NDA Paper Mathematics 2014

7/25/2019 NDA Paper Mathematics 2014

1/40


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1

2

.

3 .

4

E ver

y

quadra

tic

eq

uat ion

ax

2

+

b

x

+

c

=

0

wh

ere a,

b, c e

R a *

0

has

(a)

ex

actly o

ne rea

l

r

oot.

(b)

at

leastone

real

root.

c)

at le

ast two

real root

s.

(d

)

a

t

m

ost tw

oreal

ro

ots.

The

relat io

n S is d

efined o

n

the set of int

egers

Z

as xSy

i f nteg

er

x d

ivides i

nteger

y. Then

(a)

S is

a

n

equiva

lence re

lation.

(b)

S

is only

reflexiv

e an

d

s

ymmetr

ic.

c)

S is o

nly refle

xive

and t rans

it ive.

(d)

Sis onl

ysymm

etric

and t ransi

t ive.

If

a

* b * c

are all

positive

,

then t

he

val

ue of

a

b c

the

d

etermi

nant b

c a

is

c

a b

(a)

non-

negat iv

e

(b)

n

on-posit

ive

c)

neg

at ive

(d)

positive

L e

t A

andB be tw

o mat r

ices suc

h

that AB = A

an

d BA =

B W hi

ch o

f

the follow

ing

stat

ements

are

corre

c t

?

1.

A

2

=

A

2.

B

2

=

B

3.

(

AB)

2

=AB

S

elect

the

correc

t answe

r using

the cod

e given

below

(a

) 1

and 2 onl

y

(b) 2

an

d

3

only

c

) 1 a

nd

3

only

(d)

1,

2

and

3

5

6

7

Wha

t

i

s (1001)

2

equal

t

o?

(a

)

5)10

(b)

9

)10

c)

(

17)10

(d)

(1 1

)10

.

. ..

6

--:

c

What

is

l

rqual

to, w he

re

i

=

?

(a)

1

(b)

1

/6

c)

6

(d)

2

Let

zbe a co

mplex

num

bers'uch

th a

t Iz I= 4

and

a

rg z

=

5

. Wh

atis

z

eq

ual to ?

6

a) 2. /3 +

i

(b)

2./3-

i

c)

- 2

. /3 + i

(d)

-

./3

+

i

wherei-

=F

i

6i -

i 1

8

If

4

3i

- 1

= x

+ iy wher

e

i

=

Fl

.

20

3

i

thenwhat is

x equa

l to ?

a)

3

b) 2

c)

d) 0

8 0E

BBN N

BS

2 -A

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3/40

1. ~ t1lii'h


4/40

9

10

I

f a

f arethe

r

oots of

ax

2

bx c

= 0 and

12

+ ,

f +

a

re th

e roots

of px

2

+x

+ = 0,

If A

is an

inv

ert ible

m atr ix

, then

wha t

is

det

A

l

equ

a l

t

o ?

the

n what

i

s

h

equal

to ?

a)

E.

-

)

2

a

p

(b )

(_E.

+ )

2

a p

c)

(d)

I f

G

to?

a)

-4

1)

b)

:

c)

-1 4)

0

-1

d

)

. 1

4)

0

-1

A is such

th at

1

) ,

then w

ha tis

A

equal

-1

a)

(b )

c)

d

etA

1

detA

1

(d)

Non

e of

th

e above

13

From

the mat

rix eq u

a tion

AB = A

C, w

here

A, B

, Care

the squa

re m at

rices o f

sa m e o

rder,

we c

anconc

lu de B

=C pro

vided

(a

) A is

non-si

ngular .

b)

c)

d)

A

is sing

u lar .

A

is sym

m etric.

A is ske

w symm

etric.

14

I

f

A =

4

x

+

2

)

is symm

etric, the

n

2x-

3 x

+ l

w

ha t is

x e

q ual

to ?

a

)

2

b)

3

c)

- 1

d

)

5

a

b

0

a

b =

0

, then

w hich o

ne

of th

e

11

C onsid

er

the

f

ollowin

g st

atemen

ts

:

1

5 I f

0

b

0

a

1

. Determ

inant

i

s

a squ

are m

atrix .

