CBSE[ All India ]_XII_Mathematics_2006_Set I
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Q1
Evaluate: 
Marks:3View AnswerAnswer:
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Q2
Find the image of the point (1, 2, 3) in the plane x + 2y + 4z = 38 . Marks:3View AnswerAnswer:
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Q3
A bill for Rs.5,050 is drawn on April 13, 2005 . It is discounted on July 4,2005 at 5% per annum. If the banker’s gain in the transaction is Rs. 0.50 find the nominal date of maturity of the bill. Marks:3View AnswerAnswer:
No longer in CBSE class 12th syllabus -
Q4
In a bolt factory, machines A, B, C manufacture 25%, 35% and 40% respectively of the total bolts. Of their output 5%, 4% and 2% respectively are defective bolts. A bolt is drawn at random and is found to be defective. Find the probability that it is manufactured by machine B. Marks:3View AnswerAnswer:
Let events B1, B2, B3 are defined as the following:
B1 : the nut is manufactured by machine A
B2 : the nut is manufactured by machine B
B3 : the nut is manufactured by machine C
And E : the nut manufactured is defective
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Q5
Express the following matrix as the sum of a symmetric and a skew symmetric matrix. 
Marks:3View AnswerAnswer:
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Q6
Using properties of determinants, prove the following: 
Marks:3View AnswerAnswer:
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Q7
Solve the following differential equation: sinxdy/dx + cosx.y = cosx.sin2x. Marks:3View AnswerAnswer:
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Q8
Verify that y = Acosx - Bsinx is a solution of diff erential equation d2y/dx2 + y = 0. Marks:3View AnswerAnswer:
Here y = Acosx - Bsinx
Differentiating y w.r.t. x, we get
y' = - Asinx - Bcosx
Again differentiating w.r.t. x, we get
y'' = - Acosx + Bsinx
y'' = - y
y'' + y = 0, or
d2y/dx2 + y = 0. -
Q9
Solve the following differential equation: (y2 - x2)dy = 3xydx. Marks:3View AnswerAnswer:
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Q10
Evaluate: 
Marks:3View AnswerAnswer:
