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Board Paper of Class 12-Humanities 2008 Maths (SET 1) - Solutions

General Instructions:
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)

VIEW SOLUTION
• Question 2

Evaluate: sin VIEW SOLUTION
• Question 3

Find the value of xand y if: VIEW SOLUTION
• Question 4

Evaluate: VIEW SOLUTION
• Question 5

Find the co-factor of a12in the following: VIEW SOLUTION
• Question 6

Evaluate: VIEW SOLUTION
• Question 7

Evaluate: VIEW SOLUTION
• Question 8

Find a unit vector in the direction of VIEW SOLUTION
• Question 9

Find the angle between the vectors VIEW SOLUTION
• 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: VIEW SOLUTION
• 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 A2−4A − 5I = 0

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• Question 14

For what value of kis the following function continuous at x= 2? VIEW SOLUTION
• Question 15

Differentiate the following with respect to x: VIEW SOLUTION
• Question 16

Find the equation of tangent to the curve x= sin 3t, y = cos 2t, at t = VIEW SOLUTION
• Question 17 VIEW SOLUTION
• Question 18

Solve the following differential equation:

(x2y2) 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: VIEW SOLUTION
• 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 VIEW SOLUTION
• 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 y2= 4x and the circle 4x2+ 4y2= 9.

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• Question 26

Evaluate: VIEW SOLUTION
• 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 VIEW SOLUTION
• 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 m2 12 men 60 B 1200 m2 8 men 40

He has maximum area of 9000 m2available, 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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