# Board Paper of Class 10 2015 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) State whether the following sequence is an A.P. or not? 1, 4, 7, 10, ………………..

(ii) A card is drawn from the pack of 25 cards labeled with numbers 1 to 25. Write the sample space for this random experiment. (iii) Find the value of *x*+*y*, if 12*x*+ 13*y*= 29 and 13*x*+ 12*y*= 21(iv) For a sequence if $\mathrm{Sn}=\frac{\mathrm{n}}{\mathrm{n}+1}$ then find the value of S _{10}.(v) Verify whether 1 is the root of the quadratic equation :

*x*^{2}+ 3*x*– 4 = 0(vi) If *x*+*y*= 5 and*x*= 3, then find the value of*y*.

- Question 2
**Attempt any four sub–questions from the following:****[8]**(i) Solve the following quadratic equation by factorization method : *x*^{2}– 5*x*+ 6 = 0.(ii) Find the term t _{11}of an A.P. :

4, 9, 14, …………..(iii) If the point A(3, 2) lies on the graph of the equation 5 *x*+*ay*= 19, then find*a*.(iv) A die is thrown. If A is the event that the number on upper face is less than 5, then write sample space and event A in set notation. (v) For a certain frequency distribution, the value of Mean is 101 and Median is 100. Find the value of Mode. (vi) If one root of the quadratic equation

*kx*^{2}– 7*x*+ 12 = 0 is 3, then find the value of*k*.

- Question 3
**Attempt any three of the following sub questions:****[9]**(i) Area under different crops in a certain village is given below. Represent it by a pie diagram :

Crops Area (in Hectares) Jowar

Wheat

Sugarcane Vegetables80

20

60

20(ii) If two coins are tossed, then find the probability of the event that at least one head turns up. (iii) Solve the following simultaneous equations by using graphical method :

*x*+*y*= 6;

*x*–*y*= 4.(iv) There is an auditorium with 35 rows of seats. There are 20 seats in the first row, 22 seats in the second row, 24 seats in the third row and so on. Find the number of seats in the twenty–first row. (v) Solve the following quadratic equation by completing square method :

*x*^{2}+ 10*x*+ 21 = 0.

- Question 4
**Attempt any two sub–questions from the following:****[8]**(i) Two digit numbers are formed using the digits 0, 1, 2, 3, 4, 5 where digits are not repeated.

P is the event that the number so formed is even.

Q is the event that the number so formed is greater than 50.

R is the event that the number so formed is divisible by 3.

Then write the sample space S and events P, Q, R using set notation.(ii) The following table shows ages of 3000 patients getting medical treatment in a hospital on a particular day :

Age (in years) No. of Patients 10-20

20-30

30-40

40-50

50-60

60–7060

42

55

70

53

20

Find the median age of the patients.(iii) If α + β = 5 and α ^{3}+ β^{3}= 35, find the quadratic equation whose roots are α and β.

- Question 5
**Attempt any two of the following subquestions:****[10]**(i) Babubhai borrows Rs. 4,000 and agrees to repay with a total interest of Rs. 500 in 10 instalments, each instalment being less than the preceding instalment by Rs. 10. What should be the first and the last instalments? (ii) On the first day of the sale of tickets of a drama, in all 35 tickets were sold. If the rates tickets were Rs. 20 and Rs. 40 per ticket and the total collection was Rs, 900, find the number of tickets sold of each rate. (iii) Given below is the frequency distribution of driving speeds (in km/hour) of the vehicles of 400 college students:

Speed (in km/hr) No. of Students 20-30

30-40

40-50

50-60

60-706

80

156

98

60

Draw Histogram and hence the frequency polygon for the above data.