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:2View AnswerAnswer:
In triangle BAC and triangle AD,
D = A (Given)C = C (common angles)By AA,
BAC is similar to ADCSo AC/AD = CB/AC
Proved.
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Q2
Solve the following system of linear equations: 
Marks:3View AnswerAnswer:
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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:3View AnswerAnswer:
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 = x-2 year Two year ago the age of son = y-2 year A.T.Q case I x-2 = 5(y-2) x-2 = 5y-10 x-5y = -8 5y-x = 8 5y-8 = x case II x+2 =3(y+2) +8 putting the value of y 5y-8+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: 4x2 - 2(a2 + b2)x + a2b2 = 0
Marks:3View AnswerAnswer:
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Q5
The HCF and LCM of two polynomials P(x) and Q(x) are (2x - 1) and (6x3 + 25x2 - 24x + 5) respectively, if P(x) = 2x2 + 9x - 5, determine Q(x). Marks:3View AnswerAnswer:
Out of syllabus -
Q6
If (x - 2)(x + 3) is the GCD of the polynomials 
, find the value of a and b. Marks:3View AnswerAnswer:
It is out of syllabus -
Q7
If
as a rational expression in lowest terms.
Marks:3View AnswerAnswer:
It is not in syllabus.
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Q8
The 7th term of an A.P. is 32 and its 13th term is 62. Find the A.P. Marks:3View AnswerAnswer:
Let the first term of A.P be a and the common difference be d 7th term = a + 6d = 32 …(1) 13th 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 tn = 2 - 3n. Marks:3View AnswerAnswer:
Let n = 1 t1 = 2 - 3 = -1 t2 = 2 - 6 = -4 t3 = 2 - 9 = -7 first term = -1 , common difference = -4 - (-1) = -3 t25 = 2 - 3 
25 = -73S25 = (n/2)(a + l) S25 = (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:3View AnswerAnswer:
Out of syllabus
