# Rajasthan Board Secondary Examination 2011 – Maths Paper I

## Rajasthan Board Secondary Examination 2011 – Maths Paper I

1 (i)The amount of Rs. 1,600 for 2 years at the rate of 5% compound interest per annum is
(A) Rs. 1600 x (105/100)²      (B)Rs. 1600 x (105/100)
(C)Rs. 1600 x (105/100)³       (D) Rs. 1600 x (100/105)²         ½

(ii) If ( x – 2 ) is a factor of the polynomial
P ( x ) = x³- 2 x² + 2x – 4 , then the value of P ( 2 ) is
(A) 2                                         (B) 1
(C)0                                          (D) -2.                                                                ½

(iii)The age of a father is three times the age of his son. If the age of
f his son will be father is x years, then after 7 years age of his son will be
(A) 3x+7                                  (B)x/3 +7
(C) x +7                                    (D)(x+7)/3                                                     ½

(iv)If the arithmetic mean of 1, 3,5, x is 4 then the value of x is
(A)4                                             (B)4.5
(C)6                                             (D)7                                                                 ½.

2. The population of a village is increased from 10,000 to 10,200 in one year. Find the rate of growth                                                       ½

3. Factorise x³ – 64.                                                                                       ½

4. Find the value of k for which the following system of equations have no solution :
3x+ky-1=0
6x+4y+2=0                                                                                                         ½

5. Solve the equation 3x²- 12 = 0                                                            ½

6. Find the quadratic equation whose roots are 3 and – 2.     ½

7. Find the median of the following distribution :

11, 14, 10, 15, 17.                                                                                                ½

8. Find the square of 35 by the Sutra Ekadhikena Purvena.     1

9. Solve the equation 3 ( x – 2 ) = 5 ( x – 2 ) by the Sutra Sunyam Samya Samuccaye.                                                                                              1

10. It was decided to buy a n article of Rs. 12,000 in three equal annual installments. With each installment simple interest a t the rate of 12% per annum is charged on the remaining amount. Find the interest to be paid with the second installment.                                1

11. Factorise x³+ y³ + 8z³ – 6xyz.                                                                    1

12. Solve the system of equations 2x – y = 3. 4x + y = 3                   1

13. Determine the nature of the roots of the quadratic equation
4x² +12 x + 9 = 0 .                                                                                                      1

14. Find the mean deviation of the distribution 2, 5, 8, 2, 6 from the median.                                                                                                                 1

15. Find the value of 102 x 103 by the Sutra Nikhilam.                   2

16. Surendra and Narendra invested equal amounts of money for one year in a business. It was agreed upon to pay 20% of the total profit to Surendra a s remuneration for being the active partner. Find the share of Surendra in a profit of Rs. 30,000 a t the end of the year.    2

17. Rekha and Seema started a business by investing Rs. 60.000 and Rs. 1,00,000 respectively. After five months Rekha invested Rs. 30,000 more in the business. If a t the end of the year the total profit was Rs. 92.300, then find the share of each in the profit.                       2

18.  Factorise x³ – 7x + 6.                                                                                               2

19. Find the L.C.M. of the expressions (x²-9)(x+3) and x²+6x+9         2

20. Solve the following system of equations graphically :

y=x+2,   y=2x

21. Find two consecutive integers whose squares have the sum 85.    2

22. Find the age specific death rate for the following data :                        2

Age group in years                         Population           Number of deaths
Under 5                                                    6,000                                   120
5 – 20                                                       10,000                                     30
20 – 60                                                    20,000                                     80
Over 60                                                  4,000                                      160

23. A cooler is available at Rs. 2,200 cash or for Rs. 600 as cash down payment and 6 monthly instalments of Rs. 300 each. Find the rate of interest.

OR

Ramesh bought a television costing Rs. 18,000 at Rs. 3.000 cash down payment and the rest to be returned in two equal annual instalments with 10% compound interest. Find the amount of each instalment to the nearest rupees ten.                                                                                              3

24. Find the compound interest on Rs. 10,000 for 3 years at the rate of 5% per annum, when interest is payable annually.                            3

25. Find the mode of the following frequency distribution :

Class-internal 0 – 10    10 – 20    20 – 30    30 – 40    40 – 50    50 – 60
Frequency             3              12             14               10               8                 7
OR
Find the mean of the following frequency distribution :
Class-internal   0 – 10       10 – 20       20 – 30       30 – 40       40 – 50
Frequency               7                  10                  15                 8                   10

26. Calculate the mean deviation from the median for the following distribution :                                                                        3
x:      3         4        5         6         7         8       9       10
f:     10      11     12      13       9       12      14       7