MBOSE Class 11 Question Paper 2022 for Statistics

( 10 ) Total No. of Printed Pages ––10

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10. (a) Define
2022
(i) Crude Death Rate (CDR)
STATISTICS
(ii) Specific Death Rate (SDR)

(iii) Standardised Death Rate (SDR) 2+2+2=6 Full Marks : 100
Time : 3 hours
(b) Prove that
The figures in the margin indicate full marks for the questions
(i) AM  GM  HM
General Instructions :
(ii) AM  HM  (GM )2 3 + 3 12 = 6 12 (i) Write all the answers in the Answer Script.
(ii) Attempt Part –––A Objective Questions serially.
(iii) Attempt all parts of a question together at one place.

( PART : A –– OBJECTIVE )

( Marks : 50 )

SECTION – I

( Marks : 20 )

1. Choose and write the correct answer : 1  10  10
a. The value of n Pn 1 is
(i) n
(ii) O
(iii) n  1
(iv) None of the above

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(8) (3)

6. (a) Write down Newton’s forward interpolation e. Two dice are thrown simultaneously. The
formula. Find the value of f (1) from the following Probability of getting even numbers on both the
dice is
data
1
(i)
x : 0 2 4 6 4
3
7 12 (ii)
f (x) : 8 11 20 41 4
2
(iii)
35
(b) Prove that (iv) none of the above.

  3
3 ae x  e  1 ae x , a being a constant. 5 3 1 1
f. If P (A )  , P (B )  and P (A  B )  , then
8 2 4
B 
P   is
GROUP –– B A
2
7. (a) Define the following with examples: 2x3=6 (i)
3
(i) Random experiment 1
(ii)
2
(ii) Conditional Probability
3
(iii)
(iii) Compound Probability 4
(iv) None of the above.

(b) What is the chance of throwing not less than 16 g. The mean of 7 variates is 12, if six of them are 5,
in a single throw with three dice? 4 13, 9, 17, 14 and 10. Then seventh variate is

(i) 11
(c) Let A and B are two events such that
(ii) 20
1 1 2
P(A)  , P(B)  and P(A  B)  , find P(A  B ) . 2 12 (iii) 16
2 2 3
(iv) none of the above.

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(5) (6)

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

(a) If log 4 (x  3)  2 . Then the value of x = . ( Marks : 30 )

x
(b) If f (x )  5 and h = 1, then the value of f (x ) 
4. Answer the following questions : 3  10  30
.

(c) The range of the data 7, 13, 6, 25, 18, 20, 16 is (a) If a2 + b2 = 23ab, show that
.
a  b 1
(d) The probability of winning a Twenty-Twenty cricket log   log a  log b .
 5  2
match by team A is 0.65, then the probability
that the team A may not win is . (b) Find the term independent of x in the expansion
9
(e) The ratio of births to deaths in a year is called  2 1
. of  x   .
 x

(c) Show that if f (E) is a polynomial in E then
3. State whether the following statements are True or
f (E )a x  a x f (a ) , a being constant.
False. 1 5  5
(a) log 1  log 1000  0 (d) If f (x )  (1  x ) (1  2x ) (1  3x ) , then find the value
of 3 f (x ) .
(b) Geometric mean G of any two numbers x and y is
1
G  (xy )2 . (e) In a class, 40% of the students study mathematics
and science. 60% of the students study
(c) If A and B be any two events such that A  B , mathematics. What is the Probability of a student
studying science given he/she is already
then P(A)  P(B) .
studying mathematics?
(d) If m and n are positive integers, we can define
(f) Define:
m [n f (x )] as m n f (x ) .
(i) Random experiments
(e) For comparing the health conditions of two towns
we have to calculate standardised death rate. (ii) Compound Probability.

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(4) (7)

h. The measure which takes into account all the (g) What are the various methods of collecting
data is statistical data?

(i) Mean (h) Calculate mode from the following frequency
distribution:
(ii) Median
Marks 0–20 20–40 40–60 60–80 80–100
(iii) Range
No. of Students 5 15 30 12 8
(iv) Mode.
(i) Calculate the standard deviation of 1, 3, 7, 9, 11,
13, 15, 17, 19, 21.

(j) Write about the different sources of vital statistics.
i. Vital Statistics is mainly concerned with

(i) births
( PART : B –– DESCRIPTIVE )
(ii) deaths ( Marks : 50 )

(iii) marriages
Answer any four questions, taking atleast one from
each Group.
(iv) all the avove.
GROUP –– A

5. (a) In how many ways can a cricket team be selected
j. Crude death rates are particularly useful for from 17 players in which 5 players can bowl? Each
cricket team must include 2 bowlers. 6
(i) comparing death rates of two regions.
(b) Find the co-efficient of x 2 in the expansion of
(ii) comparing death rates of same regions. 6
 1
 3x   Where x  0 . 3
(iii) both (i) and (ii)  x

(iv) neither (i) nor (ii). 1 1 1 1 1 3 12
(c) Show that 1     ......   e  
2! 4! 6! 2 e

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(2) (9)

b. The Binomial expansion of (a  b )n has 8. (a) For any event E, Prove that
P(E c )  P(E)  1 3 12
(i) n terms

(ii) (n  1) terms (b) How many words can be formed of the letters of
the word “SHILLONG”? 3
(iii) (n  1) terms
3 5
(iv) None of the above. (c) If X and Y are events with P(X)  , P(Y)  and
8 8
3 X Y
P(X  Y)  find P   and P   . Are X and Y
4 Y X
c. The value of 2e x , taking the interval of difference independent? 2+2+2=6
to be h is

(i) e x (e h  1)2

(ii) e x (1  e h ) GROUP –– C

(iii) e h (e x  1)
9. (a) What do you understand by the term “Vital
(iv) none of the above. Statistics”? How are such statistics collected and
what are their defects? What suggestion can you
give for their improvement? 2+2+2=6
d. Newton’s backward formula is used when the
interpolating value lies (b) Find the mean deviation from mean from the
following frequency distribution:
(i) in the middle of the series
Items 10–20 20–30 30–40 40–50 50–60
(ii) in the begining of the series
Frequency 7 10 20 10 3
(iii) at the end of the series 6 12

(iv) none of the above.

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