CBSE[ Delhi ] _XII_Mathematics_2007_Set II
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Q1
Find mean 
variance 
for the following probability distribution: X
0
1
2
3
P(X)
1/8
3/8
3/8
1/8
Marks:3View AnswerAnswer:
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Q2
Marks:3View AnswerAnswer:
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Q3
Form the differential equation of the family of curves y = Acos2x + Bsin2x , where A and B are constants. Marks:3View AnswerAnswer:
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Q4
Marks:3View AnswerAnswer:
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Q5
Solve the following differential equation:
xcosydy = (xexlogx + ex)dxMarks:3View AnswerAnswer:
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Q6
A particle starting with initial velocity of 30 m/sec, moves with a uniform acceleration of 9 m/sec2 Find: (i). the velocity of the particle after 6 seconds (ii). how far will it go in 9 seconds. (iii). its velocity when it has traversed 150 m. Marks:3View AnswerAnswer:
No longer in CBSE class 12th syllabus -
Q7
If 
, show that A2– 6A + 17 I = 0. Hence find A-1 . Marks:3View AnswerAnswer:
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Q8
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. Marks:3View AnswerAnswer:
(a) P(2 red balls) = P(First red ball).P(second red ball) = 7/11 x 7/11 = 49/121.
( b ) P(2 blue balls) = P(First blue ball).P(second blue ball) = 4/11 x 4/11 = 16/121. (c) P(one red and one blue ball) = P(First red and second blue ball) or P(First blue and second red ball
= (7/11 x 4 x 11) + (4/11 x 7/11) = 56/121. -
Q9
A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability that it is neither an ace nor a king. Marks:3View AnswerAnswer:
The total number of cards in a pack of cards is 52.
The total number of card neither an ace nor a king are 44
Therefore, P(neither an ace nor a king) =44/52 = 11/13. -
Q10
Solve the following differential equation: dy/dx + 2y = 6ex. Marks:3View AnswerAnswer:
Here dy/dx + 2y = 6ex This is a linear equation of the form dy/dx + Py = Q, Where P = 2 and Q = 6ex 
