VNSGU BA 2019 1st Year 2235 Statistics Higher Question Paper

VNSGU (Veer Narmad South Gujarat University) BA (Bachelor of Arts) 2019 1st Year 2235 Statistics Higher Previous Question Paper

*RAN-2235*
* R A N - 2 2 3 5 *
RAN-2235
F.Y.B.A. (External) Examination
March / April - 2019
Statistics Higher Paper : 1
k|Q"p : / Instructions
"uQ? v$ip?h?g r"ip"uhpmu rhNsp? D?fhlu `f Ah?e gMhu.
Seat No.:
Fill up strictly the details of signs on your answer book
Name of the Examination:
F.Y.B.A. (External)
Name of the Subject :
Statistics Higher Paper : 1
Subject Code No.: 2
2
3
5
Student's Signature
(1) S>dZu bpSy>"p A,,L$ ?p?"p `|fp NyZ v$ip?h? R>?.
(2) kpv$p (?p?N?pd flus) L?$?eyg?V$f"p? D`ep?N L$fu iL$pi?.
(3) Apg?M `? rh",,su'u Ap`hpdp,, Aphi?.
?. 1 (A) dp,,N A"? `yfhW$p"p rh^?ep? Dv$plfZ klus kd?hp?.
(6)

f (- 4) - f ( )
2
(b) ?
2
x
f (x) = x -
lp?e sp?
ip?^p?.
(5)
2
f (- 2)

(L$) "uQ?"p"u qL,,$ds d?mhp?.

(6)
3
2
3

(1)
x
2
- x
5
+ x
4
x + x - 12
lim
(2) lim
3
2
2
x " 0
x
3
+ x
2
- x
2
x " 3 x - 4x + 3

(X$) L$p?V$L$"u dv$v$'u lim x
2 2 + 1 "u qL,,$ds d?mhp?.
(3)
x " - 1
A'hp

(A) kd?hp?.

(6)

(1) kyf?M rh^?e
(2) rh^?e"p? rh?spf
(3) rh^?e"p? ?v$?i A"? kl?v$?i
(b) f(d) = 30 ? 2d ? d2 dpV?$ d = 0, 1, 2, 3, 4 qL,,$dsp? gC Apg?M v$p?fp?.
(5)
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[ P.T.O. ]

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(L$) "uQ?"p"u qL,,$ds d?mhp?.
(6)
2
3
(1)
x - 4
x + 1
lim
(2) lim 2
x " 2
x - 2
x "- 1 x - 1
(X$) gn"u ?ep?ep Ap`p?. gn"p L$p?C `Z b? r"ed S>Zphp?.
(3)
?. 2 (A) rhL$g""u ?ep?ep Ap`p?. rhL$g""p? A'?ip?dp,, D`ep?N S>Zphp?.
(5)

(b) rhL$g" d?mhp?.
(6)
(1)
1
1
Y = X
3
1
` -
j 1
x c -
m (2)
Y =
^x - 1h
4 - X
(L$) "uQ? Ap`?g dp,,N A"? `yfhW$p rh^?e"p? D`ep?N L$fu b?f kdsp?g qL,,$ds ip?^p?.
(5)
p
p
8
2
D = 50 -
,
S = 10 +
7
3
(X$) rh^?e Y = x2 "y,, rhL$g" ?ep?ep"u dv$v$'u d?mhp?.
(4)
A'hp

(A) kd?hp?.
(6)
(1) dp,,N"u d|?ekp`?nsp
(2) Ly$g MQ? rh^?e A"? kf?fpi MQ? rh^?e
(b) A?L$ h?sy dpV?$ Ly$g AphL$ rh^?e R = 20X ? 4X2 A"? MQ? rh^?e C = 4X R>?.
(6)
dl?d "ap dpV?$ L?$V$gp A?L$dp b"phhp `X?$? dl?d "ap? `Z ip?^p?.
(L$) rhL$g" d?mhp?.
(8)
(1)
log
Y
x
=
x (2) Y = X3 - 3X2 - 9X dpV?$ ?e|"sd qL,,$ds
?. 3 (A) k,,Qe"u ?ep?ep Ap`p?. kprbs L$fp? L?$ nCr + nCr-1 = n+1Cr.
(6)

(b) 4 R>p?L$fp A"? 3 R>p?L$fuAp?"? A?L$ lpfdp,, L?$V$gu fus? Np?W$hu iL$pe L?$ S>?'u 2 R>p?L$fuAp? (5)
kp'? "p Aph? ?
(L$) ? nPr = 360 A"? nCr = 15 lp?e sp? n A"? r ip?^p?.
(5)
(X$) 4, 5, 7, 6, 2, 8, 1 A,,L$p?"p? D`ep?N L$fu 3 A,,L$p?"u L?$V$gu k,,?ep b"phu iL$pe?
(4)
s?dp"u L?$V$gu k,,?epAp? A?L$u li?
A'hp

(A) ?Qrgs k,,L?$sp? ?dpZ? kprbs L$fp? L?$
!
n
n
Pr =
(6)
^n - rh!
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[ Contd.

