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Algebra Set 1 2019-2020 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

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Algebra [Set 1]
Marks: 40 Academic Year: 2019-2020
Date & Time: 12th March 2020, 11:00 am
Duration: 2h
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  1. All questions are compulsory.
  2. Use of calculator is not allowed.
  3. The numbers to the right of the questions indicate full marks.
  4. In case of MCQ’s Q. No. 1(A) only the first attempt will be evaluated and will be given credit.
  5. For every MCQ, the correct alternative (A), (B), (C) or (D) of answers with subquestion number is to be written as an answer. 

[8] 1
[4] 1.A | For every subquestion 4 alternative answers are given. Choose the correct answer and write the alphabet of it:
[1] 1.A.i

Write the correct alternative for the following.

In the format of GSTIN there are ____________ alpha-numerals.

15

10

16

9

Concept: GST - Introduction
Chapter: [0.04] Financial Planning
[1] 1.A.ii

From the following equations, which one is the quadratic equation?

`5/"x" = 3 = "x"^2`

x(x + 5) = 4

n – 1 = 2n

`1/"x"^2("x" + 2) = "x"`

Concept: Quadratic Equations
Chapter: [0.02] Quadratic Equations
[1] 1.A.iii

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: [0.01] Linear equations in two variables
[1] 1.A.iv

Choose the correct alternative answer for the following question.

If n(A) = 2, P(A) =`1/5`, then n(S) = ?

10

`5/2`

`2/5`

`1/3`

Concept: Basic Ideas of Probability
Chapter: [0.05] Probability [0.05] Probability
[4] 1.B | Solve the following subquestions:
[1] 1.B.i

Find second and third terms of an A.P. whose first term is – 2 and the common difference is – 2.

Concept: Sum of First n Terms of an AP
Chapter: [0.03] Arithmetic Progression
[1] 1.B.ii

‘Pawan Medical’ supplies medicines. On some medicines the rate of GST is 12%, then what is the rate of CGST and SGST?

Concept: GST - Tax Invoice
Chapter: [0.04] Financial Planning
[1] 1.B.iii

Find the values of a and b from the quadratic equation 2x2 – 5x + 7 = 0.

Concept: Quadratic Equations
Chapter: [0.02] Quadratic Equations
[1] 1.B.iv

If 15x + 17y = 21 and 17x + 15y = 11, then find the value of x + y.

Concept: Pair of Linear Equations in Two Variables
Chapter: [0.01] Linear equations in two variables
[12] 2
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[4] 2.A | Complete and write any TWO activities from the following:
[2] 2.A.i

Complete the following table to draw the graph of 2x – 6y = 3:

x −5 `square`
y `square` 0
(x, y) `square` `square`
Concept: Graphical Method of Solution of a Pair of Linear Equations
Chapter: [0.01] Linear equations in two variables
[2] 2.A.ii
First-term and the common differences of an A.P. are 6 and 3 respectively; find S27.
Solution:
First term = a = 6 , common difference = d = 3, S27 = ?
Sn = \[\frac n2 [\Box + (n-1) d ]\]
S27 =  `27/2` [12 + (27 - 1)\[\Box ]\]
      =`27/2` ×\[\Box\]
      =27 ×45 = \[\Box \]
Concept: Sum of First n Terms of an AP
Chapter: [0.03] Arithmetic Progression
[2] 2.A.iii

A card is drawn from a well-shuffled pack of 52 playing cards. Find the probability of the event, the card drawn is a red card.

Solution:

Suppose ‘S’ is sample space.

∴ n(S) = 52

Event A: Card drawn is a red card.

∴ Total red cards = `square` hearts + 13 diamonds

∴ n(A) = `square`

∴ p(A) = `square/("n"("s"))`   ....formula

∴ p(A) = `26/52`

∴ p(A) = `square`

Concept: Type of Event - Complementry
Chapter: [0.05] Probability
[8] 2.B | Solve any FOUR subquestions from the following:
[2] 2.B.i

Find the value of the determinant:

`[(7/3,5/3),(3/2,1/2)]`

Concept: Determinant of Order Two
Chapter: [0.01] Linear equations in two variables
[2] 2.B.ii

Solve the quadratic equation by factorisation method:

x2 - 15x + 54 = 0

Concept: Solutions of Quadratic Equations by Factorization
Chapter: [0.02] Quadratic Equations
[2] 2.B.iii

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: [0.03] Arithmetic Progression
[2] 2.B.iv

A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is an odd number ?

