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7/29/2019 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 dd_duttamath@yahoo.co.in
Phone No. 09816055445
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