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Algebra Set D 2015-2016 SSC (Marathi Semi-English) 10th Standard [इयत्ता १० वी] Question Paper Solution

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Algebra [Set D]
Marks: 40Academic Year: 2015-2016
Date & Time: 8th March 2016, 11:00 am
Duration: 2h

[5]1 | Attempt any five of the following subquestions:
[1]1.i

Write the first two terms of the sequence whose nth term is tn = 3n ‒ 4.

Concept: Arithmetic Progression
Chapter: [0.03] Arithmetic Progression
[1]1.ii

Find the value of a, b, c in the following quadratic equation : 2x2 ‒ x ‒ 3 = 0

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

Write the quadratic equation whose roots are ‒2 and ‒3.

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

Find the value of the determinate:

`|(4,-2),(3,1)|`

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

Write the sample space for selecting a day randomly of the week.

Concept: Sample Space
Chapter: [0.05] Probability
[1]1.vi

Find the class mark of the classes 20-30 and 30-40.

Concept: Basic Ideas of Probability
Chapter: [0.05] Probability [0.05] Probability
[8]2 | Attempt any four of the following subquestion
[2]2.i

If for an A.P. the first term is 2 and the common difference is 3, then find first three-term of A.P.

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

Solve the following quadratic equation using factorization method:
`"x"^2-11"x"+24=0`

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

If the value of determinants `|(3, 4),(-2, "x")|` is 23, then find the value of` x.

Concept: Quadratic Equations Examples and Solutions
Chapter: [0.02] Quadratic Equations
[2]2.iv

A die is thrown, then find the probability of the following events:

A is an event: getting a perfect square.

B is an event: getting a prime number.

Concept: Basic Ideas of Probability
Chapter: [0.05] Probability [0.05] Probability
[2]2.v

Below is the given frequency distribution of words in an essay:

Number of words   Number of Candidates
600  -  800             12
800  -  1000             14
1000 - 1200              40
1200 - 1400              15
1400 - 1600              19

Find the mean number of words written.

Concept: Median of Grouped Data
Chapter: [0.06] Statistics
[2]2.vi

The marks obtained by a student in an examination are given below:

Subject Marks
Marathi 85
Hindi 80
English 95
Mathematics 100
Total 360

Represent the data using pie diagram.

Concept: Concept of Pie Graph (Or a Circle-graph)
Chapter: [0.06] Statistics [0.06] Statistics
[9]3 | Attempt any three of the following subquestions:
[3]3.i

Solve the equation by using the formula method. 3y2 +7y + 4 = 0

Concept: Nature of Roots
Chapter: [0.02] Quadratic Equations
[3]3.ii

There are three boys and two girls. A committee of two is to be formed. Find the probability of the following events:
Event A: The committee contains at least one girl
Event B: The committee contains one boy and one girl

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

The measurements (in mm) of the diameters of the head of the screws are given below :

Diameter (in mm)    no. of screws
33 - 35 9
36 - 38  21
 39 - 41 30
 42 - 44 22
 45 - 47 18

Calculate the mean diameter of the head of a screw by the ' Assumed Mean Method'.

Concept: Mean of Grouped Data
Chapter: [0.06] Statistics
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[3]3.iv

The marks scored by students in Mathematics in a certain examination are given below :

Marks Scored Number of Students
0 - 20  6
20 - 40 9
40 - 60 14
60 - 80 16
80 - 100 5

Draw histogram for the above data.

Concept: Graphical Representation of Data as Histograms
Chapter: [0.06] Statistics [0.06] Statistics
[3]3.v

Draw the frequency polygon for the following frequency distribution

Rainfall (in cm) No. of Years
20 — 25 2
25 — 30 5
30 — 35 8
35 — 40 12
40 — 45 10
45 — 50 7
Concept: Graphical Representation of Data as Histograms
Chapter: [0.06] Statistics [0.06] Statistics
[8]4 | Attempt any two of the following subquestions:
[4]4.i

The 11th term and the 21st term of an A.P. are 16 and 29 respectively, then find:
(a) The first term and common difference
(b) The 34th term
(c) ‘n’ such that tn = 55

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

Solve the following simultaneous equations.
\[\frac{7}{2x + 1} + \frac{13}{y + 2} = 27 ; \frac{13}{2x + 1} + \frac{7}{y + 2} = 33\]

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

In a certain race, there are three boys A, B, C. The winning probability of A is twice than B and the winning probability of B is twice than C. If P(A) + P(B) + P(C) = 1, then find the probability of win for each boy.

Concept: Basic Ideas of Probability
Chapter: [0.05] Probability [0.05] Probability
[10]5 | Attempt any two of the following subquestions:
[5]5.i

The divisor and quotient of the number 6123 are same and the remainder is half the divisor. Find the divisor.

Concept: Quadratic Equations Examples and Solutions
Chapter: [0.02] Quadratic Equations
[5]5.ii

Find the sum of all numbers from 50 to 350 which are divisible by 6. Hence find the 15th term of that A.P.

Concept: Sum of First n Terms of an AP
Chapter: [0.03] Arithmetic Progression
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[5]5.iii

A three digit number is equal to 17 times the sum of its digits. If 198 is added to the number, the digits are interchanged. The addition of first and third digit is 1 less than middle digit. Find the number.

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method
Chapter: [0.01] Linear equations in two variables
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