PU 11 MATHEMATICS ANNUAL EXAM QUESTION PAPER

KARNTAKA PUC 1ST YEAR ANNUAL EXAM MATHEMATICS QUESTION PAPER

1. PUC FIRST YEAR DIST. LEVEL ANNUAL EXAM FEBRUARY 2015

Code : 35 Subject : MATHEMATICS Duration : 3 Hrs 15 Min.
Date Max. Marks : 100

Instructions: ) The queston paper haste Pars A,B, C, D and E Answer al the paris
58) Use ne graph sheet or ne question on Linea Inequates in Part D

PART =A

Answer ALL the following questions. 10x1=10
4 te all the subsets of the set À = (1,2).
“2/ LetA=(1,2,3,4,5, 8), Define a relation R from À to A by

R = ((x Y) 2 y 2 x + 1, y € A} wite this elation in roaster form,
37 Express 240° in radian measure e

AT Express: LLL in the fom a + ib

Or oe" min

3° Woe he ft vee terms ofthe sequence a, = 1

A Find the slope ofthe in passing through ie points (3, -2) and (+, 4
O) some in, [exe oes +x0] 5

97° Write the negation of "Every natural number is an integer."
“AC Dee a Sample Space

ps
o IO

Buc) =
13/11 X and Y are to sets such that n(X) = 17, n(Y) = 23 and

XV = 38, fd 1X Y.
13 Deine aration Ron te st of natural numbers by
R= (Y) y 2x2 8x € Ai x y e N) wit te domain ad he range
cs arto
| Bang an 6-9) fora, he va of Sis?

ie + Cos? = - ton? = ©
hn ots? + oat 2 + 2 2

ee ci en ee

IL She ax à 3 < 64 +7 and wit the skion set

18. Find the equation of th ne parle ote ne Se—4y +2 = 0 and
poesia tough tw Pa (-2 3.

39 Find ine angle between the ines Ox + y =1 end x + ‘Ty = 1 re

29 Show that the pons 2, 35), Q(1.2. 3) and RUT. 0. -1) re colinas on

2. MATHEMATICS. PU. FIRST YEAR (ANNUAL EXAM) PAGE NO. 2
a

O |

un |

122, (fte the converse and contrapostve ofthe statement. "IF x is an even
number then is divisible by H°

28. Coefficient of variation of distribution are 70 and ther standard deviation
is 16.

18 the arithmetic mean of the distribution.

nt ou ny Pt te lee?

m,
sone lo ut ane
A om a2 mn 2 ec 6 a
qd a a oe
en bu

= {(1, 2), (2, 3), (0, =1), (=1, -3)) be a linear function from z
into z Find 100)

EE Son

cen BEA sad
BT asi me

Sade ee ofthe word INDEPENDENCE,
In how many of these arrangements,

1) do the words start wth p
1) do all the vowels always occur together

„3 Fit wm independent fx a espanol

32. Insert fve numbers between 8 and 26 such thatthe resulting sequence

war

a Gar um ie name TT, eme
3. Find the centre and ras of the cle x + y — 4x y — 45 = 0

{SFr tne date of Sins wet tom est pile

¡35 Very by the method of contradiction that YT Is rational.

37. In cass XI ofa school, 40% of the students study Mathematics, 30% study
ology and 10% ofthe class study bot Mathematics and Biology. a student
is selected at random from the cass Find the probably that he wil be study
Mathematics and Biology

3. (MATHEMATICS P.U.C. FIRST YEAR (ANNUAL EXAM)

28. A car set rom a pack o 52 cade
2), How many pints ae tere inthis sample space 7
©) Cale te probably tat he cris an ace of spades 3

(©) Calculate the probably that the card is an ace co

PART - D

Answer any SIX of the following questions. we

em ‘Signum function. Draw the graph of Signum function. Wirte is
‘domain and range ofthe function

AE
osx + Cosdr + Cos2x Y
40, Prove nat SEL Coss COREE Co 34
15 Provo by Mathematical induction that
Peers DENN, ere n €

EPT lig Ue a Fe ze
xe21210. xtyzt x-ys0 x20 yzo À
43. À group consists of 4 oils and 7 boys In how many ways can a tar ofS

=p
members be selected f the team has atleast one boy and one git ? za

ET

eg te ES N)

45, Derive the equation of a ine À + -/ = 1, where a and b are

Pk ir ec a nc ct un (AC

An ¢ 2y = 12 = Onto interest for. %)
Sasse

the pots Pl. Y: 2) and Qt, Y 2, intemal in the ratio m:n se

ma ¿o (222) = 1 (0 beng in ane)

47,

sr vu (22)

48. Find the mean deviation about the mean for the following data,

Marks | 1020 | 20-30 | 30-40 | 40-50 | 50-50 | 60-70 | 70-20
Obtained
Number of
2 14
ES ES DES

(ero) —

4. MATHEMATICS P.U.C. FIRST YEAR (ANNUAL EXAM) PAGE NO. 4

PART — E
Answer any ONE of the following questions. 10 x 1 = 10
49, a) Prove geometrically that Cos (x + y) = Cosx Cosy — Sinx Siny.
b) Find the sum to n terms of the series
1X2+2xX3+3x4+4X5 +.
la
50. a) Define an ellipse. Derive the equation of an ellipse in the standard form

2 2
2 = À:

LES

a2 p?
b) Find the derivative of Sin2x w.r.tx by using product rule.

Roo CR o