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Question Paper - Algebra 2015 - 2016-S.S.C-Board Exam Maharashtra State Board (MSBSHSE)

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SubjectAlgebra
Year2015 - 2016 (March)


Marks: 40
Q: 1 | Attempt any five question from the following[5]
Q: 1.1[1]

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

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Q: 1.2[1]

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

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Q: 1.3[1]

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

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Q: 1.4[1]

Find the value of determinant

`|[4,-2],[3,1]|`

 

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Q: 1.5[1]

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

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Q: 1.6[1]

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

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Q: 2 | Attempt any four sub-questions from the following:[8]
Q: 2.1[2]

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

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Q: 2.2[2]

Solve the following quadratic equation by Factorisation method:
x2 + 7x + 10 = 0

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Q: 2.3[2]

If the value of determinant `|[m,2],[-5,7]|`is 31, find the value of m

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Q: 2.4[2]

A die is thrown, then find the probability of the following events:
A is an Event: getting an odd number on the top upper surface of the die.
B is an Event: getting a perfect square on the upper surface of the die.

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Q: 2.5[2]

Below is the given frequency distribution of words in an essay

Number of WordsNumber of Candidates
600 – 8008
800 – 100022
1000 – 120040
1200 – 140018
1400 - 160012

Find the mean number of words written.

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Q: 2.6[2]

Subjectwise marks obtained by a student in an examination are given below

SubjectMarks
Marathi85
Hindi85
Science90
Mathematics100
Total360

Draw pie diagram

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Q: 3 | Attempt any three of the following sub questions:[9]
Q: 3.1[3]

Solve the following quadratic equation by using formula method:
5m2 + 5m – 1 = 0

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Q: 3.2[3]

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

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Q: 3.3[3]

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

Diameter (in mm)No. of Screws
33 — 3510
36 — 3819
39 — 4123
42 — 4421
45 — 4727

Calculate mean diameter of head of a screw by ‘Assumed Mean Method’.

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Q: 3.4[3]

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

Marks ScoredNumber of Students
0 — 203
20 — 408
40 — 6019
60 — 8018
80 — 1006

Draw histogram for the above data.

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Q: 3.5[3]

Draw the frequency polygon for the following frequency distribution

Rainfall (in cm)No. of Years
20 — 252
25 — 305
30 — 358
35 — 4012
40 — 4510
45 — 507
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Q: 4 | Attempt any two of the following sub questions:[8]
Q: 4.1[4]

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

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Q: 4.2[4]

Solve the following simultaneous equations:

`7/(2X+1)+13/(Y+2)=27,13/(2X+1)+7/(Y+2)=33`

 

 
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Q: 4.3[4]

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.

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Q: 5 | Attempt any two of the following sub questions:[10]
Q: 5.1[5]

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

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Q: 5.2[5]

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

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Q: 5.3[5]

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.

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