Mathematics2011 set 1

~~,

65/1

1

P.T

00

1

:

100

-""'",

~;~~~~:;"".;

~t~,~;.,

l1fUffi

.0.

'

.J!

am

I

if

~

,~,c.;t

I

~

qj)

I

f(;r&

tf{

~-~

~

I

~

11

~

not write

~

~

~

~

'qjT

I

~

~

~-~~

fcfaUT

"q:jT

~-~

I

't1

~

~

~,

~

students will read the question paper only and will
on the answer script during this period.

qj)

~-~

~

~

"(fq:)"

~

~

~

~

29

~

if

the

a.m.,

10.30

to

a.m.

10.15

From

a.m.

10.15

question

The

paper.

question

this

read

to

allotted

been

has

time

before

question

the

of

Number

Serial

the

down

be

should

paper

question

the

of

side

hand

right

the

on

given

~~~I

~

-

~

m

-~"q)T

3"(R"

~

Q5)s

a:rrtif

~

answer-book.

the

of

page

title

the

I

I

I

I

I

I

I

Candidates

*

I

~

~

10.30

~

~

at

distributed

be

write

I

1~(9.1

"~I

~

-q:;r

if

~

~-~

~

fCfj

~

"qj"{

J

Marks:

tf{
~

~

~

3lT

~

ffl

~

I

I

.,;,.,.;

fiR"?:

15

~-~

~

fCfj

~

"qj"{

.

I

q")1~

~

10.15

~

~

f<-I~-t1

,

IIi

I

~

~

qj)

'qjT

number

Code

I

3:rfi:rq;frif

MATHEMATICS

~-:1I"I'111

~

M

attempting

4.

~

4-

Please

I

q

GI~I'1

~

will

minutes

15

';f

I

Maximum

hours

3

if

~

paper

.

I

f!TJi

~

~

~

.

m

~-~

~

.

~-~

~

.

.

3

"'~

~

.

.

.

~ql~

10.15

.

No.

:

~

.

~

Roll

allowed:

llme

65/1

No.

Code

I

SOS

Series

I

'frirlr

R~

;'

qj)-s ;{.

must write the Code on

0.

";1.

Please check that this question paper contains 11 printed pages.

written on the title page of the answer-book by the candidate,.

Please check that this question paper contains 29 questions.

it.

any answer

~j{

0"
...",.-c'

-.f

/

i?

.

/

i?

fit

1qj

1

e9":

J
j

rf/

q,

<{

:t

q

/

~

it

fIJr;rif

~

12

if

-ar

~

/

i?

q;r

3iq;

~

~

it

fIJr;rif

if

~

10

if

3T

~

/

~.

31Rqp;f

~

I:/W

:

permitted.

not

is

calculators

of

Use

(v)

questions.

such

all

in

alternatives

the

of

one

only

attempt

to

have

You

each.

marks

six

of

questions

2

and

each

marks

four

of

questions

4

in

provided

been

has

choice'

internal

However,

choice.

overall

no

is

There

(iv)

question.

the

of

requirement

exact

the

per

as

or

sentence

one

word,

one

in

answered

be

to

are

A

Section

in

questions

All

(iii)

each.

marks

six

of

questions

7

of

comprises

C

Section

and

each

marks

four

of

questions

12

of

comprises

B

Section

each,

mark

one

of

questions

10

of

comprises

A

Section

C.

Band

A,

sections

The question paper consists of 29 questions divided

3i'

;:.tt

if'

~

7

if

tT

~

/

i?

q;r

3iq;

:qn-

~

it

fIJr;rif

if

~

ff/4I/o<I

All questions are compulsory.

(ii)

nPn"

if

m

~

31P.fCfT

qr;.p;r

~

~

~

a-frf

iJi

JI;'l;if

/

i?

q;r

3iq;

~

if..

31Jrrq;1

it

4

qJc?

aiW

~

7ft

(fi"(

(

if'

;r(ff

~

if

I:/W

if

3T

~

if iiit i:ft;r
?9U-.sT
if ~

if

JI;'l;if

I:/W

'l!:«

/

i?

~

31T;:rrfi:q;

if

JI;'l;if

w

~~;1T~if/

w if 29 ~

~

3rj11frr

;:.tt

Jr2177J

2

~

1[Uf

W~

iJi

qJc?

aiW

iii
)

(

ii)

'q:jl;;rT

~

,

(iv)

(

<"1;~~

(v)

(i)

2

65/1

(i)

-

--'

.

General Instructions:

into three

aT,-ar Z1"
nPn" /

-llllllr

~

-

65/1

3
',..

)
.

sm

sm

+

.

cos 75°
-1

I

'~~:

_c"::~~t

,

~
'Q

3

cos

2n)

~

I

~

"j:fR"

(

~

3]
A.

of

-1

~

if

~

cos

0

ue

va

f

~

~

~

-1
terms

.
"q:jT

3

sm

. 2n)

~

sin 75°

m

sin 15°

A

3]

I

~

A

cos 15°

i:I1T

15°

sm-

I

m

[ 2'
1(

A-I

[2

.

~,

sin 75°

wrIte

,

sin

prrnCIpa

..

m

~,

5
+

3)
2n

~

5
e

t

IS

at

W

. h

5

:

~

( cos

if

i
15°

cos

1

=

cos-

=

~

3.

A

"j:fR"

h

3W3lif;

5.
If

I
I

A

~

.

2

~

*

4.

( . 2n)

.
.

3

I

~

arI;rqr

~

f~

~

fqj

~

I

~

~

~

~

B

A~

6)}

(3,

5),

(2,

4),

{(I,

=

f

~

m

7}

6,

5,

{4,

=

B

3},

2,

{I,

=

A

trRT

not.

or

one-one

is

f

whether

State

B.

to

A

from

function

a

be

6)}

(3,

5),

(2,

4),

{(I,

=

f

let

and

7}

6,

5,

{4,

=

B

3},

2,

{I,

=

A

Let

1.

I

-ff

qj7

3iCli

1

~

~

n-q;

10

:if

1

~

~

each.

mark

1

carry

10

to

1

numbers

Question

'

~3:r

~r

SECTION
:

A

";4;!'ii1Y~&

c/fi~1~f(:!

?

Evaluate:

cos 75°

:'"

,.

-2

.

-2

If a matrix has 5 elements, write all possible orders it can have.

P.T.G.

~

~

-.c~'-

1:fT";f~

.

dx

b)3

~
f

:

(ax

+ b)3

dx

Evaluate:

In

7.

+

(ax

Evaluate:

f

6.

~

:

In

1:fT";f
~

Write

of the

(1, 0, 0) "(f~ (0, 1, 1) ~

Write

the

points

(1,

~

I

vector

1

- j

i

1

on the vector

4

7

I

~4-iIct>(UI~

~~'1:&r'qjT~

2

z-6
-.

. y+4
=

x-5

-

b

=

.

-

1.

y

0

equatIon
~

=

~

=

~
I

65/1

7

1

i + j.

