# Board Paper of Class 10 2018 Maths - Solutions

General Instructions:Answers to this paper must be written on the paper provided separately.You will not be allowed to write during the first 15 minutes.This time is to be spent in reading the question paper.The time given at the head of this paper is the time allowed for writing the answers.

- 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 = 25, D = 5 are the values of the determinants for certain simultaneous equations in_{x}*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*+ 2*y*= 7.(vi) If S _{5 }= 15 and S_{6}= 21 find t_{6}.

- 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 x ^{2}– 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.

- Question 3
3. **Attempt any three of the following sub questions:**9 (i) For an A.P., find S _{9}if a = 4 and d = 2.(ii) Solve the following quadratic equation by formula method:

3x^{2}+ 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

Mathematics80

80

100

100Total 360

- Question 4
4. **Attempt any two of the following sub equations :**8 (i) If α + β = 5 and α ^{3}+ β^{3}= 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- 20020

45

22

09

04

- Question 5
5. **Attempt any two of the following sub questions :**10 (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 – 4520

30

50

40

2525