e 4- C 2) 2nf

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After removing the Polythene bag, without opening the Paper seal
take out Answer Sheet from this side.
1'1 :2019
566936
ESO-14
j1jjq kU1 3tt

D
STATISTICS/MATHEMATICAL STATISTICS
'II: 2.00 Time 2.00 Hours
'jiI': 100 Maximum Marks : 100

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8. 311TT TU ii4U.ici it iit '1Irl ij1i i it ltiii1 IIc1 1ich.-f (Negative Marking) aPT9TZft I izff m

, i rr -' sjtI 1i1 I tiit r

tTr1IL 1 II I
9. aiit aiiit 3TM it TT.3TR. L3flt
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12. 3T 9 3{1t it Piii , T 319T fic,i it ail a iL1iT.3Trt R
it3T 91 t , ft r4t it, n iiit -iq )ci it nc1l I
13. sitT.1R. (O.M.R. Answer Sheet) T 31TR thz aifi TA fi nrr
14. -Iiqi (Question Booklet) * (O.M.R. Answer Sheet) flc'1I T1 11.3R. t
s (A, B, C & D) T Iv1frf 3T t, 3H.1tTh3TR. -4i
t, it i (Invigilator) T *i'II-r ittr it IT.TZar.3n. i- t -fi'ii TW * I
.rhIk1k i4'iit -if it '.1Ici t, it T3f 11t( TT11 F14 kR lii1 I

r qi w 'r - fiqi i

41çf: -iqu vil -Riqi ft-iiIhk I tr-1tqa fi: 'IfI

1r ti4tt, 'il 1w i
 •

1. At t =0, the function f(t) — has

(a) a minimum (b) a discontinuity
(c) a point of inflexion (d) a maximum

2. The characteristic function of Wishart distribution if A W (, n) is given by

(a) 4A(0) = I I — i 0 11/2 (b) $A(0) = I I — i 0 I_h1'2
(ni)

(c) A(°)
= I — 2i E 0 I 2 (d) A(0) = I — 2i

3. For large sample size n, the distribution of Hotelling's T2 is approximately

(a) Normal (b) Chi-square (c) F distribution (d) None of these

4. In atr var ate distribution, the variance — co-variance matrix is given by

1
10—
01 0
1
_2 0
The values of R123 and r132 are respectively
11 31 11 .1
(a '- (b) ' (c) (d) 2' 4

5. Let = [X1 X2 X3]' follows N3 (0, ) where

1 001 rxi rxi

= 0 2 —1 j write = [x'J where X(1) = Then the conditional mean and

Lx'
conditional variance of givenX(1) = [ ] are respectively

(a) —' (b) (c) —' (d) 1'

6. If X is a random variable assuming only positive values, then which of the following is
true? _____ _____

(a) E(/Y)>\JE(X) (b) E(J)='JE(X)

(c) E(Ji)=±\/E(X) (d) E(J)<JE(X)

7. Hotelling's T2 statistic for testing significance of mean vector H0 : = ji 0 based on a

random sample of size N from N (jt, E), where is unknown, is

(a) T2 = ( — j)' S' ( — t) (b) 12 N ( — pj Y' (1 —

(c) T2 N—'S'(—) (d) T2 =NNl _JS 1(_)

Series-D 2 ESO-14
 ___ sint
1. t =0 ti f(t) -

(a) -z111 (b)

(c) 3f

2. rl 1A-W(E,n)t,ti 31b'MI1l 'sIIc1I, HI4I:

(a) 4A(°) = I 0 ff2 (b) A(0) = I I i 0 I -

(c) A() = I - 2i 0 I' (d) A(0) = I 2i

- 0

3 3it'ii'i n Iff r kfii T2 r cl&i wn:ir ij

(a) w-ii--i (b) i,i-f (c) Fii (d)

4. 1&1 M1I - lWuI 31Ioq

1 0
-±

= 0 1 0
1
-- 0 1
Ri 1'l TP1T IR 2 r132 1 çb-lI:

(a) (b) (c) (d)

5. '1HT{b~(=[X1 X2 X3]',N3 (O,)1ti

t1flT 3 cii:

(a) (b) (c) (d) 1'

6.
(a) E(f)>-JE(X) (b) E('fi)='JE(X)
(c) E(fi)=±E(X) (d) E(j)</E(X)
7. N(ji, ), '31T f9T[ N 3i.ii'i {I1T 3T1Tt 3 i''ii H0 :

=
T2 rd1 frr ttc1l 1i-.i IkI:

(a) T2 = ( - i')' S ( -
j) (b) T2 = N ( - pj ( -

(c) T2 =N - J S' - ) (d) T2 _ NN 1 t0)' S1 - )

ESO-14 3 Series-D
8. The limit urn equals
z -~0 Z

(a) 0 (b) 1 (c) (d) Does not exist.

