Board Paper of Class 12Humanities 2004 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, show that
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 Question 2
Using properties of determinants, solve for x:
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 Question 3
An urn contains 7 white, 5 black and 3 red balls. Two balls are drawn at random. Find the probability that
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(i) both the balls are red
(ii) one ball is red, the other is black
(iii) one ball is white
 Question 4
A fair die is tossed twice. If the number appearing on the top is less than 3, it is a success. Find the probability distribution of X.
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 Question 5
Evaluate:
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 Question 6
Evaluate:
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 Question 7
Form the differential equation corresponding to where a andb are arbitrary constants.
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 Question 8
Solve the differential equation: given that y = 1, when x= 0.
OR
Solve the differential equation:
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 Question 9
Show that in a Boolean algebra, B:
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(i)
(ii)
Out of current syllabus
 Question 10
Evaluate:
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 Question 11
Differentiate w.r.t. x from first principles.
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 Question 12
Differentiate w.r.t. x.
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 Question 13
Find the equations of the tangent and the normal to the curve at.
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 Question 14
Evaluate:
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 Question 15
Evaluate:
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 Question 16
Using matrix method, solve the following system of linear equations:
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 Question 17
Show that a right circular cylinder, which is open at the top and has a given surface area, will have the greatest volume if its height is equal to the radius of its base.
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 Question 18
Using integration, find the area of the circle x^{2}+ y^{2}= 16, which is exterior to the parabola y^{2}=6x.
OR
Find the area of the smaller region bounded by the ellipse and the line.
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