MBOSE Class 11 Question Paper 2019 for Statistics

Total No. of Printed Pages ––10 (2)

HS/XI/A.Sc./S/19
n
(iii) Cn
2019 (iv) None of the above.

STATISTICS
b. The general term in the Binomial expansion of

Full Marks : 100 (1  x )n is

Time : 3 hours (i) (1)r .n Cr x r

The figures in the margin indicate full marks for the questions (ii) (1)n .n Cr x r

General Instructions : (iii) (1)r .n Cr x n
(i) Write all the answers in the Answer Script. (iv) None of the above.
(ii) Attempt Part –––A Objective Questions serially.
(iii) Attempt all parts of a question together at one place. c. If f (x )  (x  1) and interval of difference is unity.
Then 2 f (x ) is
( PART : A –– OBJECTIVE ) (i) 1

( Marks : 50 ) (ii) 2
(iii) 0
SECTION – I
(iv) None of the above.
( Marks : 20 )

1. Choose and write the correct answer : 1  10  10 d. Newton’s backward interpolation formula is used
to interpolate
a. The number of all permutations of ‘n’ distinct
objects, taken ‘r’ at time is denoted by (i) near beginning
(i) n
Cr (ii) near central position

n
(iii) near end
(ii) Pr
(iv) None of the above.

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(3) (4)

e. A die is tossed once. The probability of getting an h. The range of the numbers 70, 75, 60, 22, 58, 80,
even number is 36 is

1 (i) 58
(i)
6
(ii) 48
1
(ii) (iii) 68
2
2 (iv) None of the above
(iii)
3
(iv) None of the above.
i. If Total Fertility Rate (TFR) = 5000 per thousand,
male and female ratio is 60 : 40. Then Gross
f. If E1 and E2 are mutually exclusive events. Then Reproduction Rate (GFR) is

(i) P (E1  E 2 )  0 (i) 2 per woman

(ii) P (E1  E 2 )  0 (ii) 3 per woman

(iii) 1 per woman
(iii) P (E1  E 2 )  0

(iv) None of the above. (iv) None of the above.

g. The marks obtained by 15 students in a class are j. Mean is a measure of
12, 14, 07, 09, 23, 11, 08, 13, 11, 19, 16, 24, 17,
03, 20. Then the mean of their marks is (i) Location
(i) 12.4 (ii) Dispersion
(ii) 13.4
(iii) Correlation
(iii) 12.8
(iv) None of the above.
(iv) 13.8

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(5) (6)

2. Fill in the blanks : 5 1  5 (d) Histogram is a graph of cumulative frequencies
of a frequency distribution of continuous series.
(a) If log 2 (x  1)  6 . Then the value of x = .
(e) If 12C r 12C 3 , then r = 9.
(b) If f (x )  x (x  1)( x  2) and h = 1, Then f (x ) 
.

1 1 SECTION –– II
(c) If A and B are two events, such that P (A )  , P (B ) 
2 2
( Marks : 30 )
1
and P ( A  B )  . Then P ( A  B ) = .
4

(d) In asymmetrical distribution the mode and mean 4. Answer the following questions : 3  10  30
are 32.1 and 35.4 respectively. Then the
median = .
(a) Find the coefficients of x7 in the expansion of
11
(e) The ratio of number of females to number of males  2 1
is called . x   .
 x

(b) If 2nC3 : n C3  11 : 1 , then find the value of n.
3. State whether the following statements are True or
False : 5 1  5

(a) 3 log 2  log 5  log 30.  f (x )
(c) Show that  log f (x )  log 1   , where h = 1
 f (x ) 
(b)  
If h = 1, then n ax n  bx n 1  a n

(c) If E1 and E2 be any two events such that E1  E 2 , 1 2
(d) Prove that 2    , where h = 1
 x  x (x  1)(x  2)
then P (E1 )  P (E 2 ) .

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(7) (8)

(e) If A and B are two events such that P(A)=0.4, ( PART : B –– DESCRIPTIVE )
P ( A  B )  0.7 and P(B)=k. Then find the value of k
( Marks : 50 )
such that A and B are independent.
Answer four questions, taking atleast one from
each Group.
(f) Two coins are tossed simultaneously. Find the
GROUP –– A
probability of getting at least one head.

5. (a) (i) Find how many arrangements can be made
with the letters of the word ‘MATHEMATICS’.
(g) Find the mean of first n natural numbers.
2+4=6

(ii) In how many of them are the vowels together?
(h) Calculate mode from the following frequency
distribution :
(b) Using the Binomial theorem, find the value of
Marks 0-20 20-40 40-60 60-80 80-100 (102)6. 4
No. of Students 5 15 30 12 8

n
(c) If log(m  n )  log m  log n , show that m  . 2 12
n 1
(i) Find the median of the following frequency
distribution.

Number 5 10 15 20 25 30 6. (a) Using Newton’s Forward Interpolation Formula,
find the value of f (14) from the following data. 6
Frequency 2 5 12 14 15 11
x : 12 16 20 24
f (x) : 1 5 10 17

(j) Write a short note on Crude Birth Rate (CBR). (b) Show that the first difference of f (x )  5x  4 at
x  2 is 5, interval of difference being unity. 3

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(9) ( 10 )

(c) Define the operator E and show that E  1  . 3 12 (c) If three fair coins are tossed. Find the probability
that the outcomes are all tails if atleast one of
the coins shows a tail. 4
GROUP –– B

GROUP –– C
7. (a) State and prove the addition Theorem of
Probability for two events A and B. 2+3=5
9. (a) Prove that (i) AM  GM  HM . (ii) AM  HM  (GM )2 6

(b) Three coins are tossed. Express the following (b) Draw a histogram and frequency polygon from
events by appropriate sets 4 the following data. 6 12
A : Certain event. Wages 10–15 15–20 20–25 25–30 30–35 35–40 40–45
B : Event that exactly one head appears.
No. of 50 140 110 150 120 100 80
C : Event that head appears more than once. Workers
Examine if A and B are exhaustive events.
10. (a) Define (i) Crude Death Rate (CDR) (ii) Specific
Death Rate (SDR) and (iii) Standardised Death
Rate (SDR). 2+2+2=6
(c) If A and B are two independent events, prove that
A and B are also independent. 3 12 (b) Calculate General Fertility Rate (GFR), Age-
Specific Fertility Rate (ASFR) and Total Fertility
Rate (TFR) from the following data. 6 12
8. (a) A die is thrown twice and the sum of the numbers Age No. of women No. of live Births
appearing is observed to be 8. What is the Group (in ’000) (in ’000)
conditional probability that the number 5 has 15-19 55 20
appeared at least once? 5 12 20-24 70 180
25-29 65 200
(b) Let A and B be any two events such that 30-34 64 170
5 35-39 60 120
2P ( A )  P (B )  and P (A /B )  2 . Find the value 40-44 58 60
13
of P ( A  B ). 3 45-49 50 10
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