2n
9. The sequence {x}, wherex = + , converges to

(a) e (b) e2 (c) \[ (d)

10. The series

x x2 x 3
+ + + ... is convergent, if

(a) Ix <1 (b) Ix >1 (c) 1 <j x <2 (d) None of these

11. The test statistic for testing the hypothesis H0 : = 0 based on a random sample of size n
from a normal population with unknown variance is t with degrees of freedom
(a) n (b) (n—i) (c) (n-2) (d) (n-3)

12. Let X1, X2, X3 and X4 be independent random variables. Then which of the following pairs
of random variables are independent?
(a) (X1 + X, X2 + )(3) (b) (X1 + X2, X3)
(c) (X1,X1 +X2 +X3) (d) (X1 +X2,X2 +X4)

13. A ball is thrown in the air. It's height at any time is given by h 3 + 14 t 5 t2, then what -

is the maximum height to which the ball reaches?

(a) 18.2 (b) 14.8 (c) 12.8 (d) 11.2

14. If X has exponential distribution with mean 2, then P[X <2] is

(a) (b) (c) (d) 1-

15. If total fertility rate of a region is 1050 and the ratio of female births to male births is
100: 110, then the gross reproduction rate, is
(a) 500 (b) 550 (c) 1155 (d) 2500

16. Let A and B be any two events with P(A) = 0.5, P(B) = 0.4 and P (A n BC) = 0.2, then
P(Bc I A u B) is
(a 1/3 (b) 1/2 (c) 1/4 (d) 0
Series-D 4 ESO-14
8. rr urn Z
z—>O

(a) 0 (b) I (c) (d) I

9. ibi-i {x},l.ix=(I

(a) e (b) e2 (c) '[ (d)

____ x x2 x3
10. aitf

(a) x<1 (b) xj>1 (c) I <!xl< 2 (d) i1

11. 3T1T? 1RU1 cI li1.Ifr1 &1 f li 1T n 31HI'- vt 1Kf ' RI '1Fbc'*1I H0: .i= O'
ir1t Id4

(a) n (b) (n—i) (c) (n-2) (d) (n-3)

12. cbf c1 114 )III ?

(a) (X1 + X2,X2 + X3) (b) (X1 + X2, X)
(c) (X1 , X1 +X2 +X3) (d) (X1 +X2,X2 +X4)

13. if It
[hi 3i1ki1c1l?

(a) 18.2 (b) 14.8 (c) 128 (d) 11.2

14. rlkz1Ic1ic, 1i4I

(a) (b) (c) —I (d) I —

15. Fb41 ?1T1 E 1050 3 '(fl 3Th E 3Ic1 100: 110 t, ?1

jcb1 1±1

(a) 500 (b) 550 (c) 1155 (d) 2500

16.
P(Bd/AB)
(a) 1/3 (b) 1/2 (c) 1/4 (d) 0

ESO-14 5 Series-D
17. The distribution from the following that possesses memoryless property, is
(a) Gamma distribution (b) Geometric distribution
(c) Hypergeometric distribution (d) Normal distribution

18. In a normal distribution with mean 110 and standard deviation 20, between which two
values approximately 68% of the data will fall?
(a) 80-120 (b) 90-130 (c) 70-150 (d) 55-195

19. What is the probability that the three cards drawn at random from a pack of 52 cards are all
black?
(a) 1/17 (b) 2/17 (c) 3/17 (d) 3/52

20. If P(X = x) = is a probability distribution of a random variable X, where x =0, 1, 2, 3, 4,

then the value of k is
(a) 15/16 (b) 16/15 (c) 16/31 (d) 7/16

21. If the mean and variance of a binomial distribution are 2 and I respectively, then the value
of the number of trials n is
(a) 1 (b) 2 (c) 3 (d) 4

22. Let (X, Y) has bivariate normal BN (4, 2, 16, 25, 3/5) distribution. Then the value of
E(Y/X = 8) will be
(a) 5 (b) 4 (c) 2 (d) 98/25

23. Let X and Y be independent Poisson variates, then the distribution of [X / X + Y = k] is

(a) Poisson Distribution (b) Geometric Distribution
(c) Binomial Distribution (d) Hypergeometric Distribution

24. Let X has Poisson distribution with P(X = 1) = P(X = 2), then the variance of random
variable X is
(a) 4 (b) 3 (c) 2 (d)

25. Let E(X) = 3 and E(X2) = 13, then the Tchebychev's lower bound for P[-2 < X <8] is
(a) 21/25 (b) 24/25 (c) 4/25 (d) 1/25