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(b) A?L$ ?`?dp,, b? rhcpN R>?. rhcpN A A"? rhcpN B dp,, A"y?$d? 4 A"? 3 ?p? (6)
R>?. v$f?L$ rhcpNdp,,'u Ap?R>pdp,, Ap?R>p 1 ? dmu Ly$g 5 ?p?"p,, S>hpb Ap`hp"p
lp?e sp? L$p?C `Z Dd?v$hpf L?$V$gu fus? S>hpb `k,,v$ L$fu iL?$?
(L$) ? 10C3 + 2(10C4) + 10C5 = 12C5 lp?e sp? x ip?^p?.
(5)

(X$) A?L$ AcfpB `f 3 A,,N?, 4 rl?v$u A"? 5 NyS>fpsu `y?sL$p? R>?. Ly$g L?$V$gu
(3)
Np?W$hZu i?e b"?
?. 4 (A) k,,cph"p"u NprZsuL$ ?ep?ep Ap`p?. s?"u dep?v$pAp? S>Zphp?.
(5)

(b) A?L$ il?fdp,, ?Z v$?r"L$ hs?dp"`?p? A, B A"? C ?L$pris 'pe R>?. il?f"p `y?s
(6)
he"p "pNqfL$p?"u A?L$ s`pkdp,, S>Zpey,, L?$ 20% "pNqfL$p? A hp,,Q? R>?, 16% B hp,,Q?
R>?, 14% C hp,,Q? R>?, 8% A A"? B hp,,Q? R>?, 5% A A"? C hp,,Q? R>?, 4% B A"?
C hp,,Q? R> A"? 2% A, B A"? C ?Z? hp,,Q? R>?. sp? L?$V$gp "pNqfL$p? Ap?R>pdp,, Ap?Ry>,,
A?L$ hs?dp"`? hp,,Q? R>? s? ip?^p?.
(L$) ? P(A) 1
=
, P^B
1
h =
,
1
P(A + B) =
lp?e sp?
(3)
3
4
6
P (A , B) A"? P (Ar / r)
B ip?^p?.

(X$) gu` hj? " lp?e s? hj?dp,, 53 frhhpf Aphhp"u k,,cph"p ip?^p?.
(3)
A'hp

(A) kd?hp?.
(1) r"v$i? AhL$pi (2) r":i?j OV$"pAp? (3) `f?`f r"hpfL$ OV$"pAp?.
(6)

(b) 52 `?pdp,,'u 2 `?p ep?R>uL$ fus? g?hpdp,, Aph? sp? A?L$ bpv$ipl A"? A?L$ fpZu"y,,
(5)
`?y,, lp?hp"u k,,cph"p ip?^p?.
(L$) A?L$ kd|ldp,, 5 R>p?L$fpAp? A"? AdyL$ R>p?L$fuAp? R>?. s?dp,,'u 3 R>p?L$fpAp? `k,,v$ 'hp"u (6)
k,,cph"p 1 R>?. sp? s? kd|ldp,, R>p?L$fuAp?"u k,,?ep ip?^p?.
2
(X$) ? P(A) 2
=
,
1
P(B) =
,
4
P(A + B) =
lp?e sp?
(3)
3
2
15
P (A + B') 1
=
ip?^p?.
6
?. 5 (A) A,,sh?i""u ^pfZpAp? A"? D`ep?Np? S>Zphp?.
(6)
(b) 4, 6, 8, 10 A"? 12 Ahgp?L$"p? dpV?$ "7" "? A"ygnu"? ?'d ?Z kpv$u ?Ops ip?^p?. (8)
Ap kpv$u ?Opsp? `f'u ?'d ?Z L?$?ue ?Opsp? d?mhp?.
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[ P.T.O. ]

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(L$) e?R> Qg x "y,, k,,cph"p rhsfZ "uQ? dyS>b R>?. s? `f'u e?R> Qg X "u
(6)
A`?nus qL,,$ds A"? rhQfZ ip?^p?.
X
0
1
2
3
4
5
P(X)
K
0.2
0.1
K
0.05
0.05
A'hp
?. 5 (A) NprZsue A`?np kd?hp?. NprZsue A`?np"p NyZ^d? gMp?.
(6)
(b) "uQ?"u dprlsu `f'u X = 18 dpV?$ Y "u qL,,$ds A,,v$p?.
(8)
X
14
15
17
20
22
Y
8
30
35
42
50
(L$) "uQ?"p L$p?V$L$ `f'u M|V$su dprlsu ip?^p?.
(6)
X
11
12
13
14
15
16
17
18
Y
8
10
13
?
24
30
36
45
ENGLISH VERSION
Instructions:
(1) Figures to the right indicates full marks of the questions.
(2) Simple calculator (without programmable) can be used.
(3) Graph and statistical table can be provided on request.
Q 1. (a) Explain demand and supply function with illustration.
(6)
-
-

(b)
2
f( 4) f(2)
If f(x) = x
x
-
then find
.
(5)
2
f(- 2)

(c) Find the values of the following.

