# Algebra 2013-2014 SSC (Marathi Semi-English) 10th Standard [इयत्ता १० वी] Question Paper Solution

Algebra
Date: October 2013

[5]1 | Attempt any five sub-question from the following :
[1]1.i

Find Sfor the A.P. 3,5,7,9,......

Concept: Arithmetic Progression Examples and Solutions
Chapter: [0.03] Arithmetic Progression
[1]1.ii

If a = 1, b = 8 and c = 15, then find the value of  "b"^2 - 4"ac"

Concept: Nature of Roots
[1]1.iii

Find the width of class 35 - 45.

Concept: Ogives (Cumulative Frequency Graphs)
Chapter: [0.06] Statistics
[1]1.iv

By using two variables, write the following statement in mathematical form:
The cost of two tables and five chairs is 2,200.

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

If n(A) = 1 and n(S) = 13 then find P(A).

Concept: Type of Event - Complementry
Chapter: [0.05] Probability
[1]1.vi

For solving the quadratic equations "x"^2 +  8"x" =-15 by completing the square method, find the third term.

Concept: Solutions of Quadratic Equations by Completing the Square
[8]2 | Attempt any four sub-questions from the following :
[2]2.i

Find the first four terms in A.P. When a = 10 and d = 3.

Concept: Arithmetic Progression Examples and Solutions
Chapter: [0.03] Arithmetic Progression
[2]2.ii

Prepare the cumulative frequency (less than types) table from the following distribution table :

 Class 0-10 10-20 20-30 30-40 40-50 Frequency 2 3 7 8 5
Concept: Ogives (Cumulative Frequency Graphs)
Chapter: [0.06] Statistics
[2]2.iii

From the quadratic equation if the roots are 6 and 7.

Concept: Nature of Roots
[2]2.iv

Find  the value of the determinant [(5,2),(7,4)]

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

Find tfor the A.P. 3,8,13,18,.....

Concept: Arithmetic Progression Examples and Solutions
Chapter: [0.03] Arithmetic Progression
[2]2.vi

Three coins are tossed simultaneously, find S and n(S).

Concept: Probability of an Event
Chapter: [0.05] Probability
[9]3 | Attempt any three sub-questions from the following :
[3]3.i

Find the first three terms to the sequence, whose nth term is t= 4n - 3

Concept: Introduction to Sequence
Chapter: [0.03] Arithmetic Progression
[3]3.ii

Solve the following quadratic equation by factorization method : "x"^2 - 5"x" - 36 = 0

Concept: Solutions of Quadratic Equations by Factorization
[3]3.iii

Two-digit numbers are formed from the digits 0,1,2,3,4 where digits are not repeated. Find the probability of the events that:

(a) The number formed is an even number.

(b) The number formed is a prime number.

Concept: Probability of an Event
Chapter: [0.05] Probability
[3]3.iv

Below is given the distribution of money (in) collected by students for flood relief fund:

 Money(in) 0-10 10-20 20-30 30-40 40-50 Number of students 5 7 5 2 6

Find the mean of money (in) collected by a student using 'Direct Method'

Concept: Introduction to Normal Distribution
Chapter: [0.06] Statistics
[3]3.v

The number of hours, spent by a school boy in different activities in a day is given below :

 Activity Sleep School Play Homework Others Total Number of Hours 7 7 2 4 4 24

Represent the above information using a pie diagram.

Concept: Concept of Pie Graph (Or a Circle-graph)
Chapter: [0.06] Statistics [0.06] Statistics
[8]4 | Attempt any two sub-questions from the following :
[4]4.i

Babubhai borrows Rs. 4,000 and agrees to repay with a total interest of Rs. 500 in 10 instlments, each instalment being less than the preceding instalment by Rs. 10. What should be the first and the last instalments?

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

Solve the following simultaneous equations.

27/(x -2) + 31/(y + 3) = 85, 31/(x -2) + 27/(y + 3) = 89.

Concept: Linear Equations in Two Variables
Chapter: [0.01] Linear equations in two variables
[4]4.iii

Two dice are thrown, find the probability of getting
(1) The sum of numbers on their upper faces is at least 10.
(2) The sum of the numbers on their upper faces is divisible by 5.
(3) The number on the upper face of the first die is greater than the number on the upper face of the second die.

Concept: Sample Space
Chapter: [0.05] Probability
[10]5 | Attempt any two sub-questions from the following :
[5]5.i

When the son will be as old as his father today, the sum of their ages then will be 126 years. when the father was as old his son is today. The sum of their ages was 38 years. Find their presents ages.

Concept: Quadratic Equations Examples and Solutions
[5]5.ii

The following is the frequency distribution with unknown frequencies :

 Class 60-70 70-80 80-90 90-100 Total frequency "a"/2 (3"a")/2 2a a 50

Find the value of a, hence find the frequencies. Draw a histogram and frequency polygon on the same coordinate system.

Concept: Ogives (Cumulative Frequency Graphs)
Chapter: [0.06] Statistics
[5]5.iii

From the same place at 7 a.m. A started walking in the north at a speed of 4 km/hr. after 1 hour, B started cycling in the east at a speed of 8 km/hr. at what time will they be at a distance of 20 km apart from each other?

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

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