26. Three letters are to be put in three addressed envelopes. The probability that none of the
letters is in correct envelope, is
(a) 0 (b) 1/6 (c) 1/3 (d) 1/2

27. Let x1 ... x be a random sample from a population with probability density function
f(x, a) = 32e c?; x >0
a>0
The maximum likelihood estimate of a is

(a) n/ (b) n / x12 (c) (d)

Series-D 6 ESO-14
17. 11H I k1JI11c1 t T kc1l
(a) Ifl11TId1 (b) '1I1ZcIl'4&I
(c) (d) iiii

18. iiiii-i cii T1tWt1103 Hi Ilt1c1'.1

31t?
(a) 80-120 (b) 90-130 (c) 70-150 (d) 55-195

19. 52 iit t ii ui (sJT 1I i dl-1 qf 'i rr i1'iii

(a) 1/17 (b) 2/17 (c) 3/17 (d) 3/52

20.
(a) 15/16 (b) 16/15 (c) 16/31 (d) 7/16

21. 1I 1E1IT21311.siRuI bHI: 23{ 1t,3T 1t1(1I n:

(a) I (b) 2 (c) 3 (d) 4

22. 1 H1 rb(x, Y)T if ii- BN(4, 2,16,25, 3/5) I 9E(Y/X=8)'t'T1 )iIi

(a) 5 (b) 4 (c) 2 (d) 98/25

23.
(a) it&i (b) idii
(c) fq j (d)

24. T1 X t (c4 ck.1 P(X = 1) = P(X =2) * P-1 , X T ii

(a) 4 (b) 3 (c) 2 (d) 1

25.
(a) 21/25 (b) 24/25 (c) 4/25 (d) 1/25
26.
'PTF
(a) 0 (b) 1/6 (c) 1/3 (d) 1/2
27. flRTrbX1 ...X
f(x,a)=3 ax2 e;x>0
a>0

(a) n/ x13 (b) n / (c) x13 (d)

ESO-14 7 Series-D
28. The absolute mean deviation of first 2 n + 1 natural numbers about its mean is given by
(a) (n2 -1)/12 (b) 2n(n+1)/(2n+1)
n(n+1)
(c) n(n+1)/(2n+1) U)
2(2n+1)
29. The probability mass function of a random variable X is given by P(X = x) = k(C);
x =0, 1,2, n, where k is a constant. The moment generating function of X is
2 (1 + et)n
(a) [2(1 + et)]_n (b) [2(1 + et)] (d) ' 2
(c) (1 ±et'
30. If the possible values of the random variable X are x = 1, 2, 3, ..., then E(X) is
00 00

(a) P{X x] (b) P[X <xJ (c) P[X > x] (d) P[X <x]
x1 x=1

31. if the moment generating function of a random variable X is given by M(t) = (& - 1),
then the variance of X is
1
(b) (c) 2 (d)

32. The relationship between student's t and F - distribution is

(a) F(l, 1) t (b) F(l , n) = t (c) F( , 1) t1 (d) F( , ) =t

33. ifa leap year is selected at random, what is the probability that it will contain 53 Tuesdays?
(a) 2/7 (b) 3/7 (c) 53/366 (d) 7/366
34. Which test is used to check the significance in Kruskal - Wallis test?
(a) t test (b) F test (c) Z test (d) x2 test
35. The range of regression coefficient is:
(a) Otol (b) -lto+1 (c) —coto+co (d) Oto+co
36. If the two lines of regression are x + 9y = 7 and 4x + y = 16, then the ratio of standard
deviations of x to standard deviation of y is
(a) 3:2 (b) 2:3 (c) 9:4 (d) 4:9
37. In usual notations, which of the following is correct?
(a) R 23 =1-(1-r 2)(1-r 32) (b) R 23 = 1 -(1 -r 2)(1 -r)
(c) R 23 = 1 - (1 - r 2) (1 - r 23) (d) None of these
38. if the standard deviation of variable X iso, then the standard deviation of Y =8- 3X is
(a) 5c (b) 9i (c) -3a (d) 3
39. if the two lines of regression are coincident, the relation between two regression
coefficients is

(a) (b) =I (c) (d) None of these

Seiies-D 8 ESO-14
28. 31%t 2n +1 IFIb 1&4I3 T T24 H11W Tflffjj.j 1I 'tIc1l 1I—I Rl:
(a) (n2 — 1)/12 (b) 2n (n + 1)! (2 n + 1)
n(n+1)
(c) n(n+1)1(2n+1)
(d) 2(2n+1)

29. iPictcii ci-i 4kP(X=x)=k(h1C);x=O, 1, 2,...n,

X3flqf\311Id 11.1
2
(a) [2(1 + et)]_fl (b) [2(1 + et)] (c) (d)
(1 + et)n

30.

