AHSEC HS 2nd Year Question Paper 2020 Commercial Mathematics and Statistics

Total numhr of Pages -1'2

2020

COMMERCIAL MATIIEIVTATICS
AND STATISTICS

Full Marks : 100
Pass Marks : 30

Time : Three hours

marks
The fiwres in the matgin inilicate lull
fot the questtons'

7 fiark each 1x8 = I
Q. No. 1
2 fllrks eaalt 2x5 = 10.
Q. No. 2
3 natks eaah 3x5 = 1s
Q.Nos.3-7
5 nll,rks eoah 5x7 - 35
Q. Nos. I-14
8 mfirks eacll 8r4 = 32
Q. Nos. 15-18
Total =100

Cornd.

1. Answer the following questions as directed: lxg=g
w{ EdKqtR fr.fi Wrn tei frrr:
(a/ On what condition A|JB = AltB ?
ft Egs AUB = AnB ?

(b) tt
3x7
3 5tl=0. find x.

{fr
3xT
35 =o,fi.fi<tx.

(c) If P, =2520 , 6nd. r.
7

<R ' p, = zszo ar, ce-(n€rq r < $q fi6 fEt I

(d/ Find the number of terms in the expansion (Sx_2g)7 .
(sx -2s)? -v r+gt qq qr{ frlll I

fel Find the mode of the following distribution :
qdF <tTF]-{ <E{s fi.f{ Gl s

7,9, 10,8, 9, 11, 6, a, 4,9
A FiU in the blank:
{ta rR "I{.f f{t s
A.M. x H.M. =

mM{ ftI x a{NFF :t{i =

3OT CMST 121

fgl If S.D. of ,lc is 5, find S.D. of {+1.
5

lfi x< $r+ frr+r S ql, rccRa( I5 + 1 < r{Frs Rurq fr {<r

(11) lvli.at is the minimum value of the probability of an event ?

eil d{r< {slFsl< qn {i;rsn FF t< '|ft< ?

2. Answer the following questions in brief: 2x5= 1O

Eto Ed< sdr$tr{ Es{ fi-Tt s

(a,) Express { - 1, 1 } in the set builder form.

{-1, 1} o xcfu{ {1s fr'{t

[b.) In how many years S.l. on RS.5OoO at the rate of SY"o/o is
Rs. 1 10O ?

c+t <trs 5y,% Ef<s Sooo Bo< rqq l9 11oo trst {{?
(c,) Using property of determinant prove that
I -3
2
-4 -2 6l=0.
302
fi{'-r<md erqn <R e${ Gl G
2 | -3
-4 -2 6l=Ol
302
t3l Contd.

25C2,,r, hnd
@) lf 2sc, = 'C..

lfi "c, = 2tcr,.,, 'q fiof* <lt

(ei lf A.M. ol x-6, x 3, r(+3 and .16a$ is 10, then find x'
<fi x-6, x-3, x+3 qls ,+6< 5ts 10 ei FCg x< TF fi6fI GTI

3. The difference in simple interest on a certain sum of money at
1,4'5o/o p.a in 3 years and h 4Yz years is Rs 696'
Find the sum'
3

<6 14.5% {<s c$lcql Tn{d< 3 <5s qFF 47' <5s I{d {s< 4?F+I 696
io r lotr* 6fi <tt

4. Draw the graph of the inequality : 2x-936' 3

6dq lnffi cl 2 2x-V <6

3
5. If nCo + "Q+ "C, = 4, flnd n.
{fr 'co + "cr+ "c, = 4, n fi'rt ql t

or/qfit
many ways a father
ln a small town there are five schools ln how
them cannot study in
can send his three daughters so that two of
the same school ?

3OT CMST [4]

,{rE ESs 5 fi Iq qESt ,CSr nER FC.ls-{ 3 d 6{rfi-s 6i?s<(a TdE
,m< lrcs fi'{q< Eg{ qrs'4d ids 4fr{ c{ma{t
'tffo<

6. Find rhe rerm independenr of x - (2, 1 )t

sEs fi$r<n< frel-<E x aqFfl 4161 fi"fs €t I

,tr9
l'-- r" )
or / qq4

Following is the height (cm) of 11 students. From this determine
quartile deviation.
t24, \27, 126, 123, 127, 129, 125, 130, 132, 130' l2l

sEts ,4!FrW Sqi t6st ( rqfr E) fi$ q(q | ,sl Ear{ "r{t EPd$ FEai fi'fu
{<l L

124, 127,126, 123, 127,129, 125, 130, 132, 130' 121

7. What are the essential qualities of a good average ? 3

qv< qr-( ?<FEr<r B-crl €l I

8. A limited company intends to create a depreciation fund to replace
at the end of 25th vear an asset costing t 2'OO'O00 Calculate
the
rate is
amount to be retained out of proflt every year' if interest
5
3o/o P.a.

Isl Contd..

dBr fifrds csf.'trftrn 2,oo,ooo n+r fq,r {qfr qH zs <qs cqq sR'fr
qA q€t-< d&6t <'rs I rfr Iq{ {{ 3% q{, curs qE< "Kl sfr <Fs ftTli bafc{
elt qR< qtR-{r

9. Solve using Cramer's Rule :

cq'{]r{ fi'{cqr{ ITI${ ct s

2x+3A+z=9
x+29+32=6
3x+ g +22 =8

or/q.{{t

^ A=l fl 1l B=llx 1l
If ({rE) L
L2 -Li Lv -tl
I

and (ql+) (A+ B)2 = 62 a Bz ,

find t}te value of x and y. 5

(x wr y <mfift <t)

10. Prove lbat a" -b" is divisible by a-b. 5

S:rn FI Cl a'-b", o-b SF frv=M, t

3OT CMST I6l

or /w4al

A.M. of the following data set is 117.

uff Rglq{d]-{ A.M. {a 1171
Welght No. of peoPle

(€w) <rr-tq< xttl
100 1

110 4
c
120
c
x+25
140 1

5
Find x.
xfitr +<t

5
11. Prove that (cqts<l 6{)
l2a a-b-c 2a

lro 2b b-c-a =(a+b+c)3.
l"-o-a 2c 2c

are tossed simultaneously' Find the probability of
12. Three coins 5
getting at least two tails '
{"""""""slkq fifi
3tl wI q(f,dltl ficsq o<t {E t na"rcts 2H {ElE ta c"ll-{F
G{II

Contd.
t7l

13. What is correlation ? Explain witJl the help of a diagram, different
types of correlation. 2+3=5

{t{?{ ft? effi"f 6-q< €{\5 F&e eFFf+i qqqri$r{Fi qfiafiE[ rF-{ r

f.i. fina the mean and standard deviation of the given data: 5

Il(J q{rm RFdr{ ffi <t g

320, 290, 265, 300, 270, 200, 3r5.

ts. (a) tf A=\2,3\, B={4,s}, c={s,6},
find (AxB)U(BxC). 4

ffi a= \2,3l, B={4,s}, c={s,6},
(AxB)U (B x c) fi'fr fitl

of / E,a,iI

Out of 52 students, 20 play cricket and 16 play hockey'
10 students play both cricket and hockey' Find
the number of
*t o Jo not play either of the game 4
"ttd"nt" qan fur+t [ilF ql+ 16q.1n € c16 I 10 q{
52 q{ E1-4{ B5<s, 20
qits c"n a,Ha] €-q-< ff?fi fi'fr
sd wlBr ffi [ffi tcil& ur<{< <R
Flt
(b) compound lnGrest and-simple
moneY lor 2 Years are t""P"t:'l?--::'
:l;"$;;;r"'ffi"-:ff14
Find the sum and the rate of interest'
ql{ r<d {s @1{ 92O 25 Bd
q{ 900
fsliFl {d<n< 2 <6< E6{fr {o
Ro {m, lar< ql$ {5< {r< fi'f{ o<ll

t8l

16. /a/ Calculate mean deviation from mean from the given data :
4

Tl{f{ 'f{ mean deviation fi'fu <t :
7, lo, 15, 22, 26
(b) lf mean=16, S.D.=sO, find coefficient of variation' 3

q{l
<fi llql =ro, qFro R54{ =so, em<q e'rrc fi"fs I

in case of
(c) What measure oI central tendency is appropriate
open class interval ?
1

(<& qd91?
{6 c{ft qwldls (sln F6{ eRqq dR$"i

numbered from 1 to 10. Find
the
17. ia) A bag contains 10 balls
random bears a number
probability that a ball selected at 4
that is a multiPle of 2 or 5'
qEqlsti:< <q
,4bt c<fls 10 {d q(Eq$ 1 c{r4 1o {i:111 fr{ 'F '!B
ffi; qt , z < st slavs ci{i c'il < {.tfu fi'rir .< I

thrown simultaneously at random'
fu) A pa:r of unbiased dice is
Find the Probability of getting
/, at least a 6 4
/ii) a total of 9 Points'
fr'mq fi t?l
ttt qrfuu{v< sfi ffryw< 'qrtrcn
{, q& {Fs sA 6 cail<F
r"{X 6$tF clxE6r< fln 9 c{r<K
6, qg< eF ltl<
qsiGq fi6 clr
Contd.
1e1

Or / qqat

Compound Interest ior 2nd year on a certain sum of money
at 4o/o p.a is Rs 25. Find C.I. for 3rd year. 4

<qR aol" To{ qFs cftnl {dw{ fr6:{ <F{ rqh p zsFo <e EQr
<q<< uqfr w Fffi?

18. (a,l Calculate Karl Pearson's correlation coefflcient. 5

Tl{ Ar<Td< T{-i{rffi e6fRT fr.fl 4-{ I

')c:1234567
g : 3 5 6 8 10 11 12

Or / qs.?

tf f (x)=v2 -3t+2, find /(A) if

[ 3 ', ')
ot o
^=l[-r I o-l I

rft;1x;=;'-3r+2 qr, Frs /(A) fifrGl{fi

r 3 r 2)
o=l o r 4ll
L-t , o]

3OT CMST [10]

@/ Under what condition two matrices are conformable for
addition or subtraction ? 1

ft E6E ttt cfrasm clFt <l Rcfltsa qs< t
(c,f What are the subsets of the set
e={ L {3, s},6 } ? 2

s-+< q@'&F ts'rq".,'*,r{F fr{:
A={ 1, {3, s},6 }

3OT CMST [11]