CBSE [ All India]_X_Mathematics_2005_Set I
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Q1
Solve for x:
Marks:3Answer:

Q2
The cash price of a machine is Rs 9,000. It is also available at Rs. 2,200 cash down payment followed by five equal monthly installments of Rs 1,400 each. Find the rate of interest under the installment plan.
Marks:3Answer:
Out of syllabus 
Q3
Add the difference of
Marks:3Answer:
Out of syllabus 
Q4
Find the sum of all two digit odd positive numbers
. Marks:3Answer:
Two digit odd positive numbers are
11, 13, 15, 17, ..., 99
a = 11, d = 13  11 = 2
l = 99
a + (n  1)d = 99
11 + (n  1) 2 = 99
(n  1) 2 = 88
n  1 = 44
n = 45
S_{n} = (n/2)(2a + (n  1) d)
= (45/2)(22 + 44 2)
= (45/2)(2 55)
= 45 55 = 2475

Q5
Solve for x and y:
Marks:3Answer:

Q6
A two digit number is four times the sum of its digits and twice the product of the digits. Find the number.
Marks:3Answer:
Let the unit place digit be x and tens place digit be y
Sum of the digits = x + y
Number = x + 10y
According to the question
x + 10y = 4(x + y) (1)
and
x + 10y = 2xy (2)
On solving equation (1)
x + 10y = 4(x + y)
3x = 6y
x = 2y
Putting the value of x in equation (2)
x + 10y = 2xy
2y + 10y = 4y^{2}
12y = 4y^{2}
y = 3
x = 2y = 6
Number = x + 10y = 6 + 30 = 36

Q7
Find a and b so that the polynomials: P(x) = (x² + 3x + 2)(x² + 2x + a) and
Q(x) = (x² + 7x + 12)(x² + 7x + b)Marks:3Answer:
O ut of syllabus. 
Q8
Solve for x:
Marks:3Answer:

Q9
The 8th term of an Arithmetic progression is zero. Prove that its 38th term is triple its 18th term.
Marks:3Answer:
Let the first term of an A.P be a and the common difference be d
8th term of A.P. = a + 7d
According to the question
a + 7d = 0
a = 7d
18th term of A.P. = a + 17d = 7d + 17d = 10d
38th term of A.P. = a + 37d = 7d + 37d = 30d
3 x 18th term = 38 term
Proved

Q10
Deepak borrowed a sum of money and returned it in three equal quarterly instalments of Rs 1,40,608. If the rate of interest charged is 16% per annum compounded quarterly, find the sum borrowed. Also find the total interest charged.
Marks:3Answer:
Out of syllabus