108264210Preboard Examination XII 5th Feb 09

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Guess Paper 2012

Class XII

Subject Mathematics

Time: 3 hrs 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.

SECTION A

Q.1 If A and B are two sets such that n (A) = m and n (B) = n then write number of function

from A B

Q.2 Find value of sin-1(sin 10)

Q.3 Given that 0. =ba and 0=ba . What can you conclude about the vectors a and b ?

Q.4 Construct a 2 x3 matrix whose elements are given by ijaij log=

Q.5 For any 2 x 2 matrix A, |A| = 5 find the value of kA

Q.6 Find the maximum and minimum values, if any of 32cos)( += xxf

Q.7 Write all unit vector in XY plane

Q.8 Evaluate: dxxx

2/

2/

47sin

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Q.9 State reason why all diagonal elements of skew symmetric matrix are zero.

Q.10 Evaluate: + xxdx

SECTION B

Q.11 Consider{ } { }cbaf ,,3,2,1: and { } { }catballapplecbag ,,,,: defined by f(1) = a, f(2)

= b , f(3) = c , g(a) = apple , g(b) = ball , g(c) = cat. Show that f, g and gof are

invertible. Find out f-1 , g-1 and

(gof)-1 and show that (gof)-1 = f-1o g-1

OR

Show that operation * on Q {1},defined by a * b = a + b ab for all a, b Q {1}

satisfies (i) the closure property, (ii) the associative property (iii) the commutative

property (iv) What is the identity element? (v) For each a Q {1}, find the inverse of a.

Q.12 Find the value of x if

Q.13 Prove by using properties of determinant222

22

22

22

4 cba

bacbca

bcacba

acabcb

=

+

+

+

OR

If A and B are square matrices of the same order such that AB = BA, then prove by induction that ABn =

BnA. Further , prove that (AB)n = AnBn for all Nn

Q.14 Prove that [ ]xxf =)( , 0 < x


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Q.15 If2

log1

t

tx

+= ,

t

ty

log23+= , t > 0 prove that 12 211 = xyyy

Q.16 If E and F are independent events prove that E and F are independent.

Q.17 Integrate ++

dxxx

xx42

sincos

cossin

Q.18 For the curve ,2453

xxy = find all the points at which the tangent passes through the

origin. OR

Find the interval in which the function ( )2

0,cossin 44 += xxxxf is increasing o

decreasing.

Q.19 Solve the differential equation: ( ) ( )ydxxdyx

yyxdyydx

x

yx =+ sincos

Q.20 Find the equations of the line intersecting the lines111

zayx=

+= and

112

zyax==

+and

parallel to the line 2

2

12

azayax =

+

=

Q.21 If A,B,C,D are four points in space prove that AB x CD + BC x AD + CA x BD = 4 (Area

ABC)

OR

If 0=++ cba and 3=a , 3=b and 7=c find angle between a and b

Q.22 Solve the differential equation: ( ) ( )dxydyxy 21 1tan +=

SECTION C




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Q.23 Given that A =

321

121

211

find A-1. Hence using A-1 solve the system of equations: x y + z

= 4, x 2y 2z = 9, 2x + y + 3z = 1

Q.24 The sum of the perimeter of a circle and square is k, where k is some constant. Prove that

the sum of their areas is least when the side of square is double the radius of the circle.

Q.25 Find distance of the point (2, 3, 4) from the line26

2

3

3 zyx=

=

+

, measured parallel to the

plane

3x + 2y + 2z + 5 = 0

OR

Find image of the point (3,-2,1) in equation of plane through the intersection of planes

x + y + z = 1 and

2x + 3y + 4z = 5 which is perpendicular to the plane x - y + z = 0

Q.26 Prove that the curves y2 = 4x and x2 = 4y divide the area of the square bounded by x = 0,

x = 4, y = 4 and y = 0 into three equal parts.

OR

Find the area of the region bounded by the curves y = x2 + 2, y = x, x = 0 and x = 3

Q.27 Prove: 2log)cos1log(0

= dxx

Q.28 Two godowns A and B have grain capacity of 100 quintals and 50 quintals respectively

They supply to 3 ration shops D, E and F whose requirements are 60, 50 and 40 quintals

respectively. The cost of transportation per quintal from godowns to the shops is given

below:

Transportation cost per




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quintal (in Rs)

From / To A B

D

E

F

6

3

2.50

4

2

3

How should the supplies be transported in order that the transportation cost is minimum?

Q.29 If a machine is correctly set up, it produces 90% acceptable items. If it is incorrectly set

up, it produces only 40% acceptable items. Past experience shows that 80% of the set ups

are correctly done. If after a certain set up, the machine produces 2 acceptable items, find

the probability that the machine is correctly set up.

Paper Submitted By:

Name Deepak dutta

Email [email protected]

Phone No. 09816055445



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108264210Preboard Examination XII 5th Feb 09