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Question Paper Solutions - Algebra 2016 - 2017-S.S.C-10th Maharashtra State Board (MSBSHSE)


Marks: 40
[5]1 | Attempt any five of the following subquestions
[1]1.1

State whether the following sequence is an Arithmetic Progression or not:
3, 6, 12, 24,......

Chapter: [1] Arithmetic Progression
Concept: Arithmetic Progression
[1]1.2

If one root of the quadratic equation is `3 – 2sqrt5` , then write another root of the equation.

Chapter: [2.03] Quadratic Equations
Concept: Nature of Roots
[1]1.3

There are 15 tickets bearing the numbers from 1 to 15 in a bag and one ticket is drawn from this bag at random. Write the sample space (S) and n(S).

Chapter: [7] Probability
Concept: Sample Space
[1]1.4

Find the class mark of the class 35 - 39.

Chapter: [4] Probability
Concept: Probability Examples and Solutions
[1]1.5

Write the next two terms of A.P. whose first term is 3 and the common difference is 4.

Chapter: [1] Arithmetic Progression
Concept: Arithmetic Progression
[1]1.6

Find the values of a, b, c for the quadratic equation 2x2 = x + 3 by comparing with standard form ax2 + bx + c = 0.

Chapter: [2.03] Quadratic Equations
Concept: Quadratic Equations
[8]2 | Attempt any four of the following subquestions:
[2]2.1

Find the first two terms of the sequence for which Sn is given below: `S_n=n^2(n+1)`

Chapter: [1] Arithmetic Progression
Concept: Introduction to Sequence
[2]2.2

Find the value of discriminant (Δ) for the quadratic equation: `x^2+7x+6=0`

Chapter: [2.03] Quadratic Equations
Concept: Quadratic Equations
[2]2.3

Write the equation of X-axis. Hence, find the point of intersection of the graph of the equation x + y = 5 with the X-axis.

Chapter: [2.02] Pair of Linear Equations in Two Variables
Concept: Graphical Method of Solution of a Pair of Linear Equations
[2]2.4

For a certain frequency distribution, the values of Assumed mean (A) = 1300, `sumf_id_i` = 900 and `sumfi` = 100. Find the value of mean (`barx`) .

 

Chapter: [5] Statistics
Concept: Median of Grouped Data
[2]2.5

Two coins are tossed simultaneously. Write the sample space (S), n(S), the following event A
using set notation and n(A), where ‘A is the event of getting at least one head.’

Chapter: [4] Probability
Concept: Probability Examples and Solutions
[2]2.6

Find the value of k for which the given simultaneous equations have infinitely many solutions:
kx + 4y = 10;
3x + 2y = 5.

Chapter: [3] Linear equations in two variables
Concept: Linear Equations in Two Variables Applications
[9]3 | Attempt any three of the following subquestions :
[3]3.1

How many three digit natural numbers are divisible by 5?

Chapter: [1] Arithmetic Progression
Concept: Introduction to Sequence
[3]3.2

Solve the following quadratic equation by factorization method : `3x^2-29x+40=0`

Chapter: [2.02] Quadratic Equations
Concept: Solutions of Quadratic Equations by Factorization
[3]3.3

Solve the following simultaneous equations by using Cramers’s rule: 3x-y =7, x +4y =11

Chapter: [3] Linear equations in two variables
Concept: Cramer'S Rule
[3]3.4

Two dice are thrown. Find the probability of the event that the product of numbers on their upper faces is 12.

Chapter: [4] Probability
Concept: Probability Examples and Solutions
[3]3.5

The following is the frequency distribution of waiting time at ATM centre; draw histogram to
represent the data:

Waiting time
(in seconds)
Number of
Customers
0 -30 15
30 - 60 23
60 - 90 64
90 - 120 50
120 - 150 5

 

Chapter: [6] Statistics
Concept: Histograms, Frequency Polygon and Frequency Curve
[8]4 | Attempt any two of the following subquestions:
[4]4.1

Three horses A, B and C are in a race, A is twice as likely to win as B and B is twice as likely to win as C. What are their probabilities of winning?

Chapter: [5.02] Probability
Concept: Probability - A Theoretical Approach
[4]4.2

The following is the distribution of the size of certain farms from a taluka (tehasil):

Size of Farms
(in acres)
Number of Farms
5 – 15 7
15 – 25 12
25 – 35 17
35 – 45 25
45 – 55 31
55 – 65 5
65 – 75 3

Find median size of farms.

Chapter: [5] Statistics
Concept: Median of Grouped Data
[4]4.3

The following pie diagram represents the sectorwise loan amount in crores of rupees distributed by a bank. From the information answer the following questions:

a. If the dairy sector receives `20 crores, then find the total loan disbursed.
b. Find the loan amount for agriculture sector and also for industrial sector.
c. How much additional amount did industrial sector receive than agriculture sector?

Chapter: [5] Statistics
Concept: Pie Diagram
[10]5 | Attempt any two of the following subquestions
[5]5.1

If the cost of bananas is increased by Rs. 10 per dozen, one can get 3 dozen less for Rs.600. Find the original cost of one dozen of bananas.

Chapter: [2.02] Pair of Linear Equations in Two Variables
Concept: Simple Situational Problems
[5]5.2

If the sum of first p terms of an A.P. is equal to the sum of first q terms, then show that the sum of its first (p + q) terms is zero where p ≠ q.

Chapter: [2.04] Arithmetic Progressions
Concept: Sum of First n Terms of an AP
[5]5.3

Solve the following simultaneous equations

`1/(3x)-1/(4y)+1=0`;

`1/(5x)+1/(2y)=4/15`

Chapter: [2.02] Pair of Linear Equations in Two Variables
Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method
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