Board Paper of Class 12Commerce 2007 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 A=, show that A^{2}− 6A+ 17I = O. Hence find A^{−1}.
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 Question 2
An urn contains 7 red and 4 blue balls. Two balls are drawn at random with replacement. Find the probability of getting (a) 2 red balls (b) 2 blue balls (C) one red and one blue ball.
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 Question 3
Using properties of determinants prove the following:
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 Question 4
A card is drawn at random from a wellshuffled pack of 52 cards. Find the probability that it is neither an ace nor a king.
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 Question 5
Evaluate:
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 Question 6
 Question 7
Form the differential equation of the family of curves y = A cos 2x + B sin 2x, where A and B are constants.
Or
Solve the following differential equation:
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 Question 8
Evaluate:
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 Question 9
Using properties of definite integrals, prove the following:
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 Question 10
Evaluate:
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 Question 11
 Question 12
Differentiate sin (x^{2}+ 1) with respect to xfrom the first principle.
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 Question 13
Write the Boolean expression for the following circuit:
Simplify the Boolean expression.
Or
Show that the following argument is valid:
s_{1}: p ∧ q
s_{2}: ∼ q
s: p ∨ ∼ q
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 Question 14
If y= sin (log x), prove that
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 Question 15
Verify Rolle’s Theorem for the function f (x) = x^{2}− 5x+ 4 on [1, 4].
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 Question 16
Using matrices solve the following system of equations:
x+ 2y + 3z= 6
3x+ 2y − 2z = 3
2x− y+ z = 2
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 Question 17
Using integration, find the area of the region enclosed between the circles:
x^{2}+ y^{ 2}= 1 and (x− 1)^{2}+ y^{2}= 1
Or
Evaluate as limit of sums.
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 Question 18
Find the point on the curve x^{2}= 8y which is nearest to the point (2, 4).
Or
Show that the right circular cone of least curved surface and given volume has an altitude equal totimes the radius of the base.
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