2 Deter

minant

i

s a numb

er ass

ociated

witha s

quare m at

rix .

Which

of th

e ab ove s

ta temen

tsis/ar

e correc

t ?

(a)

1 onl

y

b)

2 only

c)

Both

1and 2

(d)

Neithe

r 1

nor2

B OEB

B NNB

S

4

-A

followi

ng is co

rrect ?

(a

)

is one

of the cu

be root

s of unit

y .

(b)

is one

of

the

cube

roots

of -

1

c)

a i

s

o

ne o

f thecube

roots

of unity .

(d)

bis one

of the

r

u e

ro

ots o

f

un

ity .

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5/40

9.

~ ax

2

i -bx+c=0 ~ liR a f ~ ail\

12.

px

2

+ qx + r 0 ~ liR a h, f + h t m

~ < m a R t ?

~ A

~

ci : i'lli4Uft4

3lfOIIli t_


6/40

16.

The

function f : N -- N, N being the set of 20. A

and

B are two

sets

having 3 elements in

17

natural

numbers, defined by f(x) =

2x

+ 3

is

common.

If

n(A) = 5, n(B) =4, then what is

(a) injective and sUijective

(b) injective

but

not

sUijective

c) not injective but surjective

(d)

neither

injective nor sUijective

What

is

(

1

+

i)4n + 5 .

- ---- -:

4

..---

3

equal to, where n IS a

(1-i) D+

natural

number

and

i

=

F1 ?

(a)

2

(b)

i

c)

2 i

(d)

i

n(A

x

B) equal

to

?

a)

0

b)

9

c) 15

d) 20

21.

I f f(x) =

ax

+ b and g(x) = ex + d such that

f(g(x)) = g(f(x)), then which one

of

the

following

is

correct ?

(a)

f c)

=g(a)

(b) f(a)

=

g(c)

c)

f c) = (d)

(d)

f(d) = (b)

22.

18.

What is the number of

ways in which one

can

post 5

letters in

7

letter

boxes ?

I f

A and

B are

square

matrices

of

second order

such that lA I = 1, IBl = 3, then what

is

I3AB I equal to ?

19

(a)

3

(b)

-9

c)

27

c)

5

7

(d)

None of the above

d) 2520

or the next three 03) items that follow :

What is the.

number

of ways

that

a cricket Consider the function f(x)

=

x -

1

.

x+1

team of

players can be made

out of

15

players?

a) 364

(b)

1001

c)

1365

d) 32760

23.

What

is

f(x)

+

1

al

to

?

+x equ

.

f(x) -1

(a)

0

(b)

1

c)

2x

(d)

4x

B-OEBB-N-NBS (

6 -A

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7/40

16.

f : N ~ N lit, ~ N ~ ilfqd l1t.f-m

(

1

+ i)4n +5

v:Tm

I;

f(x) -1

(a) 364

b)

1001

(c) 1365

(d) 32760

B-OEBB-N-NBS

(a) 0

b)

1

(c)

2x

(d) 4x

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8/40

2

4 . Wh

at

is f 2

x) eq

ual t

o ?

a)

b)

c)

d

)

f x)

+ 1

f x)

+

3

f x)

+

1

3f

x)

+ 1

3

f x

) + 1

f x)

+

3

f x)+

3

3

f x)+

1

25. W

hat

is f

f x))

equa

l to

?

a

)

x

b)

X

c)

1

X

d)

Non

e ofthe

ab

ove

or

th e

ne x

t fiv

e05

)

item

s t

hat

fo

llow

:

1

)15

C o

nsid

er

th

e

exp

ansio

n x

2

+;-

26 .

What

is

the

independent

term in the

giv en

e

xpan

sion

?

27.

a)

21 03

b)

30

03

c)

4

50 3

d)

N on

e ofth

e ab

ove

Wha

t

is the

ratio

o

f co e

fficie

nt o

f x

1

5

to

t

he

te

rm

ind

epen

dent

of

x

in

the

giv e

n

expansion

a)

1

b

)

1/2

c)

2 /3

d)

3/4

28.

C on

sid er

the

follow

ingstat

emen

ts

:

1

2.

Ther

e a

re 1

5

terms

n the

give

n

e

xpan

sio n.

