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Algebra Set 1 2018-2019 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

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Algebra [Set 1]
Marks: 40Academic Year: 2018-2019
Date: July 2019
  • All questions are compulsory. 
  • Figures to the right of questions indicate full marks. 
  • Use of calculator is not allowed.

[8]1
[4]1.A | Attempt any FOUR of the following:
[1]1.A.i

If |7| × |-4| = a, then find the value of a. 

Concept: Linear Equations in Two Variables
Chapter: [0.01] Linear equations in two variables
[1]1.A.ii

If x + y = 5 and  x - y = 1, then find the value of x.

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

Find the median of the scores 7, 10, 5, 8, 9. 

Concept: Median of Grouped Data
Chapter: [0.06] Statistics
[1]1.A.iv

Write the degree of Polynomial 5x2 + 2x + 3x4 + 4. 

Concept: Quadratic Equations Examples and Solutions
Chapter: [0.02] Quadratic Equations
[1]1.A.v

If A = {1, 2, 3, 4, 5} and B = {1, 3, 7}, then A ∩ B = ? 

Concept: Basic Ideas of Probability
Chapter: [0.05] Probability [0.05] Probability
[1]1.A.vi

Find out the ratio of 1 mm to 1 cm. 

Concept: Arithmetic Progression Examples and Solutions
Chapter: [0.03] Arithmetic Progression
[4]1.B | Attempt any two of the following :
[2]1.B.i

Find the factors of the Polynomial 3x2 - 2x - 1. 

Concept: Solutions of Quadratic Equations by Factorization
Chapter: [0.02] Quadratic Equations
[2]1.B.ii

`square` ABCD is a parallelogram. the ration of `angle`A and `angle`B of this parallelogram is 5 : 4. Find the measure of `angle`B.

Concept: Concept of Ratio
Chapter: [0.03] Arithmetic Progression
[2]1.B.iii

Alka spends 90 % of the amount sent to her and saves Rs. 120 per
month. Find the amount sent to her per month.

Concept: Inconsistency of Pair of Linear Equations
Chapter: [0.01] Linear equations in two variables
[8]2
[4]2.A | Choose the correct alternative:
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[1]2.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: [0.01] Linear equations in two variables
[1]2.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
Chapter: [0.02] Quadratic Equations
[1]2.A.iii

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
[1]2.A.iv

For a given A.P., a = 3.5, d = 0, then tn = _______ .

0

3.5

103.5

104.5

Concept: General Term of an Arithmetic Progression
Chapter: [0.03] Arithmetic Progression
[4]2.B | Attempt any two of the following :
[2]2.B.i

Find k if x = 3 is a root of equation kx2 – 10x + 3 = 0

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

Market value of a share is Rs 200. If the brokerage rate is 0.3% then find the purchase value of the share.

Concept: Comparison of FV and MV
Chapter: [0.04] Financial Planning
[2]2.B.iii

The following table shows the number of students and the time they utilized daily for their studies. Find the mean time, spent by students for their studies: 

Time (hrs.) No.of.students
0 - 2 8
2 - 4 14
4 - 6 18
6 - 8 10
8 -10 10
Concept: Tabulation of Data
Chapter: [0.06] Statistics
[8]3
[4]3.A | Complete the following activities (Any two):
[2]3.A.i

There are 9 tickets in a box, each bearing one of the numbers from 1 to 9. 
One ticket is drawn at random from the box.  
Event A: Ticket shows an even number. 
Complete the following activity from the given information: 

Activity:

S = {__________}

n(S) = ____________

A = {________}

n(A) = ___________

Concept: Sample Space
Chapter: [0.05] Probability
[2]3.A.ii

Complete the following activity to form a quadratic equation.  
Activity: 

Concept: Quadratic Equations Examples and Solutions
Chapter: [0.02] Quadratic Equations
[2]3.A.iii

Complete the following activity to find the number of natural numbers between 1 and 171, which are divisible by 5:  

Activity : 

Concept: Arithmetic Progression Examples and Solutions
Chapter: [0.03] Arithmetic Progression
[4]3.B | Attempt any TWO of the following :
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[2]3.B.i

Solve the following simultaneous equations :

4 x + 3y = 11;  3x + 4y = 10  

Concept: Graphical Method of Solution of a Pair of Linear Equations
Chapter: [0.01] Linear equations in two variables
[2]3.B.ii

Find the 23rd term of the following A.P.: 9, 4,-1,-6,-11.

Concept: General Term of an Arithmetic Progression
Chapter: [0.03] Arithmetic Progression
[2]3.B.iii

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]4 | Attempt any Three of the following :
[3]4.A

Solve the following simultaneous equations graphically:  

x + y = 2 ; x - y = 4. 

Concept: Graphical Method of Solution of a Pair of Linear Equations
Chapter: [0.01] Linear equations in two variables
[3]4.B

Sachin invested some amounts in National Saving Certificates in a specific way. In the first year, he invested  4,000 in the second year  6,000 in the third year  8,000 and so on for  12 years. Find the total amount he invested in 12 years. 

Concept: Sum of the First 'N' Terms of an Geometric Progression
Chapter: [0.03] Arithmetic Progression
[3]4.C

A readymade garment shopkeeper gives 5% discount on a dress of  2,000 and charges  5% GST on the remaining amount. What is the purchase price of the dress for the customer?

Concept: GST - Tax Invoice
Chapter: [0.04] Financial Planning
[3]4.D

A bag contains 3 red, 3 white, 3 green, and 3 black balls. One ball is picked up from the bag at random. What is the probability that the ball drawn is:

a. white

b. not white. 

Concept: Probability of an Event
Chapter: [0.05] Probability
[4]5 | Attempt any ONE of the following:
[4]5.A

Out of 555 km, Vishal travelled certain distance by bus and
remaining distance by car. A bus travels with an average speed of 60 km/hr and the average speed of a car is 75 km/hr. He takes total 8 hours to complete the journey. Find the distance that Vishal travelled by bus.​ 

Concept: Simple Situational Problems
Chapter: [0.01] Linear equations in two variables
[4]5.B

The time required for some students to complete a science experiment and the number of students is shown in the following grouped frequency distribution table. Draw the frequency polygon with the help of histogram using given information: 

Time required for experiment (minutes)  Number of Students 
20 - 22 6
22 - 24 14
24 - 26 20
26 - 28 16
28 - 30 12
30 - 32 10
Concept: Frequency Polygon
Chapter: [0.06] Statistics
[3]6 | Attempt any ONE of the following :
[3]6.A

Construct a word problem on quadratic equation, such that one of its answers is 20 (years, rupees, centimeter, etc.). Also, solve it.

Concept: Quadratic Equations Examples and Solutions
Chapter: [0.02] Quadratic Equations
[3]6.B

A student made a cube-shaped die from a card sheet. Instead of writing numbers 1,2,3,4,5,6 on its face, he wrote letters a,b,c,d,e,f one on each face randomly. If he rolls the die twice, find the probability that he gets a vowel on the upper face both times​.

Concept: Random Experiments
Chapter: [0.05] Probability
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