CBSE [ All India]_X_Mathematics_2004_Set I
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Q1
Solve the following system of linear equations:
Marks:3Answer:

Q2
The sum of the digits of a two digit number is 15. The number obtained by interchanging the digits exceeds the given number by 9. Find the number. Marks:3Answer:
Let the unit digit of the number be x and tens digit of number be y
Original number = 10y + x
According to the question
x + y = 15 (1)On interchanging the digits, number is 10x + y
According to the question
10x + y – 10y  x = 99x  9y = 9
x  y = 1 (2)
On adding (1) and (2)
2x = 16
x = 8
putting the value of x in (2)
8  y = 1
y = 1  8 = 7
y = 7
number = 78

Q3
Using quadratic formula, solve the following quadratic equation for x.
p^{2}x^{2} + (p^{2}  q^{2})x  q^{2} = 0Marks:3Answer:

Q4Marks:3
Answer:
Out of Syllabus

Q5Marks:3
Answer:
Not in Syllabus

Q6
The 8th term of an Arithmetic Progression (A.P.) is 37 and its 12th term is 57. Find the A.P. Marks:3Answer:
8^{th} term = a + 7d = 37 ...(1)
12^{th} term = a + 11d = 57 ...(2)
Subtract (1) from (2)
4d = 20
d = 5
Put the value of d in (1)
a + 35 = 37
a = 2
A.P. is 2, 7, 12, 17, …

Q7
Find the sum of the first 25 terms of an A.P. whose nth term is given by t_{n} = 7  5n.
Marks:3Answer:

Q8
Which term of the Arithmetic Progression 3, 10, 17, ... will be 84 more than its 13 th term? Marks:3Answer:
First term of the series a = 3 Common difference of series d = 7 Required number = T_{13}+84 a + 12 d + 84=? 3 + 12 (7) + 84 =? 3+84+84 = 171 let nth term be 171 t_{n} = a+(n1)d 171 = 3+(n1)7 168 = (n1)7 24 = n1 n = 24+1 n = 25 
Q9
An electric fan is available for Rs 600 cash or for Rs 250 cash down payment followed by 3 monthly installments of Rs 125 each. Find the rate of interest charged under the installment plan.
Marks:3Answer:
Not in syllabus 
Q10
A loan of Rs 4,200 is to be returned in two equal annual installments. If the rate of interest is 10% per annum, compounded annually, calculate the amount of each installment.
Marks:3Answer:
Not in syllabus