T

he c

oef fi c

ie nt

of x

12

is e

qual

to t

hat o

f

x3.

W hic

h of the

ab

ove stat

emen

ts

is/a

re co

rrect

?

{a)

1

only

{b)

2 o

nly

c)

B

oth1

and

2

d)

Neit

her1

nor 2

29

. C on

sid er

thef

ollow

ing

state

ment

s :

1

2.

T h

e te r

m co

nta in

ing x

2

do e

s not

ex is t

i

n

th

e

give

n exp

ansi

on.

T he

sum

of t

he c

oe ffi

cients

of

all th

e

t

. t

h .

. .

2

1

5

erm

s m

eg

iVen

ex pan

siOn

IS

.

W

hic h

o f th

e abo

ve state

men

ts

is/are

corr

ect ?

a )

1

only

{b)

2 on ly

{c)

B

oth1

an

d

2

{d)

Ne

ither

1 no

r 2

30. W

hat

is the

sum

ofth

e c

oe ffi c

ie nts

ofthe

m

idd

le

t

erms

in the

giv en

e xp

ansio

n ?

a)

C

15, 9

)

{

b)

C 16

, 9 )

c

)

C

16, 8

)

{d

)

N o

ne o

f

the

above

8-0E

BB-N

-NBS

8

-A

3

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9/40

24. R2x) a m < ~ \ ~

?

(a)

f x) + 1

f x) + 3

b)

f x) + 1

3 f x) + 1

I

3f x)+1

c)

f x) + 3

d)

f x) + 3

3f x)+1

25.

f{f{x))

~ a m < ~ \ ~

?

(a)

X

(b)

X

c)

1

d)

i i ~ ~ - : r @

m : m : l ~ r i k l ( o s ) J J R i i i l ~ f F n :

(x

2

+ ~ r i i > ~ R h ~ 1

26.

~ '11 ;

ii

tfG

1fliT ~

?

a)

2103

b)

3003

c)

4503

d)

i i ~ ~ : r @

a) 1

b) 1/2

c) 2/3

(d) 3/4

B-OEBB-N-NBS

28.

f . i ' l ~ f u l d R fcRm: :

1.

~

'11 ;

if

15

tfG

~ I

2. x

12

Iii

x

3

il il a m < ~ \ ~

I

ii

cm mffi l M?

a)

~

(b) ~ 2

c) 1afu: ~

d) ~ o) 1 f t \ ~ ~ 2

29. f . i ' l ~ f u l d R

fcRm:

~ :

9 -A )

1. ~

'11 ;

ii x

2


10/40

31. What is

.}1

+ sin 29 equal to ?

(a)

cos

9 - sin 9

(b)

cos

9

+

sin 9

c)

2 cos 9 + sin 9

(d) cos 9 + 2

sin

9

'

32. A lamp post stands on a horizontal plane.

From a point situated

at

a distance 150 m

from

its

foot, the angle of elevation of the top

Wh

.

1 3 14.

al

?

35. at1s

SID

- SID

-

equ to.

5 5

' '

(a) tr/2

(b) tr/3

(c) tr/4

' (d) tr/6

is 30 .

What

is

the

height of the lamp post ? 36.

What 18

cos

7x - oos 3x al to ?

. . . equ .

SID

7x

2siD5x

+siD3x

a)

50m

b)

(c)

d)

lOOm

33.

If

cot A = 2 and cot B = 3, then

what

is

the

value of

A

+

B

?

34.

(a) tr/6

b) 1I

(c) tr/2

(d) tr/4

What is

sin

2

66. .

2

(a) sin 47

b) cos

47

c)

2 sin 47

(d) 2 cos 47

D

D

equal to?

2 231

S I D

-

2

37.

(a)

tanx

(b)

cotx

(c)

tan2x

d)

cot2x

In a triangle ABC, c =2, A =45 , a =2 J2

then what is

C

equal to

?

a)

o

(b) 15

(c)

45

(d) None of the above

38. In a triangle ABC, sin A cos B

=

cos

C, then

what

is B equal to. ?

