Download Guess Paper – 2007 Class – XII MATHEMATICS Time:3hrs Marks

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Guess Paper – 2007
Class – XII
MATHEMATICS
Time:3hrs
Marks:100
Prepared by Mr:AJOY KUMAR RAVINDRAN,OUR OWN HIGH SCHOOL, DUBAI
Instructions
For section A
For section B
Questions 1-8:3 marks,9-15:4 marks,16-18:6 marks
Questions 19-22:3 marks,23-25:4 marks,26:6marks
SECTION A

 tan 
2 and I be the identity matrix of order 2.

0 

cos   sin  
Show that I+A = (I-A) 

 sin  cos 

 0
1. If A = 

 tan
2

2.Using properties of determinants prove that:
1 a
1
1
1
1 b
1
1
1
1 c
 ab  bc  ca  abc
3. Two bad eggs are mixed accidently mixed with 10 good ones.Find the
probability distribution of the number of bad eggs in 3 draws at random with
out replacement from this lot
4. A and B throw two dice simultaneously turn by turn. A will win if he throws a
total of 5, B will win if he throws a doublet. Find the probability that B will win the
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game, if A started it.
5. Evaluate
6.
1
 ( x  1)
Evaluate
x2
dx
( x 2  1)e x
 ( x  1) 2 dx
OR
x  sin x
 1  cos x
7.Show that y  Ax 
dx
2
B
dy
2 d y
is a solution of the differential equation x
x y0
2
x
dx
dx
OR
Find the equation of the curve represented by (y-yx)dx+(x+xy)dy=0 and passing
through the point (1,1)
8.Solve
(1  y 2 )dx  (tan 1 y  x)dy
 
1 , 2, 3, 1,2, 1,3, 2,3, 1,2,3show thatB,,, ' , , 1,2,3is a Boolean
9.Let B=  ,
algebra.
OR
Using Boolean algebra simplify the circuit:
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2 x , if x 2

10.Discuss the continuity of f(x)= 2 , if x  2
 x 2 , if x 2

at x=2.Is it a removable discontinuity.
If so remove it.
11.Using the definition of derivative,differentiate log(2x-3) w.r.t. x
12. If x=tan(y e
x
) then show that
(1  x 2 )
d2y
dy
 2(1  x  x 2 )  (1  x) 2 y  0
2
dx
dx
3
13. Water is dripping out from a conical funnel at a uniform rate of 4 cm /sec through a
tiny hole at the vertex in the bottom. When the slant height of the water is 3 cm, find
the rate of decrease of the slant height of the water-cone. Given that the vertical
angle of the funnel is 120o.
OR
Find the points on the curve
intercepts with the axes.
9 y 2  x 3 ,where the normal to the curve makes equal

4
14. Evaluate :
sin x  cos x
 9  16 sin 2 x
dx
0

a
15. Prove that

0
a
f ( x) dx   f (2a  x) dx and hence prove that
0
4
1
0
1
cot x
dx
16.Using determinants ,solve the following system of linear equations
x  y  z 1
x  2 y  3z  4
x  3 y  5z  7
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17. A given quantity of metal is to be cast into a half cylinder with a rectangular base and
semi-circular ends. Show that in order that the total surface area may be minimum,the
ratio of length of the cylinder to the diameter of its semicircular ends is  : (  + 2)
OR
Find all points of local maxima and minima and the corresponding maximum and
minimum values of the function ‘f ‘ where f ( x)  sin
find the absolute maximum and minimum values of ‘f’.
4
x  cos 4 x ,0 x .Also
18. Find the area of the region enclosed between the two circles
x 2  y 2  4 and ( x  2) 2  y 2  4
SECTION B
19. Using vectors,prove that the median to the base of an isosceles triangle is
perpendicular to the base.

20. Prove that a  b
bc
 
ca 2a b c

21.A ball dropped from the top of a tower 40 m high.At the same time another ball is
projected vertically upwards from the foot of the tower with a velocity of 2m/sec..
Find when and where the two balls will pass each other.
22.A ball is thrown horizontally with a velocity of 28 m/sec from a tower 50m high.Find
(a)the time taken by the ball to reach the ground.(b)the horizontal distance between
the foot of the tower and the point where it strikes the ground.
OR
A particle moving in a straight line with uniform acceleration described in the last of
th
its motion
9
of the whole distance. If it started from rest, how long was it in
25
motion? what distance did it move if it described 10m in the third second of its
motion?
23. The resultant of two like parallel forces P, Q passes through a point 0. when P is
increased by R and Q by S, the resultant still passes through O and also when Q, R
replaces P, Q respectively. Show that
S  R
(Q  R) 2
PQ
OR
Forces P, 2P, -P and 2P act along the sides AB, BC, CD and DA respectively of the
P 2
square ABCD and a force
acts along each of the diagonals BD and CA. show
that the forces reduce to a couple of moment 2aP, where ‘a’ is the side of the square.
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24. Find the shortest distance between the lines
x 1 y  2 z  3
x 2 y 4 z 5


  and



2
3
4
4
6
8
25. A ring of weight W, which can slide freely on the smooth vertical circle, is supported
by a string attached to the highest point. If the string subtends an angle  at the
Centre, find the tension in the string and reaction of the circle on the ring.
26. Prove that the plane x+y+2z=15 cuts the sphere x 2  y 2  z 2  2 y  4 z  11  0 in a
Circle; find its centre and radius.
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