CBSE [ Delhi ]_X_Mathematics_2004_Set I
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Q1
In Fig. 1, D is a point on the side BC of ABC, such that ADC = BAC
Prove that
AC/AD = CB/AC.Marks:2Answer:
In triangle BAC and triangle AD,
D = A (Given)
C = C (common angles)
By AA,
BAC is similar to ADC
So AC/AD = CB/AC
Proved.

Q2
Solve the following system of linear equations: Marks:3Answer:

Q3
Two years ago, a father was five times as old as his son. Two years later, his age will be 8 more than three times the age of the son. Find the present ages of father and son. Marks:3Answer:
Let the present age of the father be x year and present age of son be y year Two year ago the age of father = x2 year Two year ago the age of son = y2 year A.T.Q case I x2 = 5(y2) x2 = 5y10 x5y = 8 5yx = 8 5y8 = x case II x+2 =3(y+2) +8 putting the value of y 5y8+2=3y+6+8 2y = 20 y = 10 years Putting the value of y in equation 1 X = 5(10)8 = 42years
Present age of father =42 years
Son's present age = 10 years 
Q4
Solve for x: 4x^{2}  2(a^{2} + b^{2})x + a^{2}b^{2} = 0
Marks:3Answer:

Q5
The HCF and LCM of two polynomials P(x) and Q(x) are (2x  1) and (6x^{3 }+ 25x^{2}  24x + 5) respectively, if P(x) = 2x^{2} + 9x  5, determine Q(x). Marks:3Answer:
Out of syllabus 
Q6
If (x  2)(x + 3) is the GCD of the polynomials , find the value of a and b. Marks:3Answer:
It is out of syllabus 
Q7
If
as a rational expression in lowest terms.
Marks:3Answer:
It is not in syllabus.

Q8
The 7^{th} term of an A.P. is 32 and its 13^{th} term is 62. Find the A.P. Marks:3Answer:
Let the first term of A.P be a and the common difference be d 7^{th} term = a + 6d = 32 …(1) 13^{th} term = a + 12d = 62 …(2) Solving equation (1) and (2), we get 6d = 30 d = 5 putting the value of d in equation (1) a + 6 x 5 = 32 a = 32  30 a = 2 A.P series = 2, 7, 12, 17, ..., 
Q9
Find the sum of the first 25 terms of an A.P. whose nth term is given by t_{n} = 2  3n. Marks:3Answer:
Let n = 1 t_{1} = 2  3 = 1 t_{2} = 2  6 = 4 t_{3} = 2  9 = 7 first term = 1 , common difference = 4  (1) = 3 t_{25 }= 2  3 25 = 73 S_{25} = (n/2)(a + l) S_{25} = (n/2)(1  73) = (25/2)(74) = 25 37 = 925 
Q10
A radio is available for Rs. 1,500 cash or Rs. 360 as cash down payment followed by three equal monthly instalments of Rs. 390. Find the rate of interest charged under the instalment scheme. Marks:3Answer:
Out of syllabus