Board Paper Solutions for MAHARASHTRA Class 10 MATHS Board Paper 2018 MeritNation Set 1

Question 1

1.		Attempt any five of the following sub questions:	5
	(i)	Find next two terms of an A.P. 4, 9, 14,.......
	(ii)	State whether the given equation is quadratic or not. Give reason. $\frac{5}{4} m^{2} - 7 = 0$
	(iii)	If D_x = 25, D = 5 are the values of the determinants for certain simultaneous equations in x and y, find x.
	(iv)	If S = {2, 4, 6, 8, 10, 12} and A = {4, 8 , 12}. Find A’.
	(v)	Write any one solution of equation x + 2y = 7.
	(vi)	If S₅= 15 and S₆ = 21 find t₆ .

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Question 2

2.		Attempt any four of the following sub questions:	8
	(i)	Find ‘n’ if the nth term of the following A.P. is 64: 1, 4, 7 , 10, ......
	(ii)	If one of the roots of the quadratic equation x² – 10x + k = 0 is 2, then find the value of k.
	(iii)	A box contains 20 cards marked with the numbers 1 to 20. One card is drawn at random, where the event A is such that the number on the card is multiple of 3. Write S, n(s), A and n(A).
	(iv)	Find the value of x – y if 6x + 5y = 17, 5x + 6y = 13.
	(v)	If the roots of quadratic equation are 5 and –6, form the quadratic equation.
	(vi)	For a certain frequency distribution mean is 72 and median is 78, find the mode.

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Question 3

Attempt any three of the following sub questions:

(i)

For an A.P., find S₉ if a = 4 and d = 2.

(ii)

Solve the following quadratic equation by formula method:
3x² + 2x = 1

(iii)

Solve the following simultaneous equations by using Cramer’s rule:
4x + 3y = 4;
3x + 5y = 8

(iv)

A die is thrown, find the probability of the event of getting a square number.

(v)

The marks obtained by a student in an examination out of 100 are given below.The total marks obtained in various subjects are as follows:

Subject	Marks
Marathi English Science Mathematics	80 80 100 100
Total	360

Represent the above data using pie diagram.

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Question 4

Attempt any two of the following sub equations :

(i)

If α + β = 5 and α³ + β³ = 35, find the quadratic equation whose roots are α and β.

(ii)

Two dice are thrown. Find the probability of getting:
(a) The sum of the numbers on their upper faces is at least 9.
(b) The sum of the numbers on their upper faces is 15.
(c) The number on the upper face of the second die is greater than the number on the upper face of the first die.

(iii)

Frequency distribution of daily commission received by 100 salesman is given below :

Daily commission (in Rs.)	No of Salesman
100 – 120 120 – 140 140 – 160 160 – 180 180- 200	20 45 22 09 04

Find mean daily commission received by salesmen, by assumed mean method.

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Question 5

Attempt any two of the following sub questions :

(i)

A boat takes 10 hours to travel 30 km upstream and 44 km downstream, but it takes 13 hours to travel 40 km upstream and 55 km downstream. Find the speed of the boat in still water and the speed of the stream.

(ii)

If the 9^th term of an A.P. is zero, then prove that 29^th term is double of 19^th term.

(iii)

Draw histogram and frequency polygon on the same graph paper for the following frequency distribution :

Class	Frequency
15 – 20 20 – 25 25 – 30 30 – 35 35 – 40 40 – 45	20 30 50 40 25 25

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