Concept: Sample Space
Chapter: [0.05] Probability
[2] 2.B.v

Find the mode from the following information: 

L = 10, h = 2, f0 = 58, f1 = 70, f2 = 42. 

Concept: Mode of Grouped Data
Chapter: [0.06] Statistics
[9] 3
[3] 3.A | Complete and write any ONE activity from the following:
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[3] 3.A.i
Age group
(in years)
No. of Persons Measure of central angle
20 - 25 80 `square/200 xx 300 = square`
25 - 30 60 `60/200 xx 360 = square`
30 - 35 35 `35/200 xx square = 63^circ`
35 - 40 25 `25/200 xx 360 = square`
Total 200 `square`
Concept: Concept of Pie Graph (Or a Circle-graph)
Chapter: [0.06] Statistics [0.06] Statistics
[3] 3.A.ii

Shri Shantilal has purchased 150 shares of FV ₹ 100, for MV of ₹ 120, Company has paid dividend at 7%, then to find the rate of return on his investment, complete the following activity:

Solution: FV = ₹ 100; Number of shares = 150

Market value = ₹ 120

1. Sum investment = MV × No. of Shares

= `square xx square`

∴ Sum investment = ₹ 18,000

2. Dividend per share = FV × Rate of dividend

= `square xx square/100`

= ₹ 7

∴ Total dividend received = 150 × 7

= `square`

3. Rate of return = `"Dividend income"/"Sum inve ted" xx 100`

= `1050/18000 xx 100`

= `square`

Concept: Comparison of FV and MV
Chapter: [0.04] Financial Planning
[6] 3.B | Attempt any two subquestions from the following:
[3] 3.B.i

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: Basic Ideas of Probability
Chapter: [0.05] Probability [0.05] Probability

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 blue balloon

Concept: Basic Ideas of Probability
Chapter: [0.05] Probability [0.05] Probability
[3] 3.B.ii

The denominator of a fraction is 4 more than twice its numerator. Denominator becomes 12 times the numerator, if both the numerator and the denominator are reduced by 6. Find the fraction.

Concept: Linear Equations in Two Variables
Chapter: [0.01] Linear equations in two variables
[3] 3.B.iii

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: [0.06] Statistics
[3] 3.B.iv

In an A.P. sum of three consecutive terms is 27 and their products is 504. Find the terms.
(Assume that three consecutive terms in an A.P. are a – d, a, a + d.)

Concept: Sum of First n Terms of an AP
Chapter: [0.03] Arithmetic Progression
[8] 4 | Attempt any two subquestions from the following:
[4] 4.A

Represent the following data by histogram:

Price of Sugar (per kg in ₹) Number of Weeks
18 – 20 4
20 – 22 8
22 – 24 22
24 – 26 12
26 – 28 6
28 – 30 8
Concept: Graphical Representation of Data as Histograms
Chapter: [0.06] Statistics [0.06] Statistics
[4] 4.B

One person borrows ₹ 4,000 and agrees to repay with a total interest of ₹ 500 in 10 instalments. Each instalment being less than the preceding instalment by ₹ 10. What should be the first and the last instalments?

Concept: Arithmetic Progression
Chapter: [0.03] Arithmetic Progression
[4] 4.C

The sum of the areas of two squares is 400 sq.m. If the difference between their perimeters is 16 m, find the sides of two squares.

Concept: Solutions of Quadratic Equations by Completing the Square
Chapter: [0.02] Quadratic Equations
[3] 5 | Attempt any one subquestion from the following:
[3] 5.A

Convert the following equations into simultaneous equations and solve:

`sqrt("x"/"y") = 4, 1/"x" + 1/"y" = 1/"xy"`

Concept: Roots of a Quadratic Equation
Chapter: [0.02] Quadratic Equations
[3] 5.B

A dealer sells a toy for ₹ 24 and gains as much percent as the cost price of the toy. Find the cost price of the toy.

Concept: Solutions of Quadratic Equations by Factorization
Chapter: [0.02] Quadratic Equations

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