Board Paper of Class 12Commerce 2005 Maths Delhi(SET 1)  Solutions
(i) The question paper consists of three sections A, B and C Section A is compulsory for all students. In addition to Section A, every student has to attempt either Section B OR Section C.
(ii) For Section A 
Question numbers 1 to 8 are of 3 marks each.
Question numbers 9 to 15 are of 4 marks each.
Question numbers 16 to 18 are of 6 marks each.<o:p></o:p></span></p>
(iii) For Section B/Section C
Question numbers 19 to 22 are of 3 marks each.
Question numbers 23 to 25 are of 4 marks each.
Question number 26 is of 6 marks.
(iv) All questions are compulsory.
(v) Internal choices have been provided in some questions. You have to attempt only one of the choices in such questions.
(vi) Use of calculator is not permitted. However, you may ask for logarithmic and statistical tables, if required.
 Question 1
If, prove that A^{3} −4A^{2}+ A= O.
VIEW SOLUTION
 Question 2
Show that, where a, band care in A.P.
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 Question 3
In a single throw of three dice, determine the probability of getting
a total of 5
a total of at most 5
 Question 4
A class consists of 10 boys and 8 girls. Three students are selected at random. Find theprobability that the selected group has
(a) all boys,
(b) all girls,
(c) 2 boys and 1 girl.
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 Question 5
Evaluate:
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 Question 6
Evaluate:
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 Question 7
Form the differential equation representing the family y^{2} − 2ay + x^{2} = a^{2}, where a is an arbitrary constant.
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 Question 8
Solve the following differential equation:
Or
Solve the following differential equation:
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 Question 9
Prove that: p ↔ q ≡ (p → q) ∨ (q → p)
Or
Test the validity of the following argument:
S_{1} : p ∧ q
S_{2} : ∼ p
S : q
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 Question 10
Evaluate:
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 Question 11
Differentiate w.r.t. xfrom first principles.
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 Question 12
If and, find .
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 Question 13
The surface area of a spherical bubble is increasing at the rate of 2 cm^{2}/sec. Find the rate at which the volume of the bubble is increasing at the instant its radius is 6 cm.
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 Question 14
Evaluate:
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 Question 15
Evaluate:
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 Question 16
Using matrices solve the following system of linear equations:
Or
If, find xand ysuch that. Hence, find.
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 Question 17
A wire of length 36 cm is cut into two pieces. One of the pieces is turned in the form of a square and the other in the form of an equilateral triangle. Find the length of each piece so that the sum of the areas of the two be minimum.
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 Question 18
Find the area boundby the curve and the straight line
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