(6)
3
2
3

(1)
x
2
- x
5
+ x
4
x + x - 12
lim
(2) lim
3
2
2
x " 0
x
3
+ x
2
- x
2
x " 3 x - 4x + 3

(d) Obtain the value of lim x
2 2 + 1 with the help of table
(3)
x " - 1
OR
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[ 4 ]
[ Contd.

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(a) Explain.

(6)

(1) Linear function
(2) Range of a function
(3) Domain and Codomain of a function
(b) Draw the graph for the function f(d) = 30 - 2d - d2 for considering the
(5)
values d = 0, 1, 2, 3, 4
(c) Find the values of the following.
(6)
2
3
(1)
x - 4
x + 1
lim
(2) lim 2
x " 2
x - 2
x "- 1 x - 1
(d) Definelimit.Statetheanytworulesofalimit
Q 2. (a) Definedifferentiation.Statetheusesofdifferentiationineconomics.
(5)

(b) Obtain differentiation.
(1)
1
1
Y = X
3
1
` -
j 1
x c -
m (2)
Y =
^x - 1h
4 - X
(c) Find the equilibrium price using the below given demand and
(5)
supply function.
p
p
8
2
D = 50 -
,
S = 10 +
7
3
(d) Obtain the differentiation Y = x2 of the following function with the help (4)
ofdefinition.
OR

(a) Explain. -
(6)
(1) Elasticity of demand
(2) Total cost function and Average cost function.
(b) For a commodity total revenue function R - 20X - 4X2 and cost
(6)
functions C = 4X.
Howmanyunitsproducedformaximumprofit?Alsofindmaximumprofit.
(c) Obtain differentiation.
(8)
(1)
log
Y
x
=
x (2) Y = X3 - 3X2 - 9X for minimum value.
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[ P.T.O. ]

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Q 3. (a) Definecombination.ProvethatnCr+nCr-1=n+1Cr.
(6)

(b) In how many ways can 4 boys and 3 girls stand in a row so that no two
(5)
girls are together?
(c) Find n and r if nPr = 360 and nCr = 15.
(5)
(d) How many 3 digited numbers can be formed using the digits 4, 5, 7, 6,
(4)
2, 8, 1 only One time? How many of them are odd numbers?
OR

(a) In usual notations prove that
!
n
n
Pr =
(6)
^n - rh!

(b) A question paper which is divided into two sectionconsisting of 4 and 3 (6)

questions respectively. Answer 5 questions selecting at least one questions
from each section. In how many ways can a candidate select questions?
(c) If 10C3 + 2(10C4) + 10C5 = 12Cx,findx.
(5)

(d) There are 3 English, 4 Hindi, and 5 Gujarati books on a shelf.
(3)
How many total arrangements are possible?
Q 4. (a) Giveadefinitionofmathematicalprobability.Stateitslimitations?
(5)

(b) In a city three daily new papers A, B, C are published. It was found
(6)
from a survey that 20% read A, 16% read B, 14% read C, 8% read
both A and B, 5% read both A and C, 4% read both B and C and 2%
read all the three. Calculate the percentage of people who read at least
one of them.
(c) If P( )
A
1
=
, P^B
1
h =
,
1
P(A + B) =
thenfind
3
4
6
P (A , B) and P^A/ Bh

(d) What is the probability of getting 53 Sundays in a non leap year?
(3)
OR

(a) Explain.
(1) Sample space (2) Exhaustive events (3) Mutually exclusive events (6)

(b) Two cards are drawn from a pack of 52 cards. What is the probability
(5)
that there is one king and one queen?
(c) There are 5 boys and certain girls in a group. Three boys are selected
(6)
from that group whose probability is 1 thenfindnumberofgirlsin
2
that group.
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[ Contd.

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(d) If P( )
A
2
=
,
1
P ^Bh =
,
4
P(A + B) =
thenfind
(3)
3
2
15
P (A + '
B ) 1
=
.
6
Q 5. (a) State the assumptions and uses of interpolation.
(6)
(b) Findfirstthreemomentsabout"7"usingtheobservations4,6,8,10,12. (8)
FromtheseRawmoments,obtainfirstthreecentralmoments.
(c) The probability distribution of a random variable X is given below.
(6)
FromthatfindtheExpectedvalueandvarianceofvariableX.
X
0
1
2
3
4
5
P(X)
K
0.2
0.1
K
0.05
0.05
OR

(a) Explain mathematical expectation. Write characteristics of a
(6)
mathematical expectation.
(b) Estimate Y for X = 18 from the following data.
(8)
X
14
15
17
20
22
Y
8
30
35
42
50
(c) Find missing data from the following table.
(6)
X
11
12
13
14
15
16
17
18
Y
8
10
13
?
24
30
36
45
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