CBSE [ All India]_X_Mathematics_2006_Set I
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Q1
A man borrows Rs. 25,200 from a finance company and has to repay it in two equal annual installments. If the interest is charged at the rate of 10% per annum compounded annually, calculate the amount of installment. Marks:3Answer:
Now, out of Syllabus 
Q2
If (x + 2) (x  3) is the HCF of the polynomials p(x) = (x^{2} + x  2) (3x^{2}  8x + c) and q(x) = (x^{2} + x  12) (2x^{2} + x + b). Find the values of c and b. Marks:3Answer:
Now out of syllabus 
Q3
The sum of the digits of a twodigit number is 12. The number obtained by interchanging the two digits exceeds the given number by 18. Find the number. Marks:3Answer:

Q4
Solve the system of equations:
bx/a  ay/b + a + b = 0 and bx  ay + 2ab = 0Marks:3Answer:

Q5
Using the quadratic formula, solve the equation:
a^{2}b^{2} x^{2} – (4b^{4} – 3a^{4} )x – 12a^{2} b^{2} = 0 Marks:3Answer:

Q6
Marks:3Answer:
Now out of syllabus 
Q7
The sum of two natural numbers is 8. Determine the numbers if the sum of their reciprocals is 8/15.
Marks:3Answer:
let one umber be x, other will be 8  x

Q8
The 5^{th} term of an Arithmetic Progression (A.P.) is 26 and the 10th term is 51. Determine the 15^{th} term of the A.P. Marks:3Answer:
Let Ist terms of A.P = a and common difference be d 5^{th} term = a+4d = 26 10^{th} term = a+9d = 51 a + 4d = 26 a + 9d = 51 on subtracting 5d = 25 d = 5 putting the value of d in Ist a+4d = 26 a+20 = 26 a = 6 first term = 6 15^{th} term = a+14d 6+14(5) 6+70 = 76 
Q9
Find the sum of all the natural numbers less than 100 which are divisible by 6. Marks:3Answer:
Series of natural numbers which are divisible by 6 6, 12, 18…96 First term a = 6 Last term l = 96 Common difference d = 6 Number of terms = 96/6 = 16 S_{n} = n/2(a+l) =16/2(6+96) =8(102) S_{16} =816 
Q10
A household article is available for Rs. 970 cash or Rs. 210 cash down payment followed by three equal monthly installments. If the rate of interest charged under the installment plan is 16% per annum, find the amount of installment. Marks:3Answer:
Now, out of syllabus