Board Paper of Class 12Commerce 2004 Maths All India(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, n ∈ N.
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 Question 2
Using the properties of determinants, prove that
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 Question 3
From a bag containing 20 tickets, numbered from 1 to 20, two tickets are drawn at random. Find the probability that
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(i) Both the tickets have prime numbers on them
(ii) On one there is prime number and on the other there is a multiple of 4
 Question 4
Two dice are tossed once. Find the probability of getting an even number on the first die or a total of 8.
Or
From a lot of 30 bulbs, which includes 6 defective bulbs, a sample of 3 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.
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 Question 5
Evaluate:
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 Question 6
Evaluate:
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 Question 7
Solve the differential equation:
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 Question 8
Solve the differential equation:, given that , when x = 0.
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 Question 9
For each x in a Boolean Algebra B, prove that
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 Question 10
 Question 11
Differentiate with respect to x:
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 Question 12
Differentiate with respect to xfrom first principles.
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 Question 13
The volume of a spherical balloon is increasing at the rate of 25 cm^{3}/sec. Find the rate of change of its surface area at the instant when its radius is 5 cm.
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 Question 14
Evaluate:
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 Question 15
 Question 16
Using matrix method, solve the following system of linear equations:
x+ y − z = 1
3x+ y − 2z = 3
x− y− z= −1
Or
If, prove that A^{2}− 4A− 5I= O. Hence, find A^{−1}.
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 Question 17
Show that the maximum volume of the cylinder which can be inscribed in a sphere of radius cm is 500πcm^{3}.
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 Question 18
Find the area bounded by the circle x^{2}+ y^{2}= 16 and the line y= x in the first quadrant.
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