(a) P[X > x] (b) P[X <x} (c) P[X > x] (d) P[X <x]

31. tI1 II1 X t 9)11 Mx(t) = (& — 1) , I1 X 1 F(1I

(a) (b) (c) (d)

32.
(a) F(l, i = t (b) F(l, n) = (c) F(1 i = t (d) F( 11) = t

33• vc cI ii iiii 53 wiiii. 4) lIIlcbc1I 1T?

(a) 2/7 (b) 3/7 (c) 53/366 (d) 7/366
34. i fft1tt1%IT 'siT1 TVIT 4li fT s1IctI

(a) t 1TW1 (b) F 1TV1 (c) Z1TUT (d) x2 vr

35. Mcfll*1 41 -11i.n tfi:

(a) O1 (b) —1+1 (c) —co+co (d) Q+co

36.
T3Ic1
(a) 3:2 (b) 2:3 (c) 9:4 (d) 4:9
37.
(a R 23 = 1 —(1 — r 2) (1 — r 32) (b) R,3 = 1 —(1 — r 2) (1 — r 3)
(c) R 23 = 1 —(1 — r12) (1 — r123) (d) -i

38.
(a) 5 (b) 9 (c) — 3 a (d) 3 a
39• t çjI u' 1T c1I
b
(a) b = (b) b . =1 (c) >1 (d) .ii

ESO-14 9 Senes-D
40. Let X1, X2, ..., X60 be independently and identically distributed Bernoulli variates with
1 r 60 1
probability of success p = . Then the value of p X1 <20] is approximately
L
(a) 0.02 (b) 0.05 (c) 0.5 (d) 1

41. Let X: 10, 12, 7 andY: 5, 13, 9, 15, then the value of Wilcoxon — Mann — Whitney
statistic is
(a) 4 (b) 2 (c) 3 (d) 7

42. if the random sample has been drawn from U(0,1) distribution, the distribution of rtI order
statistic is
(a) Exponential (b) Uniform (c) Beta (d) Gamma

43. The minimum variance unbiased estimator (MVUE) of parameter 9 based on a random
1
sampleofszzenfromf(x, 0)=; 0 <x <0 is, forgiven X() =max(X1 ... X)
(n+1) n
(a) 2 X() (b) n X() (c) X (d) (n + 1) X()

44. The maximum likelihood estimator of 0 in f(x, 0) = e 01; — co <x < co based on a
random sample of size n, is
(a) sample mean (b) max (X1 ... X) (c) mm (X1 ... X) (d) Sample median

45. Cramer-Rao lower bound for the variance of an unbiased estimator of 0 from Poisson P(0)
distribution is
(a) 0/n (b) 02/n (c) 02 (d) n/0

46. Sufficient statistic for 0 in f (x, 0) = e' 0); x> 0 based on a random sample of size n:
(a) mm (X1 ... X) (b) max (X1 ... X) (c) sample mean (d) sample median

47. An unbiased estimator ofO infix, 0)= ; 0<x<0 is

(a) (b) 2X (c) sample median (d) largest observation

48. For Kolmogoroff— Smirnov one sample test, which one is correct?
(a) It is a test of goodness of fit.
(b) D= sup S(x) — F(x)I under usual notations.
(c) D= (S(x) — F(x)j
(d) The K — S statistic is distribution free.

49. Neymann — Pearson Lemma always provides

(a) a most powerflul test (b) an unbiased test
(c) Both (a) and (b) (d) Neither (a) nor (b)

Senes-D 10 ESO-14
40. TflRT rb x1, '••' 6O (.c4d; k1H 4 Z14'dcU MIPbdF p =

20
[ i=1
(a) 002 (b) 0.05 (c) 0.5 (d) 1
41. i1X: 10, 12,73Y: 5,13,9, 1iwrr
(a) 4 (b) 2 (c) 3 (d) 7
42. 1 11 rl1VM1HI.11.1 U(0,1) 1NTLr 1. NI'T.-I )II
(a) 'iiii4l'.i (b) 1 1.11.1 (c) 4ki (d) ii'ii

43. M1UI

F1tR3ThT1, 1ii, t X(1) =aTftT(X1

(n+1) n
(a) 2 X(1) (b) n X() (c) X1
(d) (n + 11) X()

44. f(x, 0) = eHx ; - co <x <co n 3ItR I1i1 1 3NTt, 0 T 3Tf4cbd1

FT1?rr 3Tc1
(a) {i11RTr.N (b) 3T&11 (x1 ... X)
(c) .-iii-i (X ... X) (d) 1ii1i

45 1c4j-j ic.-f P(0) 0 [fk[ 31!cbt4 1! T-kI F.i tt:

(a) 0/n (b) 02/n (c) 02 . (d) nl0
46. f(x, 0)=e_0);x0 0qT 'I'ci tfi, iI fn3nl.II w aimiftr

(a) -qii'i (X1 ... X) (b) aTftr(X1 ... X)

(c) M1I1T21 (d) iIcbI

47.

