AHSEC HS 2nd Year Question Paper 2022 Buesiness Mathematics and Statistics

Total number of pages - I
32T BMST

2022

BL]STNESS NTATI{EMATICS
AND STATISTICS

Full Marks : 100
Pass Marks : 30

Time : Three hours

The figres in the marght htdicate firll marks
for the questiotts.

Q. No. 1 .L nnrk enclt 1x8: 8
Q; No.2 2 nmtrks each 2x5 = 10

Q. Nos.3-7 3 nmrks enclt 3x5 = 15

Q. Nos. 8-1"4 5 nmrks enclr 5x7 = 35

Q. Nos. 15-L8 8 nmrks eoclt 8x4 = 32

Total =L00

Contd.

1. Answer the following questions as directed : 1 x8:8
sq< emr+?tn ffif wdSlr< Es< frrt:
(a) Is the set A={xl x<x} a null set ?
a = { xl x < x\ ,{Q qe&6t fu qieG qsn?

5x 101l=0. find x.
(b) rf
2 4l

(c) What is the d.ifference between permutation and combination ?
Rflq qK' cqtr< +ttq frr
(d) The marks scored by 7 students are -
. 7 q{ Wq-qffi< ir-qTq {E
-
40, 42,38, 45, 50, 52, 55
Find Median.
r<nt frfr mlr
(e) Write True or False :

sq t?qsE fr'.tt :
A.M.<G.M.<H.M.
wrsr ${l < sr6i1E"< ${l < Slsl-s ${l
I

A What is the S.D. of two values B and 4 ?
8 ql+ 4 < nl-"rc R5-qq fr ql ?

(g) What do you mean bY combination ?
R+flq firo fr fqrz
(h) Fill in the blank :

*xfr}R"FGrB
An(BUc)=(ans) (anc)

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2. Answer the following questions in brief : 2 x5= 10
rc-q< emr+?Ft< uSo Es< fut :

(a) Distinguish between {Ol, 6 ana \6}.
{o}, f qt+ {A}-< "tt*fq frur< mtr
(b) Find 'n', if 2"C3 : " Cz = 44 : 3 .
'n' fr.fu Gl, {fr 2ncr: nc, = 44:3 |

(c) In what time will Rs.2100 amount to Rs.2835 at lOo/o p.a. S.l. ?
fr${ q:[{\o <6 10% c-{{ {ee- 2100 Rsl-< "Kl 2835 t-$t qk?
(d) Using the property of determinant, prove that
o 351
-3 o zl=0.
-s -2 ol
fi.f,{€ <r'sr-snrER qilq sil cs
0 3 sl
-3 o zl=or
-s -2 0l
I

(e) Mention fi.uo advantages and fi.r-ro disadvantages of A.M.
q:tsr rr$< ranR$ q$ drE{R{r Emq m r

3. The difference in simple interest on Rs. 1450 at 5o/o p.a:. and on
Rs.1250 at the same rate for the same time is Rs. 135. Find the
time. 3
<6 sx q<s {E'{q Rs. 1450 qFr. T5IFI W qFl, q:rFr qr-{ig {ds{ Rs. 250 <
1

TFr {s< {qf$] Rs.rss I m{ fi.ft GIt

4. Find 'n' and 'r', if
-
'n'91$'r'3 qr fi.fu GI, {fr
nP,
-
= t6go, "C, =7o.

32T BMST ts l Contd.

s. rf ({fr)
U ={2,3,5,7,11,13\,
A- {s, z, 13 },
fi - {3,7,11, 13 },
show that (Cql€$ C{)
(aUr)" =A"fr}" 3

6. rf ({fr)
A:lI z 6 -s-l
l-4 2 8j',
I

.

B=lls
o -sl
L6 -1 2)'
I

nna (frft mt)
3
5.A-38=?
oR I w<EI
Find 'x' and 'A', if
'a' $fqo 'y' { TFt BRe<t, <fr

7.
{ ;l.,rl =
[]:l
calculate mean deviation from mean from the given data :
3

3

lgqs fiTI sqya a{Rv nt<l< "{<tt fl-s fiu-d{ frfr m :
6,9, 12, 15, 18
A man deposits Rs.12O0 in a bank at the end of each year @
5o/o
8.
p.a.C.t.Whatwouldbe'hisdepositafter15years?5
(Given (1'05)rs = 2'O789)
,qci{ a1TCq eA mi$s ef6qls <q-{< rF[5 <qfr 5% Eq1fr Tos 1200 tfl qqt
$'Ft15<K<etlqsNs"<qrtfiRqF{<r(firt\ffiq(1'051ts=!'Ql$9)
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9. A certain sum of money at a certain rate comPounded annually
amount to Rs.882O in 2 years and Rs.9261 in 3 years. Find the
rate of interest and the principal. 5
rst[nl T{rR .4s fifi& <{a Dqfr {oE 2 qq<s ss2o tsl qFl 3 <q<s 9261
bo qfrirw< {< qt+ IF$t fi"fu <tr
10. Draw the graph of : (ang one) 5
6E{ q({'-{ @t 2 (fr@lrnt giat)

li) x+29-2O>O
" 3x+ g-12<O
(iil 3s -2x <6
x+g>5
.x+29 > 4
g <4

( o .t9
11. In the expansion I x' -
a | , tfr" term free from x is 5376. Find the
' \x)
value of 'a'. 5

