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Algebra Shaalaa.com Model Set 5 2019-2020 SSC (English Medium) Class 10th Board Exam Question Paper Solution

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Algebra [Shaalaa.com Model Set 5]
Marks: 40Academic Year: 2019-2020
Date: March 2020
Duration: 2h

[8]1
[4]1.A | MCQs
[1]1.A.i

Choose the correct answer for the following question.

The roots of x2 + kx + k = 0 are real and equal, find k.

0

4

0 or 4

2

Concept: Quadratic Equations Examples and Solutions
Chapter: [2] Quadratic Equations
[1]1.A.ii

Choose the correct alternative answer for  the following question .

For an given A.P. a = 3.5, d = 0, n = 101, then tn = ....

0

3.5 

103.5

14.5 

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

Write the correct alternative for  the following.

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

 15

10

16

  9

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

Find the correct answer from the alternatives given.

The formula to find mean from a grouped frequency table is  \[X = A + \frac{\sum f_i u_i}{\sum f_i} \times hg\] .

\[\frac{x_i + A}{g}\] 

\[\left( x_i - A \right)\] 

\[\frac{x_i - A}{g}\]

\[\frac{A - x_i}{g}\]
Concept: Mean of Grouped Data
Chapter: [5] Statistics
[4]1.B
[1]1.B.i

Solve the following simultaneous equation.
3a + 5b = 26; a + 5b = 22

Concept: Introduction of System of Linear Equations in Two Variables
Chapter: [3] Linear equations in two variables
[1]1.B.ii

Decide whether the following equation is quadratic equation or not.

\[y^2 + \frac{1}{y} = 2\] 

Concept: Quadratic Equations Examples and Solutions
Chapter: [2] Quadratic Equations
[1]1.B.iii

The arrow is rotated and it stops randomly on the disc. Find out on which colour it may stop.

Concept: Sample Space
Chapter: [4] Probability
[1]1.B.iv

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 by direct method.

Time (hrs.) 0 - 2 2 - 4 4 - 6 6 - 8 8 - 10
No. of students 7 18 12 10 3
Concept: Tabulation of Data
Chapter: [5] Statistics
[12]2
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[4]2.A | Solve any 2 of the following
[2]2.A.i

Solve the Following Word Problem.
Places A and B are 30 km apart and they are on a st raight road. Hamid travels from A to B on bike. At the same time Joseph starts from B on bike, travels towards A. They meet each other after 20 minutes. If Joseph would have started from B at the same time but in the opposite direction (instead of towards A) Hamid would have caught him after 3 hours. Find the speed of Hamid and Joseph.

Concept: Simple Situational Problems
Chapter: [3] Linear equations in two variables
[2]2.A.ii

A tank fills completely in 2 hours if both the taps are open. If only one of the taps is open at the given time, the smaller tap takes 3 hours more than the larger one to fill the tank. How much time does each tap take to fill the tank completely?

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

The 11th term and the 21st term of an A.P. are 16 and 29 respectively, then find the 41thterm of that A.P.

Concept: Sum of the First 'N' Terms of an Geometric Progression
Chapter: [1] Arithmetic Progression
[8]2.B | Solve any 4 of the following
[2]2.B.i

Solve the following simultaneous equation.
49x – 57y = 172; 57x – 49y = 252

Concept: Introduction of System of Linear Equations in Two Variables
Chapter: [3] Linear equations in two variables
[2]2.B.ii

Solve the following quadratic equation by factorization.

 2x2 – 2x +\[\frac{1}{2}\]=0.

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

Find the fourth term from the end in an A.P. –11, –8, –5,...., 49.

Concept: Introduction to Sequence
Chapter: [1] Arithmetic Progression
[2]2.B.iv

The following table shows the income of farmers in a grape season. Find the mean of their income. 