(a) X (b) 2X (c) (d)

48. 1 4 -P4c1 i TTrb
(a) I
(b) D= sup S1 (x) - F(x)I 'ctci klbcil
(c) D= IS(x) — F(x)I
(d) -4)u11.b (K)— .H.-1cl (S)
49.
(a) iiiiT (b) TTUT
(c) 1(a)(b) (d) TRt(b)

ESO-14 11 Series-D
50. If t is a consistent estimator of 0, another consistent estimator of 0 may be given by
1
(a) ta/n (b) n (c) t+ (d) t+n

51. Let x1 ... x be a random sample from

O)={O e ; X> 0
f(x,
0 otherwise
The variance of minimum variance bound estimator of 0 is
(a) 92 (b) 0/n (c) 92/n - 1 (d) 02/n
52. Non-parametric alternative to the one sample t-test is
(a) Run test (b) Signed-Rank test
(c) Sign test (d) Mann-Whitney test
53. The maximum likelihood estimate of 0 based on a sample of size n from
f(x,0)=9(1_9)x ;x =0,1,2,... is
1
(a) (c) 1/

54. The appropriate non-parametric test to test the randomness of a sample, is

(a) sign test (b) run test (c) median test (d) signed rank test
55. If n =25 and normal population has mean and variance 4 and 25 respectively, the standard
error of sample mean is
(a) 0.16 (b) 25 (c) 1 (d) 5
56. If the prob density function of a random variable X is f(x, 0) = 0 e; x> 0, 0> 0, then for
large samples, the 95% confidence interval of 0 is
1 1.96 1.96 1.96
(a) - ± (b) ± —r- (c) 1 ± - (d) None of these
n

57. For testing H0 : 0 = 0 against H1 : 0 = based on a single observation X from U (0, 0 ± 1),

the power of the test "Reject H0 if X > ", is

(a) 1/6 (b) 1/3 (c) 2/3 (d) 5/6

58. Lx1 ... xbearandom samplefromf(x,

The estimate of 13 obtained by the method of moments is
(a) (b) 2 (c) 3. (d) 4
59. If sizes of the samples n1 and n2 in Mann-Whitney U test are large, then the test statistic
U is distributed with mean
n1 —n2 n1 n2
(a) (b) 2 (c) (d) 2
2

Series-D 12 ESO-14
50. I1 t 1, 0 { ile kiii ictc1* 0 I 11IcI 3i*ci c1

(a) tn/n (b) nt (c) tn + (d) t+

51. ...

I e 8 x 0
f(x,0)=1 0
0 ;3T1
0 ((U 'Tft-T 3q,c1c4
(a) 02 (b) 0/n (c) 02/n - 1 (d) 02/n
52. T ç-T'I1T iiic1
(a) TtTUT (b) iftjii
(c) r (d) ii 1.-111t.9Vi
-

53. n 3iI1I 1r13TftTf(x,0)=0(1_0)x;x=0,1,2,... Ø4ff

I
(a) : (b) -
(c) i/ (d) -

1 +x x
1 rdk1 c4 'I 3INIi TUT
(a) '1i TTUT (b) 1 tTUT (c) Hi1ilct TtIVE (d) fr rq

55. In=25 3Th iI4-ii-i i1kUI iI: 4aIR25, 1mtzrc1 11HclI~.

(a) 0.16 (b) 25 (c) 1 (d) 5
56. 1cMf(x,0)=0e 0x;x>0,0>0,3W11t1
T 95% fc4c1c1t 3 14ft1
1 1.96 1.96 1.96
(a) :

-
(b) (c) 1± (d)
X\TflX -sin

57.

X>" Tq9T
(a) 1/6 (b) 1/3 (c) 2/3 (d) 5/6
58. HHIx x

(a) (b) 2 (c) 3 (d) 4

59. i-11U 4WI 4 u
nl +n2 ni —n2 n1 n2
(a) (b) (c) (d)
2 2 2

ESO-14 13 Series-D
60. The expected value of runs in Y XX Y X Y Y is
(a) 3.1 (b) 4.4 (c) 4.0 (d) 3.4
61. In a randomized block design with 4 blocks and 5 treatments having one missing value, the
error degrees of freedom will be
(a) 11 (b) 12 (c) 9 (d) 13

62. Let s represents variance within the cluster in cluster sampling and s variance between
the clusters. What is the relation between s20) and s2b ?

(a) s=s (b) s > s

2 2
(c) S0) < Sb (d) No relation exists between these two.

