CBSE [ Delhi ]_XII_Mathematics_2006_Set I
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Q1
A particle is projected so as to graze the tops of two walls, each of height 10 m at 15m and 45 m respectively from the point of projection. Find the angle of projection. Marks:3View AnswerAnswer:
No longer in CBSE class 12th syllabus
Let u be the initial velocity, the angle of projection with the horizontal
Therefore, equation of path is y = xtan 
- (gx2)/2u2cos2
As A and B lie on the curve 
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Q2
Express the following matrix as the sum of a symmetric and a skew symmetric matrix.
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Q3
Using properties of determinants, prove the following:
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Q4
Solve the following differential equation: dy/dx - y/x = 2x2.
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Q5
Form the differential equation of the family of curves y = asin(x + b) where a and b are arbitrary constants. Marks:3View AnswerAnswer:
Here y = asin(x + b)
Differentiating y with respect to x, we get
y' = acos(x + b)
Again differentiate, we get
y'' = - asin(x + b)
i.e., y'' = - y
or, y'' + y = 0
or, d2y/dx2 + y = 0. -
Q6
Solve the following differential equation: 2xydx + (x2 + 2y2)dy = 0.
Marks:3View AnswerAnswer:
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Q7
Evaluate: 
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Q8
Evaluate: 
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Q9
Two dice are rolled once. Find the probability that:
(i) The numbers on two dice are different
(ii) The total of numbers on the two dice is at least 4 Marks:3View AnswerAnswer:
If two dice are rolled, sample points = 36 i.e., n(s) = 36
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Q10
A pair of dice is tossed twice. If the random variable X is defined as the number of doublets, find the probability distribution of X. Marks:3View AnswerAnswer:
Here
X is defined as the number of doublets i.e. X=0,1,2 Let event A: 'getting a doublet' P(X=0)=P(no doublets) 