( ,' -"1' frq<s, x {er<{ mdt fr sszo r 'a'-{ {F[ ffi qr I

\ x,i
t2. In a meeting, after everyone had shaken hands with everyone else,
it was found that 105 handshakes were exchanged' How many
persons were present at the meeting ? 5

,{?Fr cErs, Erer€arei-< Eolg qffq €R'llw Ct.ll fl a 6{ {5 1q5 bI G8f{
?<qr c-st"td\5 f'a lEqftffi qfut
oRl w
A box contains 6 white, 4 red and 7 green balls. In how many ways
can you draw
-
0 4 white and 3 red
(it 3 balls of the same colour ?
.A ur"w 6 il <rfl, 4 Et <q q$ 7 A c*6$ {4 qICq frNla r<rq gfr Eq VIE< 'flR{l -
r

0 4A<ilq$3bt<sl
(it 3 B qr+?<s<?
Contd.
32T BMST tsl

13. If (<fr) f(x) = x2 +7x+t2,
find /(A)
I /(A) < rFr fifr mt 1

when (cqfu)
I-r 2 rl
a=lo 1 -11 5
L. -1 1l

oR I weffi

Solve using Cramer's Rule : 5
C4TFF{ fuC{I< III{I{ F{I 3

3x+g+22=3
2x-39-z=-3
x+29*Z=4
t4. rf ({fr)
a={L2,3,4\
g = { 2,4,6,9\
c = {3,4, s,6\
prove that (0II6i ct R)
aU(rnc)=(aur)n(Auc).
oR I w<kl
In a class of 5O students, 24 students have taken Adv. Maths, 16
have taken Adv. Maths but not Geography. Find the no. of students
who have taken both Adv. Maths and Geography. 5
.{Br cqfr{ 50 q-{ Wq-EfA< q|qs 24 q"tr Ewe6- tEcqqt+ 16 qG{ Emein.
?ECqfr-s ErettE 6qrctrEr'tsF tFIo qq'ycflrE TcntrR cdm {b q-q-$fr< xlll
frfrmr
15. (a) The A.M. and H.M. of two numbers are 10 and 6'4 respectively.
Find the numbers and their G.M. 4

$t ni<it< {{l-s{ {t{i \sl+ {<lqs {'t<l @TT 10 SFt 6.4 I q("I"t nBt< Eulz"
fiw< s(6ftwr rl<i tsR€<t
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(b) Find the median of the following data : 4
gqtr fi{I ge]F ft]Tt fift <I :
Class : 101-200 201-300 301-400 401-500 501-600 601-700
oft:
Frequency : 8 10 15 6

<FiKFEl :

16. Calculate standard deviation and coefficient of variation from the
following data :
4+4=8
\'dE firt ser< 'Fl Tff$ RDq{ q+ fo<q< s"ftw fifr €l s
Ctass (c4ft) : 0-6 6-12 12-t8 18-24 24-30 30-36
Frequency ffiKFlvl) : 12 24 38 52 34 19
17. (a) A bag contains 10 white, 6 red, 4 black and 7 blue balls' 5
balls are drawn randomly. What is the probability that 2 of
them are red and 1 is black 7 4
qDf F je 10 Bt <rfi, 6 bt <sl, 4 A sH q$ 7 B ftql {q q[ql elF f{l
s Bt <E lt1FF-elr< cdKI td'l 2 DI <st qr+ I h sHl <6i cql<I< {stR-.c-l
ftqaz
(b) What is the probabilily that a leap year selected at random
will contain 53 SundaYs 2 4
{Ik-w< cqrci qDtsfk< ss Bt cqs{< 6amq nsftq Futat
oR I qSqt
'State the mathematical delinition of probability' What are its
lrmltatlons / 4
qglkq< ;ttf{&+ q<wl fi"{ r t{R qlfiqtc{q ft ft?
a
18. (a) What are the different types of correlation ?
c-{-T{i{< R&a aoKq{{ft frt
(b) Calculate Karl Pearson's correlation coefficient from
the
following data : 6
sqtr fr$-sqi-< q<r nrdFir-q<q{-< {qitffi e{trc fifr GI 3
xi 2 6 8 10 14 16 20
a" 1 3 4 57810

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