(a) "

(b) tr/3

(c)

tr/2

(d) tr/4

B OEBB N NBS

( 10-A)

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11/40

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12/40

39

If

-

m ( -x_+ ....::y...:..) a + b th h t . tan x

=-- enw a ts

sin

x -

y)

a - b tan y

equal to

a)

b

a

b)

a

b

c)

ab

d) 1

40

I f

sin A sin 60 - A) sin 60 + A) = k sin 3A,

then what is k equal to ?

a)

1/4

b) 1/2

c)

42 Which one of the following

is

one of the

solutions of the equation tan 28 tan 8 = 1 ?

a) n/12

b)

n 6

c)

n/4

d) n/3

For

the

n xt three

03)

items

that

follow

Given

that

16

sin

5

x

=

p sin 5x

+

q sin 3x

+

r

sin

x.

43 Wh:at is the value ofp

a) 1

b)

2

c) 1

d) 2

B OEBB N NBS

2

A

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13/40

sin x+y) =a+ b

39. '

sin

(x - y) a - b

GIU'R ~

a)

b

a

b)

a

b

c) ab

d)

1

tan x

tany

42.

f . l ~ < t W l f < S i d it it

m

1.% fl Jil'fiiiT ~

~ TJ


14/40

orth enext tw

o 02 )items thot

follow :

50. T he

two circles tou

ch each oth r if

Let Sn de

note

th

e sumo

f first n term

s

o

f an AP and

3Sn =

S2n

4 6

What i s S

3

n :

Sn equal

to

?

a) 4

:

1

b) 6

: 1

c)

8:

1

d

) 10: 1

47. W

hat is

S

an : S

2

n eq

ual

to?

a) 2

:. 1

b) :

1

c) 4: 1

d) 5

:1

48.

What is thele

ngth of the

latus rec tum of the

ellipse2 5

x

2

+

16fl

= 40

0 ?

51.

a) 25/

2

52.

b) 25

/4

c)

16/5

d) 32/5

o

r the

n

ext two

02)

i

tems thot

fo

llow

:

a

)

b)

c

)

d)

c= +b

2

1

1 1

=

c a2 b2

1

1

c=

-

a

2 b2

1

c = -- -

::---,-

a2 +

b2

A 3, 4)

and B 5, - 2)

are two points

and P is a

p

oint such tha

t PA = PB.

If

the

area o

f

tr

iangle PAB is

10 square u n i

t,

wha

t are the

coordinates ofP?

a) 1,0)

only

b) 7,2

)only

c)

1, 0) o r

7,

2)

d)

Neither

1

, 0)

no r 7, 2)

W h a t is

the product of

the perpend

iculars

drawn from the

points

~ a - b

2

, 0) up

on

the

l ine bx

cos a

+

ay sin

a

= ab

?

a) a

2

d

) a+ b

Co

nsider the ci rc

les +

f

+2

ax + c = 0 a

nd

x

2

+ y

2

+ 2by + c

= 0

53

. Which one

of

t

he follo

wing is corre

ct in

49. W

hat is the dis

tance between

the centres o

f

the

two circ

les ?

a)

+ b

2

b)

a

2

+ b

2

c)

a+ b

d)

2 a+ b)

8-0EB

B-N-NBS

4 A)

f

h

t

.

x 1

y 2

a

nd

respec

t o t e equ a

Ions =

2

3

2x+3y=5

?

a)

They rep

resent two li n

es

whi ch

are

parallel .

b)

They rep

resent

tw

o lines whic

h

are

perp

endicular.

c) The

y represent t

wo lines whi

ch are

neither paral

lel nor perpend

icular.

d)

The f i rs t e qu

ation does no t

represent a

line.

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15/40

m ; m ; ~ m ;;7 02)

J RiiiT


16/40

F

or

th

e ne

xt three

03

) items t

hatfo

llow :

o

r the

next

t

wo

02) items

that

follow

:

Conside

r a sp h

ere p a

ssin g t

hrough

the orig

in a

nd . The l

ine join

ing

the p o ints

2,

1

, 3

) an d

4, _ 2,

5)

the poin

ts 2,

1 - 1), 1

,

5

- 4),

- 2, 4 -

6).

54

.

What is

the rad iu s

of

the

s

p h ere ?

a)

Ji2

b)

/14

c) 12

d) 14

5

5 .

