cbse class xii mathematics set i question paper 2011

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Please check that this question paper contains 11 printed pages. . Code number given on the right hand side of the question paper should be written on the titleĀ ...

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65/1

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its surface area.

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e

error in calculating

sin

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-

=

y

fCfi

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(2

as

measured

is

sphere

a

of

radius

the

If ~

then find the approximate

.

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t"

,

f

m

.

Ion

.

.

OR

+

unc

- e .

4 sin e (2

(xe)}

mcreasmg

=

an

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IS

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{log

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2

dx

15

X

log

=

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y

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x e

-

Y X

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-{

(1 + x2) d2

show

that

d a) -L dx

-

+ (2x

~

m

~,

-d2y

x2)

(1 +

y)

log

(;

tan

=

-

+ (2x

a)

dx2 17. Evaluate: n/2

f

0

dx

:

~

f

n/2

x + sin x dx 1+cosx C

0

x dy

- y dx = .J;i-~7dx

Solve the following (y + 3x 2) -dx

""

,.

:

~

~

-qj)

~1.i1~,UI

,

~~;

"'-': '. "."

dx

equation:

R-~7

=

differe~tial

dx

~

RI'--1I(1~d

19.

y

following . -

the dy

Solve

x

18.

i

~

-dy =

x + sin x dx 1 + cosx

0 1=fr;:r

0

==

,

x

~

dx

fCfi

(; log y ),

= tan

16. If x

differential

-

equation:

=x

'

.

:

~

~1.i1~,UI

~

RI'--1I(1I(9d ~

-qj)

dy

=x

(y + 3x 2dx) -

dy 20. Using vectors, find the area of the triangle with vertices A(1, 1, 2),

5)

3,

B(2,

2),

1,

A(l,

m

~

7

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P.T.D.

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5)

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5,

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B(2, 3, 5) and C(l, 5, 5).

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b ~n'l

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--~

:

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dx ~

~J"t;;

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n/3

:

--=~~+

the

and

2k)

+

4]

+

(3i

A

+

~

1\ 2k)

+

':' 4J

':'

+

(31

A

+

1\ 2k)

+

':'

In

coins.

I

two

~

~ containing

~ each

~

~

III

and

~~

II

~

I,

5

=

and takes

out a coin. If the coin is of gold, what

box

a

chooses

person

A

coin.

silver

one

and

gold

one

is

there

III,

box

box I, both coins are gold coins, in box II, both are silver coins and in at random

is the

10

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III

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II

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t

n~,

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t

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probability that the other coin in the box is also of gold?

65/1

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6

O.

-

=

=

x

~

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x-~

~

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3

+

x

I

=

-

(21

=

r

~

~

1\

~ k)

boxes

+

1\

10)

-

j

1\

5,

identical

(i

.

1\

-

1,

(-

three

r

~

~ ~ Given

28.

to x

= 5.

j + k) 1\

Y

= (2i - ]

J"

-

1\

~

. (i

=- 6

x

(- 1, - 5, - 10), from the point of

point

2k)

of the

+

distance

r

~

'(fP-1T ~

~

above x-axis and between

intersection of the line "1 plane

+ 31 and evaluate the area under the

':'

the

= Ix

y

~

q:jf

I

3

+

Find

-q:;r

x

I

'(f'qj

0

Y

= =

x

27.

31

x +

I

of

ml:fi

=

curve y

dx

--

)(:;":

Sketch the graph

~

26.

7

-5

.J-c:x

~

J

I

~

~

1:Jr;r

3:r~

nl6

",

~

rr

Determine

desktQP

40,000

a computers

Rs.

-

the number

of

demand

and

computers

25,000 monthly

Rs.

personal

cost

of total

will

types

will not exceed 250 units.

the

that

that

two

sell estimates

model

to

plans

portable

a

He

and

merchant respectively.

model

A

-

of units

of each type

of computers which the merchant should stock to get maximum profit if he does not want to invest more than Rs. 70 lakhs and his profit on the desktop model is Rs. 4,500 and on the portable

model is Rs. 5,000.

'

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4,500~.

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~ 0

5

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m

~ 70 5,000~.~,

40,000~.

-q;~

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fC:ti

25,000~.

"5fqjT{

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Wm'{T

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W?J1R

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Make an L.P.P. and solve it graphically.

65/1

.

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