Board Paper of Class 12Commerce 2006 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
Express the following matrix as the sum of a symmetric and a skew symmetric matrix.
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 Question 2
Using properties of determinants, prove the following:
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 Question 3
Solve the following differential equation:
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 Question 4
Form the differential equation of the family of curves y = a sin (x + b), where a and b are arbitrary constants.
Or
Solve the following differential equation:
2xy dx + (x^{2} + 2y^{2}) dy = 0
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 Question 5
Evaluate:
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 Question 6
Evaluate:
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 Question 7
Two dice are rolled once. Find the probability that:
(a) the numbers on two dice are different
(b) the total of numbers on the two dice is at least 4
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 Question 8
A pair of dice is tossed twice. If the random variable X is defined as the number of doublets, then find the probability distribution of X.
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 Question 9
 Question 10
Differentiate sin (2x+ 3) w. r. t. xfrom first principle.
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 Question 11
If, then find .
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 Question 12
 Question 13
Evaluate:
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 Question 14
Evaluate:
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 Question 15
Verify Rolle’s Theorem for the following function:
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 Question 16
Using matrices, solve the following system of equations:
x+ y+ z= 3, x −2y+ 3z= 2, and 2x − y+ z= 2
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 Question 17
Find the point on the curve y^{2}= 4x, which is nearest to the point (2, −8).
Or
Prove that the height of a right circular cylinder of maximum volume that can be inscribed in a sphere of radiusRis. Also, find the maximum volume.
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 Question 18
Find the area of the region bounded by y = 4x, x = 1, x = 4, and xaxis in the first quadrant.
Or
Evaluate as limit of a sum.
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