What is

the

centr

e of

the sp h e re

?

56.

a

) -1

, 2 - 3)

b)

1,- 2, 3 )

c)

1, 2

- 3)

. d

)

-1 -

2 - 3)

C onsi

der

the followin

g stat

ements

:

1.

T h e sp

here p a

sse s t

hrough

t

he

p o

int

0

, 4, 0).

2. T h

e p o in

t 1,

1, 1)

is at a dis

ta nce o

f

5u

nit from

thecen

t re of

the sph er

e.

W

hichof

th

e

abov

e s

tatemen

ts

i

s /are co

rrect ?

a)

1o

nly

b)

2on

ly

c)

B

oth 1

and 2

d)

N

ei ther

1 no

r

2

cuts

th

e

plan

e 2x

+ y - z

=

3

.

57.

W h ere

do es

the l in e c

u t

the

p

lan e ?

a

) 0, - 4,

- 1)

b)

0,-

4 ,1)

c)

1, 4, 0)

d)

0, 4,

1)

58. W

hat is

the ratio

in

w hi

ch

the plan e d

ivides

the

line?

a)

1 :

1

b)

2:3

c)

3 :4

d)

N

oneof

the abo v

e

or

the

ne

xt two 02

)

ite

ms

that f

ollow

Co

nsider

th

e

plan

e p ass i

ng t h ro

u g h

the points

A 2, 2,

1), B

3, 4 2)

an d C

7, 0, 6

).

59.

. 60 .

W h

ich on e

of

the followin

g point

s li es o

n

the

plane?

a)

1,

0, 0)

b)

1, 0,

1)

c)

0, 0

, 1)

d)

N o

ne of th

e above

W

hat are

th

e

dire

ction r

atio s of

t

he

nor

m al

to

th

e

pl

ane?

a)

b)

< 0,

1, 0

>

c)

< 1, 0 -

1

>

d

)

N

one of

the ab o

ve

8-0

EBB-N-

NBS

6A)

www.examrace.co


17/40

1@ f.r.s. 3fu:

f.r.s.m

c2. 1 ,- 1), o.

5 ,-

4),

~ ~ ~ ~ ~ 1 \ f < r . m : ~ I

54.

~ c l i ' t ~ < ~ m ~ ?

a)

- 12

b)

J14

c)

12

d)

14

55.

~ ' P T ~ < i m ~ ?

a)

-1, 2 ,- 3)

b)

1,- 2, 3)

c)

1, 2 ,- 3)

d) -

1 , - 2 , -

3)

56.

f.l' lfeif&d

'11: f


18/40

For the

n

ex t

thr

ee 03

) it e

ms th

at

follo

w

{

x2

5

Con

sider

the f

uncti

on f(

x)

=

~

X 13

,

x:>3

X>3

61

Wha

t

i

s

lim

fx)

equ

al to

?

x->

3

(a)

2

(

b)

4

c

)

5

(d)

1

3

62

C on

side

r th

e follow

ing

sta

teme

nt s:

1. T

he fu

nctio

n is

disco

ntinu

ous

at x =

3.

For the

n

ext

th

ree 0

3) it

ems th

at

follo

w

The

line

2y

=

3

x +

12

cuts the

para

bola

4y

=3x

2

64

W

here

does

th

e

l

ine cu

t

thep ar

abola

?

(a)

A

t - 2, 3

)only

b)

A t

4, 1

2) on

ly

c) A

tboth

-

2, 3) a

nd (4

, 12)

(d

)

Neit

her

a t 2,

3) no

r a

t (4, 12

)

65

W

hat

is

the

are

a

e

nclo

sed b

y th

e para

bola

and

the

li ne

?

(a)

2

7 s

quare

uni

t

b)

36

s

quare

un

it

c

)

48

squa

re

unit

(d)

54

squa

re

unit

2

. The

func

tion

is

no

t

d

iffer

entiab

le

at 6

6

Wh

at is th

eare

aenc

losed

b y

the pa

rabo

la, th

e

x

=

0.

li n

e an

dthe

yax

is in

the

fi

rst

qu a

dran

t?

W h

ich

ofth

e above

state

men

ts is

/are c

orrec

t ?

