# Rajasthan Board Secondary Examination 2010 – Maths Paper I

## Rajasthan Board Secondary Examination 2010 – Maths Paper I

1. (i)The compounded amount of Rs. 7,500 for 2 years at the rate of
4% compound interest per annum is
(A) Rs. 7,800                                   (B) Rs. 8,100
(C) Rs. 8,112                                   (D) Rs. 8,082.                                                      ½

(ii)f x 3 + a 3 is divided by ( x + a ) then the remainder is

(A) x 2 + a 2                                       (B) x+a
(C) a                                                       (D) 0.                                                                    ½

(iii)A boy is now one third as old as his mother. What will be the age of the boy after 12 years if mother’s present age is x ?

(A) x/3 +12                                             (B)(x+12)/3
(C) x + 4                                                    (D)x/3 – 12.                                               ½

(iv)The mean of 5 numbers is 18. If one number is excluded, then mean becomes 16. Excluded number is

(A)10                                                           (B) 18
(C) 26                                                          (D) 16.                                                         ½

2. The weight of a student at the end of 14 years of his age was 36 kg. It increased to 45 kg at the end of 15 years of his age. Find the rate of growth in 15th year.

3. Factorise 8x³y – 343y.                                                                                                ½

4.The perimeter of a rectangle is 40 cm. The ratio of its sides is 2 : 3. Find the length and breadth of the rectangle.

5. Solve the equation 2x² – 8 = 0.                                                                                ½

6. Find the quadratic equation whose roots are 2 + 5 and 2 – √5            ½

7. Find median of the following distribution :                                                     ½
2, 3, 4, 7, 5, 1.

8. Find out the square of 39 by the favourite number method.             1

9. Solve the equation ( x + 1 ) ( x + 2 ) = ( x – 3 ) ( x – 4 ) by the Sutra Paravartya Yojayet.                                                                                              1

10. An article can be purchased on a cash payment or a cash down payment of Rs. 190 and 6 equal monthly instalments of Rs. 60 each. If the amount of interest is Rs. 50, find the cash price of the article.                                                                                                                                       1

11. Factorise a – b – a 3 + b  3 .                                                                                  1

12. Solve the system of equation x = 1/2y – 2, y = 1 – x.                            1

13. Comment on the nature of the roots of the equation
2x² + 3x + 4 = 0.                                                                                                                1

14. Find the mean deviation of the following distribution :
8, 7, 9, 16, 25.                                                                                                                        1

15. Find the square root of 389376 by Dwandwa Yoga method.       2

16. Narendra and Surendra started a business by investing Rs. 4,500 and Rs. 6,000 respectively. Narendra being an active partner, gets an additional 40% of the profit. If the total profit is Rs. 3,500, find the profit of each.                                                                                                              2

17.  Narmada started a fancy store by investing Rs. 5,000. After 7 months, Kaveri joined Narmada in the business by investing a certain amount. At the end of the year, if the ratio of their profits was 10 : 7, then find the capital of Kaveri.                                                                                 2

18. Factorise x ³– 7x² + 14x – 8.                                                                           2

19. Find the L.C.M. of the expressions x² – 3x + 2 and x^4+ x³– 6x² .                       2

20. Solve the following system of equations graphically :
x + y = 4,  x = y.                                                                                                                    2

21. The sum of two numbers is 48 and their product is 432. Find the numbers.                                                                                                                    2

22. Taking 2000 as base year, find the cost of living index for the year 2005 from the following data :

 Items Quantity (in kg) Per kg price(in Rs) Year 2000 Year 2005 A B C D E F 120 16 20 10 20 4 8.00 7.00 6.00 40.00 16.00 25.00 10.00 10.00 9.00 52.00 28.00 37.50

23. A cooler is available on a cash payment of Rs. 3,400 or a cash down payment of Rs. 1,000 and the remaining amount is to be paid in three equal yearly instalments. A simple interest at 9% per annum on the remaining amount is to be paid along with each instalment. If Manish purchases a cooler under instalment scheme, what amount he pays in excess of the cost price of the cooler ?

OR

A person borrows some money on compound interest and returns it in three equal annual instalments. If the rate of compound interest is
10% and the amount of each instalment is Rs. 1,331, then find the principal amount borrowed.                                                                              3

24. At what rate of compound interest will the interest on Rs. 8,000 for 3 years be Rs. 1,261, when the interest is payable annually ?        3

25. For admission to a professional college, the marks obtained by two candidates A and B, in different subjects are given below, with the weightage of each subject is given :

 S. No. Subjects Marks of A Marks of B Weightage 1. 2. 3. 4. English Mathematics Physics Chemistry 80 88 85 89 76 90 86 90 1 3 2 2

By calculating the weightage mean, state who of A and B is more suitable.

OR

Find the median of the following frequency distribution :                 3

 Class-interval 10-25 25-40 40-55 55-70 70-85 85-100 fi 6 20 44 26 3 1

26. Find the mean deviation of the following distribution :               3

 Class 0-10 10-20 20-30 30-40 40-50 Frequency 10 16 40 27 7