# Board Paper of Class 10 2014 Maths - Solutions

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

- Question 1
**Attempt any five question from the following:****[5]**(i) For an A.P. *t*_{3}= 8 and*t*_{4}=12, find the common difference.*d*(ii) ( *x*+ 5) (*x*– 2) = 0, find the roots of this quadratic equation.(iii) The following data shows the number of students using different modes of transport:

**Modes of Transport****Number of Students**Bicycle

Bus

Walk

Train

Car140

100

70

40

10

From this table, find the central angle (θ) for the Mode of Transport ‘Bus’.(iv) ‘A coin is tossed’. Write the sample space ‘S’. (v) If Σ *f*_{i}*x*_{i}= 75*and*Σ*f*=15 , then find the mean $\overline{)x}$ ._{i}(vi) Write the following quadratic equation in a standard form:

3*x*^{2}= 10*x*+ 7.

- Question 2
**Attempt any four subquestions from the following:****[8]**(i) State whether the following sequence is an AP or not:

1, 3, 6, 10………(ii) Solve the following quadratic equation by factorization method:

9*x*^{2}– 25 = 0(iii) If the point (3, 2) lies on the graph of the equation 5 *x*+*ay*= 19, then find*a*.(iv) If 12 *x*+ 13*y*= 29 and 13*x*+ 12*y*= 21, find*x*+*y*.(v) A die is thrown. Write the sample space (S) and number of sample points *n*(*S*) and also write event A of getting even number on the upper surface and write n(A).(vi) For a certain frequency distribution, the value of mean is 20 and mode is 11. Find the value of median.

- Question 3
**Attempt any three of the following subquestions:****[9]**(i) Solve the equation by using the formula method.

3*y*^{2}+ 7*y*+ 4 = 0(ii) Solve the following simultaneous equations by using Cramers’s rule:

3*x*–*y*= 7

*x*+ 4*y*=11(iii) Two coins are tossed simultaneously. Write the sample space ‘S’ and the number of sample points n(S). Write the following events using set notation and mention the number of elements in each of them:

(a) A is the event of getting at least one head.

(b) B is the event of getting exactly one head.(iv) The following table gives the frequency distribution of trees planted by different Housing Societies in a particular locality:

**No. of Trees****No. of Housing Societies**10–15

15–20

20–25

25–30

30–35

35–402

7

9

8

6

4

Find the mean number of trees planted by Housing Societies by using ‘Assumed Means Method’(v) Represent the following data by Histogram:

**Price of Sugar per kg**

**(in Rs.)****Number of Weeks**18–20

20–22

22–24

24–26

26–28

28–304

8

22

12

8

6

- Question 4
**Attempt any two sub–questions from the following:****[8]**(i) A farmer borrows Rs.1,000 and agrees to repay with a total interest of Rs. 140 in 12 installments, each installment being less that the preceding installment by Rs. 10. What should be his first installment? (ii) There are three boys and two girls. A committee of two is to be formed. Find the probability of events that the committee contains:

a) At least one girl.

b) One boy and one girl

c) Only boys.(iii) The sales of salesmen in a week are given in the pie diagram. Study the diagram and answer the following questions. If the total sale due to salesmen A is Rs. 18,000, then

a) Find the total sale.

b) Find the sale of each salesman.

c) Find the salesman with the highest sale.

d) Find the difference between the highest sale and the lowest sale.

- Question 5
**Attempt any two of the following subquestions:****[10]**(i) If *m*times*m*th term of an A.P. is equal to*n*times its*n*th term, then show that (*m*+*n*)th term of the A.P. is zero.(ii) The product of four consecutive natural numbers, which are multiples of fives, is Rs. 15,000. Find those natural numbers. (iii) Draw the graphs representing the equations 4 *x*+ 3*y*= 24 and 3*y*= 4*x*+ 24 on the same graph paper. Write the co-ordinates of the point of intersection of these lines and find the area of triangle formed by these lines and the X–axis.