(a)

7 sq

uare

un

it

(a

)

1only

(b)

14

sq

uare

un it

b

) 2

only

c

) 20

sq

uare

un it

(d

)

21

sq

uare

un

it

c)

Bot

h a

nd 2

(d

)

Neit

her 1

nor

2

67

Cons

ider

the

fu

nctio

n

63

W

hat is

the

d

iffere

ntial

coef

ficien

t of

f x)

at

X 1

2?

a) 5

/2

b)

5

c)

1/5

(d)

1/10

B

OEB

B NN

BS

18

-A )

l

an

kx

f x)

=

x

3x

+2k

2

,

x


19/40

{

x2 -5

q

)ff.f fl:x) =

~ +13,

x,;3

x>

3

61

lim fl

:x) 3

(a) 2

(b) 4

(c) 5

(d) 13

62.

~ < t B f R

:

1.

q)ff.f X =

3

R 3Rimr I

2. q) ff.f X=

0 R 3jq


20/40

68.

C o

nside

r th

e fo llo

wing

state

men

ts :

1

.

The

fu nc

ti on

f x)

= [x]

, w h e

re

[,] is t

he

g

reate

stin

teger

fun

ction

defi n

ed o

n

,

is con

ti nuo

us a

t a ll

po i

n ts

exc

ept at

x=O

.

2

.

T he f

uncti

onf

x) =

sin Ix

I i s

conti

nuou

s

fora

llxE

R.

W

hic h of

t

he ab ov

e sta

teme

ntsi

s /a re c

orrec

t?

a)

1o

nly

b)

2

only

c)

B

oth 1

and

2

d)

Neith

er 1

n

or 2

or tM

n x

t

two

02

)

i

tem

that

fo

llow

:

Co

nsid

er t

he curv

e x =a

c

os

e + e

si

n e

and

y

= a s

in

a - e

co

s 0).

69.

Wh

ati s

dy

equa

l t

o

?

dx

a)

tan

a

b )

cote

c

)

sin 2

0

{

d)

cos 2

0

d2

70

.

W

hat is

--f

eq u a

l

to

?

d

x

a) se c

2

e

b )

-cos

ec

2

e

c)

sec

3

e

e

d)

N

oneof

th

e ab ov

e

71.

Wh

at is

th

e area

of

the

p

arab

o la

l =

4bx

boun

ded b

y

its lat

us rect

um?

a)

2b

2

/3

squ

are u

nit

b)

4b

2

/3 squa

re

unit

c)

b

2

squ

are

un

it

d)

8b

2

/3

sq

uare

unit

72

. 1f

y=

x ln

x +

xex,

then

w

hat is

the va

lueof

dy

atx

= 1

?

dx

7

3.

74.

7

5.

a)

1+

e

b)

1

e

c)

1+ 2e

d

)

N

one o

f th

e abo

ve

l

ogs

l +x)

W

hat

is

lim

eq u

a l

to ?

x

-- 0

a)

b)

c)

d)

1

l

og s e

log

5

e

5

W

hat

is

lim

X-->0

a)

log 5

e

b)

log

s e

c)

5

d

)

1

W

ha ti

s lim

a) 5

b)

2

c)

1

d) 0

5x

1

eq

ua

l o?

X

-

.;1:.. .c..::::2... _ 3_ -=-

._.

. c . . : : : : n ~

a

?

eq

u to

.

12

+2

2+3

2

+

... n2

B-OE

BB-N

-NBS

2

0- A)

www.examrace.co


21/40

6

8.

f

.tq

f

ft

fl

io

~

14

tI


26/40

9

1

9

If

I a

I

= 2

, I

b I

=

5

and

I a

x b

I =

8,

t

hen

W

h

ich

on

e

o

the

fo l

low

ing

is

th

e

uni

tve

cto

r

wh

at

is a

b

e

qu

al t

o ?

a

)

6

b)

7

c

)

8

(

d)

9

-+

92

I

f I a

+

b

I =

I

a

-

b

I th

en

w h

ic h

on

e

o

the

foll

ow

ing

i s

cor

rec

t ?

(a)

b

)

I

a I =

I b

-+

a

is

p a

ra l

lel

to

b .