63. If the responses for treatments in a 22 factorial experiment with factors A and B having
3 replicates, are a0b0 = 18, a1 b0 = 17, a0 b1 = 25 and a1b1 = 30, then the sum of squares for
interaction AB is equal to
(a) 3 (b) 4 (c) 6 (d) 20
64. In a BIBD, with usual notations, which of the following is not true?
(a) r(k-1)=A(t-1) (b) X>r
(c) k<t (d) bk=rt
65. In a m2 Latin square design if the degrees of freedom of treatments and errors are same,
then the value of m is
(a) 7 (b) 4 (c) 2 (d) 3
66. In a 5 x 5 Latin square design with one missing value, the totals of row, column and
treatment having the missing value are 25, 40 and 35 respectively. If the total of available
observations is 100, the estimate of missing value is
(a) 10 (b) 15 (c) 20 (d) 25
67. The total number of mutually orthogonal contrasts in a 2 factorial experiment is
(a) 4 (b) 6 (c) 7 (d) 8
68. If k is the sampling interval, then in systematic sampling, the sample mean is an unbiased
estimator of the population mean for a sample of size n from a population of size N if
(a) N<nk (b) N>nk (c) N=nk (d) N=n/k
69. The error due to faulty planning of sample surveys is categorized as
(a) Non-sampling error (b) Non-response error
(c) Sampling error (d) Absolute error

70. In usual notations, the Ratio Estimator Y of population mean is more efficient than its
usual estimator obtained through SRSWOR if
1cx 1cx cx
(a) p< (b) p> (c) p= (d) None of these

Senes-D 14 ESO-14
60.
(a) 3.1 (b) 4.4 (c) 4.0 (d) 3.4

61. 4 5 4i& 4I i14i 34RT, 1sI 'Ri 41 ,

(a) 11 (b) 12 (c) 9 (d) 13

62. HTfs 3 1 Id91Ts tTMRuI Ii t-i

(a) s = s (b) s2 > s

(c) s<s (d) I

63. 34IH A B 4Ic41 22 3RT , ItEI 3, a0b0 = 18, a1b0 = 17,
AB1W 1T11II
(a) 3 (b) 4 (c) 6 (d) 20

64.
(a) r(k-1)=?(t-1) (b) X>r
(c) k<t (d) bk=rt

65. Lb m2 IT I31IHT 3R [T Ic14 ct1f~ m i Ft lII

(a) 7 (b) 4 (c) 2 (d) 3

66. 5 x 51A3 r1k1L c

1RT )1I cbHk 25,4031R 35 I 'i1 MILc1111 131T 4)ii 1o0t,
.qTR. uiii
(a) 10 (b) 15 (c) 20 (d) 25

67. 2 si4li 31TqU 1iIIb I4II E fbc1-fl &ftl

(a) 4 (b) 6 (c) 7 (d) 8
68. I1 k &14*1 31'clUcl 'i N 31IHi'1 1HF n 31III1 *114 1111 till MF1I
,

(a N<nk (b) N>nk (c) N=nk (d) N=nlk

69. 1~., i1c1TUT4llI RI
(a) —i11til-s 1~ (b) Th—l111lI 1~.
(c) lrdW..1 (d) 1RT ?iJ

70. (-II-'i 1c , 141r Tt?T T 31Id 3Ivbc1cbYR II1 II 3ilct 1t SRSWOR

1ftTRI MP-cl ItIcIlI
1cx 'cx
(a) (b) (d) llll1

ESO-14 15 Series-D
71. In a two way classification with m observations in each cell, 'r' rows and 'c' columns, the
degrees of freedom for total sum of squares is
(a) (rn—i) (c—i) (b) (r— i)(c— 1)
(c) (m-1)(r-1) (d) rnrc—i

72. In a simple random sampling without replacement if = 50, n = 100 and N = 500, then the
estimate of population total is
(a) 250 (b) 500 (c) 5,000 (d) 25,000

73. If Fisher's ideal index is 247 and Paasche's price index is 169, then Lespyre's index
number will be
(a) 361 (b) 304 (c) 225 (d) None of these

74. If the consumer price index for a year is 500, then the purchasing power of a rupee is:
(a) 50 paisa (b) 10 paisa (c) 20 paisa (d) 4 paisa

75. The probability of rejecting a lot of good quality is known as

(a) Consumer's risk (b) Producer's risk
(c) Operating characteristic function (d) Average sample number

76. Control limits for c — chart with process average being equal to 4 defectives, are
(a) UCL=8,CL=4,LCL=-2
(b) UCL= 10, CL=4, LCL=0
(c) UCL=10,CL=4,LCL=-2
(d) UCL= 10, CL=4, LCL=2