~~~I

+j

f

.
vector

1

3

3

0, 0) and

1

i

1
'qjT~

1

e

t

W

the

firc;rR "qR;ft '1:&r ~ ~-~~

of the

h

.

rIte

.

projection

i-j

~

1

10

joining

1).

~an

9.

line

gIven

1,

direction-cosines

me

(0,

the

a

8.

2

'0"

~~,!",",'

B
~~

a+b,

{

each.

function

the

Find

7.

+
JR'

if

:

as

defined

is

5}

4,

3,

2,

1,

{O,

set

the

on

*

operation

binary

A

OR

=

I

lOx

ii'

=

3iq;

fog

=

gof

that

marks

4

i?Ii

f(x)

JfR

as

Jffflq;

4

carry

22

11

'(fq:;

R

~

22

such

R

R

f:

~

R

Let

:

g

it

11

defined

mr

JfR

11.

numbers

be

Question

to

I

i

I

SECTION

a+b<6

6

and

element

'a'

~

~

'a'.

I

t

~

of

JR'

=

each

inverse

W~~

the

~

~

b

operation

being

:

t

~

'Sf"q)"R

~

6

*
<

b

+

~
a

~~

~

~

~
b,

5}
a

{

+

4,

3,

2,

1,

{O,

~~

~

=

gof

this

a,

7

-

+

6

lOx

=
~

+

a

for

with

R,

~

if

identity

"[T'{T

the

invertible

~

R
R

~

f:
R

:

g

is

is

fog

zero

set

~

the

f(x)

that

of

~

Show

-

a + b

6,

a*b=

12.