)

~

di

u

c

a

ISpe

rpe

n

c

a

rto

b .

d)

a

is

a

u

ni t

ve

cto

r.

93 .

Wh

at

is t

he

are

a of t

he

tri a

ng

le

OA

B

w

he

re

0

A

A

A

is

the

ori

gin

, O

A

= 3

i

- j

+

k

a

nd

-

.

A

A

A

O

B

= 2

i

j -

3 k

?

(a

)

b)

c)

5

../6

sq

ua

re

u

ni

t

5.

./6

t

-

-

sq

ua

reu

m

2 .

J

sq

ua r

e

u

ni t

d)

J3

ri

squ

are

un

it

7

li

pe

rpe

ndi

cu

la r

to

bot

h a

= -

i

+

j +

k

an

d

4

/1

A

A

b

=

i

-j

+

k

?

A

A

a)

i j

J

2

A

b)

k

A

A

c)

j

k

J

2

A

A

d)

i -

j

J2

9

5 .

W

ha

t

is

th

e i

n te

rio

r

acu

te

an

gle

o

f

t

he

p

ara

ll e

lo g

ra m

wh

ose

si

de

s

are

re

pre

sen

ted

1

A

1

A

A

by

th

e ve

cto

rs

J2

i +

J2

j +

k

and

}

A

A

A

- i

-

-

j

k

?

J

2

J2

a)

60

c

)

30

d)

1

5

96

Fo

r wh

at

v

alu

e

o

Aar

e th

e v

ect

ors

A

A

A

Ai +

1+

A

j

+

1 +

2

A k

an

d

A

A

A

(

1-

A)

i

+

A

+ 2

k

pe

rpe

nd

icu

la r

?

(a

)

-

1/

3

(b

).

1/

3

c)

2/3

(d

) 1

B-

OE

BB

-N -

NB

S

2

6 -

A )

www.examrace.co


27/40

~

- -

\

II.

A

-

\

\

11

a

=

-

i

j

k

3f

u:

b

=

i

-

j

k

G

A

T

R ~

t

?

a

)

6

A

A

b

)

7

a

)

i

j

J

c)

8

(

b )

A

k

(

d)

9

c)

A

A

j

k

J

A

A

d

)

i

-

j

J

a

)

Ia

I=

I

b

1

~

~

t

l

b

)

a

,

b

R

~

t

I

c

)

a

,

b

(d)

a

l f;

l< l

i

t

I

(a

)

6

0

(b

)

4

5

c

)

3

0

9

3.

O

AB

fiT

f

ci;

o;n

t,

0

~

-

~

O

A

3

i

-

j

+

k

(l l

fl

---

- >

O

= 2

i

+

j

3

k

t

?

A

A

A

A

i

(1

A

.

j

(1

2

1..

)

k 3f

u:

(

a)

A

,

1

-A

.)

i

+

A

.j

+

2

k '

ff i

'R


28/40

F

or t

hene

xt

fou

r 04

)

ite

ms tha

t f

o llo

w :

101

.

- - 1

- ~ -

- 1

- - -

- -

4

a +

b

+

c

=0

su

ch

tha

t

I

a I

=

3,

I

b I=

5 a

nd

rr

/2

W

ha

ti s

0

--

I

c I =

7.

a

)

2ab

b

)

27t

ab

--

97

.

--

hat i

st

hean

gle

bet

w ee

n a

a

nd

b

?

c

)

t

2

ab

a

)

n

6

b)

rr./

4

c)

rr./

3

d

)

rr./2

--+

--+

--+-

-+

--

--

98.

hat

is

a

b

+

b

c

+

c

. a

to ?

a)

-

83

b)

-8

3/2

c)

7

5

d

)

-

75/

2

99.

Whatis co sine of

the

angle betw een

--

c

?

a)

1

1/1

2

b)

13

/14

c)

-1

1/1

2

d)

-13

/14

--+

--

100. Whatis

I

a

+

b

I

equal

to

?

a)

7

b)

8

c

)

10

d)

11

8

-0E

BB

-N -N

BS

d)

t

ab

F

or th

e nex

t

two

02

)

ite

ms

tha

t

f

o ll o

w:

A cy

li nd

er i s

in s

cri b

ed in

a s

phe

re o

f ra

diu

sr.

equ

al

1

02.

hat

is

th

e h

eig

ht o

f t

he

cy

lin d

er

of

m

ax i

m um

vo

lum

e?

