MBOSE Class 11 Question Paper 2018 for Statistics

Total No. of Printed Pages ––10 (2)

HS/XI/A.Sc./S/18
(iii) nn
2018 (iv) None of these

STATISTICS
b. The r  1th term in the expansion of x  y n is
Full Marks : 100 n
(i) Cr x n r .y r
Time : 3 hours
n
(ii) Cn x n r
The figures in the margin indicate full marks for the questions
n
(iii) Cn x n y n
General Instructions :
(iv) None of these.
(i) Write all the answers in the Answer Script.
(ii) Attempt Part –––A Objective Questions serially.
c. The relation between E and  is
(iii) Attempt all parts of a question together at one place.
(i) E=1+ 

( PART : A –– OBJECTIVE ) (ii)  =1+E

( Marks : 50 ) (iii) 2 = 1 + E
(iv) None of these
SECTION – I

( Marks : 20 )
d. The Value of  2e x, taking the interval of difference
1. Choose and write the correct answer : 1  10  10 to be h is
a. The number of all Permutations of n differents (i) e x (e h – 1) 2
things taken all at a time is
n (ii) e x (1– eh)
(i) Pn
(iii) e h (e x – 1)
(ii) n
cr
(iv) None of these

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(3) (4)

e. Three unbiased coins are tossed once. The h. For the set of observations, given that median = 8
Probability of getting all tails are and mode = 4 then mean is
1 (i) 10
(i)
8
(ii) 20
3
(ii) (iii) 32
8
1 (iv) None of these
(iii)
4
3 i. Vital Statistics is mainly concerned with
(iv)
4
(i) births

(ii) deaths
f. It P(E) is the Probability of an event, then
(iii) marriages
(i) P (E )  O
(iv) All the above.
(ii) O  P (E )  1

(iii)  1  P (E )  1 j. Gross reproduction rate is defined as

(iv) P(E)>1 Total fertility  Female births
(i)
Total births

g. The mean of 7 variates is 12. If six of them are Total births
5, 13, 9,17, 14 and 10. Then the 7th variate is (ii)
Female Population.
(i) 16
Total fertility  Total births
(ii) 20 (iii)
Female births.
(iii) 11
(iv) None of these
(iv) None of these

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(5) (6)

2. Fill in the blanks : 1 5  5 SECTION –– II

( Marks : 30 )
(a) If nC 7 n C 5 , then nC1 is .

(b) If f (x) = 3 x and h =1 then the value of  f (x) is
4. Answer the following questions : 3  10  30
.

(c) If A and B are two events then P  BA  = . (a) How many words can be formed of the letters of
the word “MBOSE” ?
(d) The ratio of births to deaths in a year is called
. (b) If the 21st and 22nd terms in the expansion of
(1 + x) 44 are equal, then find the value of x.
(e) The mean of first 5 natural numbers is .

(c) If f (x ) = (1–x )(1–2x )(1–3x), then find the value of
 3f (x ).
3. State whether the following statements are True or False.
1 5  5 (d) Prove that E  =  E, where E and  are usual
(a)  [ cf ( x )]  c f(x) , where c is a constant. notations in finite difference.

(b) The number of combinations of n different things
n! 1
n (e) If X and Y are two events such that P (X )  ,
taken r (  n ) at a time is defined as Cr  2
r ! n  r  !
7 1
P (X Y )  , P (X Y )  , then find P(Y) and
(c) For the sure event S, P(S) = 0 10 10
X 
P .
(d) Geometric Mean cannot be calculated if any value Y 
of the set is Zero.

(e) For comparing the health conditions of two towns (f) Define : (i) Random experiments.
we have to calculate standardised death rate.
(ii) Compound Probability.

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(7) (8)

(g) What are the characteristics for an ideal measure 6. (a) Write down Newton’s forward interpolation
of central tendency? formula. Find the cubic polynomial interpolation
which takes on the values
(h) Calculate the standard deviation of 3, 6, 8, 12, 8, f 0  5 , f 1  1 , f 2  9 ,
6, 15, 8, 9, 7. f 3  25 and f 4  55 . 2 12  5  7 12

(i) Write three uses of vital statistics. 2 3
(b) Evalute : x 2
E
(j) Give short note on Mortality Rate.
 1 
(c) Show that 2 logx = log 1  2  if h = 1 (unity). 3
 (x  1) 
( PART : B –– DESCRIPTIVE )

( Marks : 50 )
GROUP –– B
Answer any four questions, taking atleast one from
each group.
7. (a) State and prove the theorem on total probability
GROUP –– A [only for two events]. 5

5. (a) In how many ways can a cricket team be selected
from 17 players in which 5 players can bowl? Each (b) Let X and Y are two events, such that
cricket team must include 2 bowlers. 5 1 1 2
P  X   , P Y   and P  X  Y  
2 2 3
(b) Find the value of n such that n P5  42. n P3 . 4
 
Find (i) P X
(c) Find the term independent of x in the expansion

 2 1
9
3 12

(ii) P X  Y  4
of  x  
 x

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(9) ( 10 )

(c) For any event E, Prove that P(E c ) = 1–P(E). 3 12 10. (a) Define crude death rate and point out its
limitations. Explain clearly the standardized death
rate, including the method of computation. Why
is a standardized death rate needed? 6 12
3 5
8. (a) If A and B are events with P A   , P B   and
8 8
(b) What do you understand by term “Vital Statistics”?
3 A B  How are such statistics collected and what are
P A  B   , find P   and P   . Are A and B
4 B  A their defects? What suggestions can you give for
independent? 2+2+2=6 their improvement? 6

(b) What is the chance that a leap year selected at 
random will contain 53 sundays? 3 12

(c) In a nursery school a boy is asked to write an
integer within 31 to 70. Find the probability that
he will write a number which is a multiple of 6. 3

G ROUP –– C

9. (a) Explain the term “classification” and “tabulation”
and point out their importance in a Statistical
investigation. 6

(b) Find the mode from the following data: 6 12

Class Intervel 0–10 10–20 20–30 30–40 40–50

Frequency 5 6 8 30 10

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