Income
(Thousand Rupees)
20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80
Farmers 10 11 15 16 18 14
Concept: Mean of Grouped Data
Chapter: [5] Statistics
[2]2.B.v

Grouped frequency distribution of supply of milk to hotels and the number of hotels is given in the following table. Find the mode of the supply of milk.

Age (years) Less than 5 5 - 9 10 - 14 15 - 19 20 - 24 25 - 29
No. of patients 38 32 50 36 24 20
Concept: Median of Grouped 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.
\[ \frac{2}{x} - \frac{3}{y} = 15; \frac{8}{x} + \frac{5}{y} = 77\]

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

Find quadratic equation such that its roots are square of sum of the roots and square of difference of the roots of equation

\[2 x^2 + 2\left( p + q \right)x + p^2 + q^2 = 0\]

Concept: Relation Between Roots of the Equation and Coefficient of the Terms in the Equation Equations Reducible to Quadratic Form
Chapter: [2] Quadratic Equations
[6]3.B | Solve any 2 of the following
[3]3.B.i

Fill in the blanks given in the contract note of sale-purchase of shares. 
(B - buy S - sell)

No. of
shares
MV of
shares
Total
value
Brokerage
0.2%
9% CGST
on
brokerage
9% SGST
on
brokerage
Total
value of
shares
100 B Rs 45          
75 S Rs 200  
Concept: Brokerage and taxes on share tradin
Chapter: [6] Financial Planning
[3]3.B.ii

In a game of chance, a spinning arrow comes to rest at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8. All these are equally likely outcomes. Find the probability that it will rest at an odd number.

Concept: Probability - A Theoretical Approach
Chapter: [4] Probability

In a game of chance, a spinning arrow comes to rest at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8. All these are equally likely outcomes. Find the probability that it will rest at a number greater than 2.

Concept: Probability - A Theoretical Approach
Chapter: [4] Probability

In a game of chance, a spinning arrow comes to rest at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8. All these are equally likely outcomes. Find the probability that it will rest at  a number less than 9.

Concept: Probability - A Theoretical Approach
Chapter: [4] Probability
[3]3.B.iii

The pie diagram in figure shows the proportions of different workers in a town. Answer the following question with its help.
 If the total workers is 10,000; how many of them are in the field of construction ?

Concept: Pie Diagram
Chapter: [5] Statistics
[3]3.B.iv

The following table shows the ages of the patients admitted in a hospital during a year:

age (in years)

5 − 15

15 − 25

25 − 35

35 − 45

45 − 55

55 − 65

Number of patients

6

11

21

23

14

5

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Concept: Mode of Grouped Data
Chapter: [5] Statistics
[8]4 | Solve any 2 of the following
[4]4.A

Solve the following pairs of equations by reducing them to a pair of linear equations

`5/(x-1) + 1/y-2 = 2`

`6/(x-1) - 3/(y-2) = 1`

Concept: Equations Reducible to a Pair of Linear Equations in Two Variables
Chapter: [3] Linear equations in two variables
[4]4.B

For the given trading chain prepare the tax invoice I, II, III, GST at the rate of 12% was chanrged for the article supplied.

Prepare the statement of GST payable under each head by the wholesaler, distributor and retailer at the time of filing the return to the government.

Concept: GST - Tax Invoice
Chapter: [6] Financial Planning
[4]4.C

Two dice, one blue and one grey, are thrown at the same time.

(i) Write down all the possible outcomes and complete the following table:

Event :
‘Sum on 2 dice’
2 3 4 5 6 7 8 9 10 11 12
Probability 1/36           5/36       1/36
Concept: Probability - A Theoretical Approach
Chapter: [4] Probability
[3]5 | Solve any 1 of the following
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[3]5.A

Ranjana wants to distribute 540 oranges among some students. If 30 students were more each would get 3 oranges less. Find the number of students.

Concept: Quadratic Equations Examples and Solutions
Chapter: [2] Quadratic Equations
[3]5.B

The A.P. in which 4th term is –15 and 9th term is –30. Find the sum of the first 10 numbers.

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

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