CBSE - NEW DELHI
Guess Paper – 2012
Class – XII
Subject – Mathematics
Time: 3hrs Maximum Marks: 100
(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.
number of all one – one function from the set A with Cartesian number 4 to
Q.2 If A
is a square matrix of 3 x 3 order and
5 , find the value of
Write a unit vector in XY-
plane, making an angle of 30o with the positive direction of x-axis.
the distance between two planes: 2x + 3y +4z = 4 and 4x + 6y + 8z = 12.
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.
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.
the differential equation: (1 + y + x2y) dx + (x +x3) dy =
0, y(1) = 0
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,
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?
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 :
of hrs Required on Machines
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?
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.
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.
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