Prove

that:

[

,Ji-,;-x

-

.J:f+x

-1

+.J~

.Jl-=-x

]

x

1

7t

=

4

-

"2

-1

cos

'a'

~

~

-~:S:
x1
:S:
1

'

x,

~~~:

tan

q;r

~

6

~

~

b

+

"(fm

a

I

t

t

~

a

-

6

d~~~

6,
~

q;r

-

b
~

+
~

~

~

t

cYj~~un(.j

~

~

~

a

a:*b=

65/1

!

~

c'

5

1

:S:

x

~

-

x,

"2

1

-1

:S:

1

7t

cos

]

-

.Ji-=x

4

-

.JI-,;-x +,Ji -=-x

.JI-,;-x

=

[

-1

tan

P.T.G.

- 2

2x - 3
2x - 9
2x - 27

:

~

~

3x - 16 = 0

x- 8

~

3x - 4

x- 4

~

x

~

RJor1I(.1I~(1

~

m

qjT

""J]um

~

~1fTJl~1

3x - 64

x

14. Find the relationship

between 'a' and 'b' so that the function 'f' defined

by:
{ ax + 1,

if

x:S 3

f(x) =

is continuous at x = 3.
if

x > 3

~,

"qft~
3

>
I

x

~

~

~

+
~

3,

~

3

x:S

~

1,

ax
qjT

~

~

'b'

~

'a'

m

bx

~,

{log (x e)}

=

f(x)

~

'f',

~

~

{

+

dx

.

2

log x

-

-

a

ow

s

Y

,

-

x

dy -

t

th

h

e

-

x

Y

If

-

OR

bx + 3,

cosO)

7t]
2

+ cose)

0.03~~F~,
I

~

~

F

~I"'~G

.q:

~R~~'1

~

~~~~~9~~~~,
~

65/1

6

m~~

3"{?AaJ

cm,
I

~

~

~

~

.q:

its surface area.

2.

~

0.03

of

error

an

with

cm

9

]

~

[

0,

e,

-

e

error in calculating

sin

4

-

=

y

fCfi

~

(2

as

measured

is

sphere

a

of

radius

the

If
~

then find the approximate

.

[0

.

-

t"

,

f

m

.

Ion

.

.

OR

+

unc

- e .

4 sin e
(2

(xe)}

mcreasmg

=

an

Prove t h at y

IS

.

{log

.

2

dx

15

X

log

=

~

~

I~

~...~~..'
G~II~~

~
(11

~
~,

y

-

x
e

-

Y
X

'-11~

-n&

3"{?AaJ

-{

(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
dx
(y + 3x 2) -

""

,.

:

~

~

-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

---~

P.T.D.

~

-

65/1

~-

~

~

~

-q)1

~

~
I

'q}""{,
~

5)

m

5,

-q)1
C(l,

~

~

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

J"'--

b
~n'l

~"l

--~

:

~11~~

dx
~

~J"t;;

J

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

~

~
~

~

~

"G1";1)
~
~

~

~

-q:;r

I~,
m
~
fu"iiiit

fiij

~

~

~

I

~
t,

t

III~,

~
}fll(.f~r:ff

~

~

~
~

~

'i;fTm-q:;rt?

~

~

~
m

t,

-q:;r

m

~

~I<!~~J

~

~

~

~

~

~
~

III

~
~

~

~

I

"G1";1)

II

I,
~

t

n~,

~
~

I

t

~

~,

~

-q:;r

~
R~I(.'1ctl

~

m

~

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

65/1

~

6

O.

-

=

=

x

~

~

x-~

~

I

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.

'

~

~

,

~

I

~

"(f4T

.

~

~

~

4,500~.

~W?J1R
~

~

m

~

~
~

~

m1ft

-;rf:r

'"!iA1m

~

~

~

~

~~
~

~m~

~

~

~

~
o;f1i't

~
0

5

2

~

~,

mG-'fq

~

1:{lfuCfi

~

m

~
70
5,000~.~,

40,000~.

-q;~

~

~
-q;~
31f~

fC:ti

25,000~.

"5fqjT{

"GT

~

~~

~. ~ "(f4T i-~ifq

~

"qj~~~~~~~?

~~

"(f4T

~ml:fi~~~1

~

r

~~

~

~

Wm'{T

~

W?J1R

~
~

~

~

~

~

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

65/1

.

rll.li..iiiiii...iii_..ii~.;;;;;;;;;;;;;

11

~~~~~

'.

t,-~

,

Mathematics2011 set 1

Recommended

Recommended

More Related Content

What's hot

What's hot (19)

Similar to Mathematics2011 set 1

Similar to Mathematics2011 set 1 (20)

More from Pratima Nayak ,Kendriya Vidyalaya Sangathan

More from Pratima Nayak ,Kendriya Vidyalaya Sangathan (20)

Recently uploaded

Recently uploaded (20)

Mathematics2011 set 1