Guess Paper – 2012

Class – XII

Time: 3hrs Maximum Marks: 100

General Instructions:
(i) All Questions are Compulsory.
(ii) The Question Paper Consists of 29 Questions Divided into Three Sections – A, B & C Section A contains 10 questions of 1 marks each. Section B contains12 questions of 4 marks each. Section C contains 7 questions of 6 marks each.
(iii) Use of Calculators is not Permitted.

Q.1 Write the number of all one – one function from the set A with Cartesian number 4 to itself.

Q.2 If A is a square matrix of 3 x 3 order and │A│= 5 , find the value of │A adjA│

Q.3 Write a unit vector in XY- plane, making an angle of 30o with the positive direction of x-axis.

Q.4 Find the distance between two planes: 2x + 3y +4z = 4 and 4x + 6y + 8z = 12.

Q.5 Consider the binary operation * : R x R →R and O: R x R →R defined a * b = │a - b│ and a o b = a for all a, b ε R. Show that * is commutative but not associative, O is associative but not commutative. Further, show that for all a, b, c ε R, a* (b o c) = (a * b) o (a * c). Does O distributes over *? Justify your answer.

Q.6 Show that the four points (0, -1, -1) , (4, 5, 1) , (3, 9, 4) and (-4, 4, 4) are coplanar. Also find the equation of plane containing them.

Q.7 Solve the differential equation: (1 + y + x2y) dx + (x +x3) dy = 0, y(1) = 0

OR

A water tank has the shape of an inverted right cone with its axis vertical and vertex lowermost. Its semi-vertical angle is tan-1(0.5). Water is poured into it at a constant rate of 5 cubic metre per hour. Find the rate at which the level of the water is rising at the instant when the depth of water in tank is 4 m,

Q.8 The probability of a shooter hitting a target is ¾. How many minimum number of times must he/ she fire so that the probability of hitting the target at least once is more than 0.99?

Q.9 A Manufacturer has Three Machines I, II, III installed in his factory. Machines I and II are capable of being operated for at most 12 hours where as machine III must be operated for at least 5 hours a day. She produces only two items M and N each requiring the use of all the three machines. The number of hours required for producing I unit of each of M and N on the three machines are given as :

Items	No. of hrs Required on Machines
	I	II	III
M N	1 2	2 1	1 1.25

She makes a profit of Rs.600 and Rs.400 on items M and N Respectively. How many of each item should she produce so as to maximize her profit assuming that she can sell all the items that she produced? What will be the maximum profit?

Q.10 A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the minimum length of the hypotenuse is ( a2/3 + b2/3 )3/2.

OR

An open toped box is to be constructed by removing equal squares from each corner of a 3 Meter by 8 Meter rectangular sheet of Aluminums and folding up the sides. Find the volume of the largest such box.

Q.11 Assume that the chances of a patient having a heart attack is 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drugs reduces its chance by 25%. At a time a patient can choose any one of two options with equal prob. It is given that after going through one of two options the patient selected at random suffers a heart attack. Find the prob. that the patient followed a course of meditation and yoga