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Algebra Set A 2016-2017 SSC (Marathi Semi-English) 10th Standard [इयत्ता १० वी] Question Paper Solution

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Algebra [Set A]
Marks: 40 Academic Year: 2016-2017
Date & Time: 13th March 2017, 1:00 pm
Duration: 2h
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[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,......

Concept: Arithmetic Progression
Chapter: [0.03] Arithmetic Progression
[1] 1.2

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

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

Concept: Sample Space
Chapter: [0.05] Probability
[1] 1.4

Find the class mark of the class 35 - 39.

Concept: Basic Ideas of Probability
Chapter: [0.05] Probability [0.05] Probability
[1] 1.5

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

Concept: Arithmetic Progression
Chapter: [0.03] 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.

Concept: Quadratic Equations
Chapter: [0.02] 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)`

Concept: Introduction to Sequence
Chapter: [0.03] Arithmetic Progression
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[2] 2.2

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

Concept: Quadratic Equations
Chapter: [0.02] 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.

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

 

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

Concept: Basic Ideas of Probability
Chapter: [0.05] Probability [0.05] Probability
[2] 2.6

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

Concept: Linear Equations in Two Variables Applications
Chapter: [0.01] Linear equations in two variables
[9] 3 | Attempt any three of the following subquestions :
[3] 3.1

How many three digit natural numbers are divisible by 5?

Concept: Introduction to Sequence
Chapter: [0.03] Arithmetic Progression
[3] 3.2

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

Concept: Solutions of Quadratic Equations by Factorization
Chapter: [0.02] Quadratic Equations
[3] 3.3

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

Concept: Cramer'S Rule
Chapter: [0.01] Linear equations in two variables
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[3] 3.4

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

Concept: Basic Ideas of Probability
Chapter: [0.05] Probability [0.05] Probability
[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
Concept: Graphical Representation of Data as Histograms
Chapter: [0.06] Statistics [0.06] Statistics
[8] 4 | Attempt any two of the following subquestions:
[4] 4.1

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?

Concept: Probability - A Theoretical Approach
Chapter: [0.05] Probability
[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.

Concept: Median of Grouped Data
Chapter: [0.06] Statistics
[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?

Concept: Concept of Pie Graph (Or a Circle-graph)
Chapter: [0.06] Statistics [0.06] Statistics
[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.

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

Concept: Sum of First n Terms of an AP
Chapter: [0.03] Arithmetic Progression
[5] 5.3

Solve the following simultaneous equations

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

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

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

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