-made garment shopkeeper gives 5% discount on the dress of Rs 1000 and charges 5% GST on the remaining amount, then what is the purchase price of the dress for the customer

Concept: GST - Tax Invoice
Chapter: [6] Financial Planning
[2]2.B.iii

Joseph kept 26 cards in a cap, bearing one English alphabet on each card. One card is drawn at random. What is the probability that the card drawn is a vowel card ?

Concept: Probability Examples and Solutions
Chapter: [4] Probability
[2]2.B.iv

Form the quadratic equation from the roots given below.

 0 and 4

Concept: Solutions of Quadratic Equations by Completing the Square
Chapter: [2] Quadratic Equations
[2]2.B.v

The following table shows the classification of number of vehicles and their speeds on Mumbai-Pune express way. Find the median of the data.

Average Speed of
Vehicles(Km/hr)
60 - 64 64 - 69 70 - 74 75 - 79 79 - 84 84 - 89
No. of vehicles 10 34 55 85 10 6
Concept: Tabulation of Data
Chapter: [5] Statistics
[9]3
[3]3.A | Solve any 1 of the following
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[3]3.A.i

Solve the following simultaneous equations.
\[\frac{1}{3x + y} + \frac{1}{3x - y} = \frac{3}{4}; \frac{1}{2\left( 3x + y \right)} - \frac{1}{2\left( 3x - y \right)} = - \frac{1}{8}\]

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

Solve the following quadratic equation by completing the square method.

 2y2 + 9y +10 = 0

Concept: Solutions of Quadratic Equations by Completing the Square
Chapter: [2] Quadratic Equations
[6]3.B | Solve any 2 of the following
[3]3.B.i

Decide whether following sequence is an A.P., if so find the 20th term of the progression.
–12, –5, 2, 9, 16, 23, 30,...

Concept: General Term of an Arithmetic Progression
Chapter: [1] Arithmetic Progression
[3]3.B.ii

Shri. Aditya Sanghavi invested Rs 50,118 in shares of FV Rs 100, when the market value is Rs 50. Rate of brokerage is 0.2% and Rate of GST on brokerage is 18%, then How many shares were purchased for Rs 50,118 ?

Concept: Brokerage and taxes on share tradin
Chapter: [6] Financial Planning
[3]3.B.iii

The table below shows the yield of jowar per acre. Show the data by histogram.

Yield per acre (quintal) 2 - 3 4 - 5 6 - 7 8 - 9 10 - 11
No. of farmers 30 50 55 40 20
Concept: Graphical Representation of Histograms
Chapter: [5] Statistics
[3]3.B.iv

Solve the following equations by Cramer’s method.
3x – 2= \[\frac{5}{2}\] ; \[\frac{1}{3}x + 3y = - \frac{4}{3}\]

 

Concept: Cramer'S Rule
Chapter: [3] Linear equations in two variables
[8]4 | Solve any 2 of the following
[4]4.A

In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.

Number of mangoe 50 − 52 53 − 55 56 − 58 59 − 61 62 − 64
Number of boxes 15 110 135 115 25

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

Concept: Mean of Grouped Data
Chapter: [5] Statistics
[4]4.B

Two water taps together can fill a tank in `9 3/8`hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Concept: Solutions of Quadratic Equations by Completing the Square
Chapter: [2] Quadratic Equations
[4]4.C

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, determine the number of blue balls in the bag

Concept: Probability - A Theoretical Approach
Chapter: [4] Probability
[3]5 | Solve any 1 of the following
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[3]5.A

A milk centre sold milk to 50 customers. The table below gives the number of customers and the milk they purchased. Find the mean of the milk sold by direct method.

Milk Sold (Litre) 1 - 2 2 - 3 3 - 4 4 - 5 5 - 6
No. of Customers 17 13 10 7 3
Concept: Tabulation of Data
Chapter: [5] Statistics
[3]5.B

Solve the following simultaneous equation graphically.
5x – 6y + 30 = 0 ; 5x + 4y – 20 = 0

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

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