Board Paper of Class 12Commerce 2008 Maths Delhi(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
If f(x) = x + 7 and g(x) = x − 7, find (fog) (7)
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 Question 2
Evaluate: sin
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 Question 3
Find the value of xand y if:
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 Question 4
Evaluate:
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 Question 5
Find the cofactor of a_{12}in the following:
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 Question 6
Evaluate:
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 Question 7
Evaluate:
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 Question 8
Find a unit vector in the direction of
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 Question 9
Find the angle between the vectors
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 Question 10
For what value of λare the vectors perpendicular to each other?
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 Question 11
(i) Is the binary operation* defined on set N, given by for all, commutative?
(ii) Is the above binary operation* associative?
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 Question 12
Prove the following:
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 Question 13
Let .Express A as the sum of two matrices such that one is symmetric and the other is skew symmetric.
OR
If, verify that A^{2}−4A − 5I = 0
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 Question 14
For what value of kis the following function continuous at x= 2?
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 Question 15
Differentiate the following with respect to x:
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 Question 16
Find the equation of tangent to the curve x= sin 3t, y = cos 2t, at t =
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 Question 17
 Question 18
Solve the following differential equation:
(x^{2}− y^{2}) dx + 2 xy dy = 0
Giventhat y = 1 when x = 1
OR
Solve the following differential equation:
, if y = 1 when x = 1
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 Question 19
Solve the following differential equation:
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 Question 20
If and , find a vector such that and
OR
If and and, show that the angle between and is 60°
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 Question 21
Find the shortest distance between the following lines:
and
OR
Find the point on the line at a distance from the point (1, 2, 3).
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 Question 22
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of the number of successes.
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 Question 23
Using properties of determinants, prove the following
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 Question 24
Show that the rectangle of maximum area that can be inscribed in a circle is a square.
OR
Show that the height of the cylinder of maximum volume that can be inscribed in a cone of height his .
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 Question 25
Using integration find the area of the region bounded by the parabola y^{2}= 4x and the circle 4x^{2}+ 4y^{2}= 9.
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 Question 26
Evaluate:
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 Question 27
Find the equation of the plane passing through the point (−1, − 1, 2) and perpendicular to each of the following planes:
OR
Find the equation of the plane passing through the points (3, 4, 1) and (0, 1, 0) and parallel to the line
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 Question 28
A factory owner purchases two types of machines, A and B for his factory. The requirements and the limitations for the machines are as follows:
Machine
Area occupied
Labour force
Daily output (in units)
A
1000 m^{2}
12 men
60
B
1200 m^{2}
8 men
40
He has maximum area of 9000 m^{2}available, and 72 skilled labourers who can operate both the machines. How many machines of each type should he buy to maximise the daily output?
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 Question 29
An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accident involving a scooter, a car and a truck are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver.
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