8/20/2019 2nd PUC Mathematics Test Sep 2015.pdf

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RURAL

PU

COLLEGE,

KANAKAPUR

A

-

56z117

RAMANAGARA

DISTRICT

FIRST TEST,

SEPTEMBER-zoI

5

Subject:

MATHEMATHICS

Time: t

hr.

30

Min

Class: II

PUC

Subject

Code

: 35

Max.

Marks

: 50

PART-A

Answer any The

question

:

t.

Define

*on

Q

by a*b:

ab

,

find

the identily

element.

5

5x1=5

5x2:10

using

determinants

5x3=15

is an

equivalence

,,

Zt.

-r.

4.

J.

Find

the;ralug

of

cot

(tan-lx+cot-ix)

rf

x+y:17

o-l

a*-y

:

fz

ol

find

x

lz

sl

[o

3l

Find'x,ii

11

Tl

:

lr_-i

l-

If

y:

log(sinx) find

{y

PART

-

B

il.

Answer

any

FIYE questions:

6. If

f(x):cos

x and

g(x):3x2find

(gof)

x

&

(fog)

x

7.

P.T.cor-'

1-r;:rr-.o.-t*,

x

€

[-1,

1]

iaFilit-n""qTmrarffioirrirrg#6"1" ,;

11.\f

Y:

\fn;ryfind

{Y

dx

12.rfy--si"''ffi

nna

#

PART-C

III.

Answer

any

FIVE

questions

:

13.

S.T.

the relation

R:{(x,y)

:

*-y

is

an integer,

yx,y

€

Z

relation

14.

P.T.

tan-t

ftE=tl:

1 tan-rx

,xfg

t

x)

2

15.

If tan-'[

*-l

)+

tan-'(

x+l)

:

r

find

.x,

'

GrJ

l"-l

T

ld.Using

elementary

operations

find

the inverse

of A:

f2

Lr

8. construct

2x2 matrix

A:[aij]

whose

elernentsgre given

by

aij:|121

i-z:

I

-n

2)

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8/20/2019 2nd PUC Mathematics Test Sep 2015.pdf

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I7.P.T.ll

a bc I

l,

u .ul

:(a-b)(b-c)(c-a)

It

c_

abl

18.

If f(*)

:J

kx+1,

if

xS

rc

is

continuous

at x:zr find

'k'

[__Cosx

,

ifx]zu

le'

if

xY:e*-Y

then

findff

'.\IV.

22.Sloveby

23.P.T

lp?*r

2x+3y+

--i

rr

25.

Differcntide

x

ffi+

lsinx)*o

w.r.

to

x

24.

Differentiate

lM

w.r.tdi

V(*-rxx-a)(x-5)

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