Board Paper of Class 12Science 2013 Maths All India(SET 1)  Solutions
i. All questions are compulsory.
ii. The question paper consists of 29 questions divided into three sections A, B and C. Section A comprises of 10 questions of one mark each, Section B comprises of 12 questions of four marks each, and Section C comprises of 7 questions of six marks each.
iii. All questions in section A are to be answered in one word, one sentence or as per the exact requirements of the question.
iv. There is no overall choice. However, internal choice has been provided in 4 questions of four marks each and 2 questions of six marks each. You have to attempt only one of the alternatives in all such questions.
v. Use of calculators is not permitted.
 Question 1
Write the principal value of.
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 Question 2
Write the value of.
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 Question 3
For what value of x, is the matrix a skewsymmetric matrix?
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 Question 4
If matrix and A^{2} = kA, then write the value of k.
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 Question 5
Write the differential equation representing the family of curves y = mx, where m is an arbitrary constant.
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 Question 6
If A_{ij} is the cofactor of the element a_{ij} of the determinant, then write the value of a_{32} · A_{32}.
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 Question 7
P and Q are two points with position vectors respectively. Write the position vector of a point R which divides the line segment PQ in the ratio 2 : 1 externally.
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 Question 8
Find, if for a unit vector .
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 Question 9
Find the length of the perpendicular drawn from the origin to the plane 2x − 3y + 6z + 21 = 0.
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 Question 10
The money to be spent for the welfare of the employees of a firm is proportional to the rate of change of its total revenue (marginal revenue). If the total revenue (in rupees) received from the sale of x units of a product is given by R(x) = 3x^{2} + 36x + 5, find the marginal revenue, when x = 5, and write which value does the question indicate.
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