2r

J3

a)

-

-

b

)

r

b and

c)

d)

J3

2r

J

r

103

. W

hat

i

s th

e

radi

us

of

th

e

cyli

nder

o

f

m a

xim

um

volu

me

?

a)

2r

J

3

b)

f

ir

J

3

c)

r

d

)

J

r

2

8 -

A

)

J

www.examrace.co


29/40

-

-

-

-

-

-

a +

b +

c

= o

~

i

f


30/40

F

orthe n x

t t

wo 0

2)

i

tems

that

follow

:

106

. Supp

ose A

an

d

B are

tw oe

vents.

vent B ha

s

occ

urred a

nd it is

known

that P(

B) < 1.

What

C

onsider

the

fun

ction f

(x)

=

se

c

4

x +4

withf(O) =

0

i

s P(A B

e) equa

l

to?.

J

and

f'(O) =

0.

10

4. W

hat

is

f'(x

) equal

to

?

a)

tan

x

ta n

3

x

+

4x

3

;Jc

(b)

tanx

+

ta

n

3

x

+

4x

3

(c)

sec

3

x

tan

x+

+4x

3

(d)

t a n x

tan

3

x

3

+

4x

105.

What is :f(x)

equ

al to ?

(a)

l

nsecx

ta n

2

x

+ 2x

2

+

3

6

(b)

3

/nsecx

oot

2

x

2x 2

--

2

6

(c)

4ln

secx

sec

2

x

.

2

2

--

X

3

6

(d)

l

n secx

+

t

an

4

x

12

+ 2x

2

B OEB

B N NB

S

a )

(b)

(c)

(d

)

P

A)-P

B)

P(B)

P

A)-P A

B)

P(B

)

P(A) +P

(Bc)

P(B )

N

one

o

f the

ab ov

e

F

orthe n x

t fo

ur

04)

ite

ms t

hat

fol low

:

C onsid

er even

ts A B

, C, D,

E

of

the

sam p

le spac

e

S =

ln : n i

s

an

in t

eger su

ch th at

10 s; n

s;

2

0} gi

ven

by

:

1

07.

30

-A )

A i sthe se

tof

al l eve

n num b

ers.

Bi

s the set of

all p

r ime nu

m bers .

c

=

151.

Dis

the set of

all in

tegers

s; 16.

E

s

the

se

t of

all d

ouble

digit n

u m b ers

ex

pressib

le

a

s a

powerof

2.

A,B

andDa

re

(a)

M u

tually

ex

clusive

even t

s

but

not

e

xhaustiv

e even

ts

(b)

E xh

aust ive

events

but not

m utu

al ly

exclusi

ve even

ts

(c)

M

utual ly

e

xclusiv

e

and

exhaus

t ive

even

ts

(

d)

lem

entary

ev

ents

www.examrace.co


31/40

3

f T

3

IR

m

o

2 >

W

til

iT

f> f

Rrt

f

(x )

=se

c

4

x

+4

R

,

f(

O)

=0

alR

f

'(O)

= 0

t,

fcr

.m

I

10

4.

f'(x

)

i ?

ta

n

3

x

a

)

ta

n x-

+4

x

3

(b

)

tan

x

+

tan

3

x +

4x

3

c)

s

t

an

x+

+4

x

3

ta

n

3

x

(d

)

- t

an

x

+ 4

x

3

10

5.

f x

)

i

?

(a

)

2

/n s

ec

x

tan

2

x

2

2

+

+ X

3

6

(

b)

3/

ns

ecx

r

ot

2

x

2

2

-

-

X

2

6

.

c)

4/n

se

cx

se

c

2

x

2

2

_ : : :

+

+ X

3

6

d

)

n

se

c x

+

ta

n4

x +

2

x2

1

2

10

6.

l iH

f. ;

A

alR

B

l

~

I

f

Rr

t

S =

{

n

:

n

~

~ ~

~

i

f

.

i

;

10

s n

s

20}

Documents

NDA Paper Mathematics 2014