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