77. In usual notations, the criterion for accepting a lot in a sequential probability ratio test is
_____
___ _____ 1+ 13
(a) (b) X> ___ (c) (d) X> —
1—a ' a —a

78. If Q1 and Q3 are the first and the third quartiles respectively, the minimum limit to detect
potential outliers is
(a) 1.5 Q3 - Q1 (b) 1.5 (Q3 - Q1) (c) 2 (Q3 Q1) (d) 3(Q3 -Q1 )

79. If the value of a series at any time 't' is a function of its value at some previous time point,
such a time series is known as
(a) Harmonic series (b) Moving average series
(c) Autoregressive series (d) Fourier series

80. Marshall and Edgeworth price index number utilizes weights as

(a) quantities of base year
(b) quantities of current year
(c) arithmetic mean of the quantities of base and current year.
(d) Prices of base year

Seiies-D 16 ESO-14
71. mT'T't11 1EI ciiI r liTff cffi 1ii 'r' 1irth..li * i

(a) (m-1)(c-1) (b) (r--l)(c-1)

(c) (m-1)(r-1) (d) mrc-1

72. Y,ci ii 1I19 1fR1T'TT &fci Mrci'cli.i y = 50, n = 100 3t( N = 500, 1HF
I 1c'T
(a) 250 (b) 500 (c) 5,000 (d) 25,000

73. 3RTf ic4,i 247 31 '-iil i 1IcbI 169, i1cItb 1lI

(a) 361 (b) 304 (c) 225 (d)

74. 4ThIT Icb 5O0kb

(a) 50IT (b) 10'iI (c) 20IT (d) 4HI

75.
(a) (b)
(c) 4IcbR4 (d) 14 IRI1 9I

76. r1 fu ir 3*ET

(a) UCL=8,CL'4,LCL-2
(b) UCL=10,CL=4,LCL=0
(c) UCL= 10, CL=4, LCL=-2
(d) UCL=10,CL=4,LCL=2

77. Hfr IlTUTTh9

13 ?." > 13 ?. < ___ (d) X' >
'-13
(a) 7. < (b) (c)
1-a a a

78. tfQ1 3 t-i kThil

(a) 1.5 Q3 — Q1 (b) 1.5 (Q3 — Q1) (c) 2 (Q3 — Q1) (d) 3 (Q3 — Q1)

rcb vft i -i 't' f1 1Ifl 11 1H f1 T bc11 t W41R cIici

1vftiic
(a) Ic4bUft (b) uf (c) it&zftvft (d)

80. Ict, 11I c4(c1I

(a) 'flT
(b) HT
(c) 3m it'ThiF3T HI-111
(d)

ESO-14 17 Senes-D
81. Which among the following is a type of control chart for variables?
(a) c chart (b) p chart (c) n p chart (d) X chart

82. The general relationship between the Gross Reproduction Rate (GRR) and Net Reproduction
Rate (NRR) is
(a) GRR> NRR (b) GRR < NRR (c) GRR = NRR (d) GRR = NRR

83. The arithmetic mean of five observations is 4 and their variance is 5.2. If three
observations are 1, 2 and 6, the other two are
(a) 3 and 8 (b) 7 and 4 (c) 4 and 8 (d) 5 and 6

84. The mean of n observations is E. If the first term is increased by 1, second by 2 and so on,
then the new mean is
n n+I
(a) +n (b) (c) :+ 2 (d)

85. If socio-economic conditions of all employees are to be assessed and a random sample of
size n is required, we should preferably use
(a) simple random sampling (b) systematic sampling
(c) stratified sampling (d) cluster sampling

86. In a frequency distribution, if the fourth central moment is double of the second central
moment where the second central moment is larger than unity, then the distribution is
(a) Leptokurtic (b) Platykurtic
(c) Mesokurtic (d) Information is insufficient.

n-1
87. The sum of the infinite geometric series 3 is

(a) 8 (b) 6 (c) 5.5 (d) 4.5

11.
88. The eigen vector corresponding to the eigen value X = 3 for the matrix A = [

(d) None of these

(a)
ED
89. The quadratic form Q (x, y) = x2 + y2 is
(a) Negative definite (b) Positive definite
(c) Negative semi-definite (d) Positive semi-definite

90. For the function f(x) = lxi, the Lagrange's mean value theorem does not hold in the interval
(a) [-1,0] (b) [0,1] (c) [—I, 1] (d) [o ,

Seiies-D 18 ESO-14
81.

(a) c1k (b) pi (c) npk (d) X'lk!

