Board Paper of Class 10 2016 Maths - Solutions

Note: -
(1) All questions are compulsory.
(2) Use of calculator is not allowed.

Question 1

Attempt any five question from the following:		[5]
(i)	Write the first two terms of the sequence whose nth term is t_n = 3n ‒ 4.
(ii)	Find the value of a, b, c in the following quadratic equation : 2x² – x – 3 = 0
(iii)	Write the quadratic equation whose roots are ‒2 and ‒3.
(iv)	Find the value of determinant: $\|\begin{matrix} 4 & - 2 \\ 3 & 1 \end{matrix}\|$
(v)	Write the sample space for selecting a day randomly of the week.
(vi)	Find the class mark of the classes 20-30 and 30-40.

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Question 2

Attempt any four sub-questions from the following:

[8]

(i)

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

(ii)

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

(iii)

If the value of determinant

|\begin{matrix} m & 2 \\ - 5 & 7 \end{matrix}|

is 31, find the value of m.

(iv)

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.

(v)

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

Number of Words	Number of Candidates
600 – 800 800 – 1000 1000 – 1200 1200 – 1400 1400 – 1600	8 22 40 18 12

Find the mean number of words written.

(vi)

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

Subject	Marks
Marathi Hindi Science Mathematics	85 85 90 100
Total	360

Draw pie diagram.

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Question 3

Attempt any three of the following sub questions:

[9]

(i)

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

(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

(iii)

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

Diameter (in mm)	Number of Candidates
33–35 36–38 39–41 42–44 45–47	10 19 23 21 27

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

(iv)

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

Marks Scored	Number of Students
0 –20 20–40 40–60 60–80 80–100	3 8 19 18 6

Draw histogram for the above data.

(v)

Draw the frequency polygon for the following frequency distribution:

Rainfall (in cm)	No. of Years
20–25 25–30 30–35 35–40 40–45 45–50	2 5 8 12 10 7

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Question 4

Attempt any two of the following sub questions:			[8]
	(i)	The 11^th term and the 21^st term of an A.P. are 16 and 29 respectively, then find: (a) The first term and common difference (b) The 34^th term (c) ‘n’ such that t_n = 55
	(ii)	Solve the following simultaneous equations: $\frac{7}{2 x + 1} + \frac{13}{y + 2} = 27, \frac{13}{2 x + 1} + \frac{7}{y + 2} = 33$
	(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.

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Question 5

Attempt any two of the following sub questions:		[10]
(i)	The divisor and quotient of the number 6123 are same and the remainder is half the divisor. Find the divisor.
(ii)	Find the sum of all numbers from 50 to 350 which are divisible by 6. Hence find the 15^th term of that A.P.
(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.

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