82. ctr11 (GRR) (NRR) 1W"11T {J4 lc1l

(a) GRR > NRR (b) GRR < NRR (c) GRR = NRR (d) GRR = NRR

83. dHI-c14. flt4T 1bI 11kUi 5.2 TTTt1, 2 6t, 3kIVE

(a) 38 (b) 74 (c) 48 (d) 56

84. n T1 ...... a lRTT

n n+1
(a) +n (b) (c) V+ (d)
2

85. 4iFTh iir I) n ij

iFt1 4131IcWtc1t L i*it 'cii1
(a) 1*c1 1I1'*F4 (b) F iFiw-i'i
(c) 4c11 irci'i*i (d) .:!: i1i*i.i

86. t lR-1RII i T 3Tf, t .ii 4 1d1i

afir
(a) (b)
(c) cc (d) jrFii 14<1 i1 I

1 n-i
87.

(a) 8 (b) 6 (c) 5.5 (d) 4.5

88.

(a) (b) (c) ( 1) (d)

(a')
89. rId1.1Q(X,Y)=X2 +Y2
(a) UlIcf1d (b) jIccbfc1
(c) (d) .jic4c,34%ffr1

90. bc11 f(x) = ki frfr -cI'uc1 4 ii

(a) [-1, 0] (b) [0, 11] (c) {—, 1] (d) [o ,

ESO-14 19 Series-D
91. 4 th x+y-1
Solution of the differential equation = . + + 1 is
(a) 2x=(x+y)+log(x+y)+c
(b) x(x+y)+log(x+y)+c
(c) 2x=(x—y)+log(x—y)+c
(d) y(x+y)+log(x+y)+c

123
92. The rank of the matrix A = 4 5 6 is
212
(a) 1 (b) 2 (c) 3 (d) 4

93. ThevalueofA3 [(1 —x)(1 —2x)(1-3x)]

(a) —24 (b) —36 (c) 24 (d) 36

94. For the following linear programming problem (LPP)

maximize z =6 x1 +8 x2
subject to 5x 1 + 1Ox2 6O
4x,+4x2 <40
x, x2 > 0,
The optimal solution is
(a) x1 2,x2 4 (b) x1 =8,x2 =3 (c) x1 =8,x2 =2 (d) x,=6,x2 =5

95. The solution to a linear programming problem is called degenerate if one of the basic
variables is equal to
(a) zero (b) a constant (c) unity (d) undefined

96. Eigen values of a real symmetric matrix are always

(a) Positive only (b) Negative only (c) Real (d) Imaginary
97. If A and B are real symmetric matrices of sizes n x n, then which of the following is
correct?
(a) AAT = I (b) A = A (c) AB = BA (d) (AB)T = BA
98. i'°isequalto
(a) —1 (b) i (c) +1 (d) 0
99. The most suitable formula for estimating a value lying in the central part of a series is
(a) Lagrange's formula (b) Stirling's formula
(c) Newton-Gauss forward formula (d) Newton-Gauss backward formula

100. The value of za where L is a circle, is

J

(a) 27ci (b) —27ti (c) iti (d) 0

Senes-D 20 ESO-14
 x+y-1
91. 1flb(UIdx x+y+1
(a) 2x=(x+y)+log(x+y)+c
(b) x=(x+y)+log(x+y)+c
(c) 2x=(x—y)+log(x--y)+c
(d) y(x+y)+log(x+y)+c
123
92. 3iIoqA= 4 5 6
212
(a) 1 (b) 2 (c) 3 (d) 4
93. A3 [(1—x)(I —2x)(1 —3x)]TTt
(a) —24 (b) —36 (c) 24 (d) 36
94. fHThb .Lciti i -ii (LPP)f
3f.WZ=6x1 +8x2
TT
5x1 + IOx2 <60
4 x1 +4 x2 <40
x1 , x2 > 0,
lHRT.TR:
(a) x1 =2,x2 4 (b) x1 =8,x2 =3 (c) x1 =8,x2 =2 (d) x1 =6,x2 =5

95. ili ii.i i -u ti ci cs—i ii iii

(a) ii (b) U (c) 511 (d) 3ftIT1c1

96. c1I-1Icb W-IIZci 3 oqTa1i.1 TF ii T1cii

(a) ckci ic (b) Uiici.1cb (c) c4c1Ih (d)

97.
(a) AAT=1 (b) A=A' (c) AB = BA (d) (A)T = BA

98. i'° 1kIR

(a) —1 (b) i (c) +1 (d) 0
99. MIl I
(a) I"1j (b) iSeiii
(c) -.JiI3-u1'II4li (d) iiiii1

dz r1iT,
100
1z —a
iLcb1, 1iii
L
(a) 2ii (b) —2iti (c) ti (d) 0

ESO-14 21 Senes-D
 Space For Rough Work

Series-D 22 ESO-I4
 Space For Rough Work

ESO-14 23 Senes-D
 Space For Rough Work IWfT1

Series-D 24 ESO-14