Board : Higher Secondary Education, Government Of Kerala
Exam : HSE Statistics
Document type : Question Paper
Website : dhsekerala.gov.in
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Statistics Sample Questions :
Part I HSE I
Time :2hours
Maximum Marks : 60 scores
Cool off time :15 minutes
1. a) If A and B are two disjoint events then P (A n B ) = ——-
b ) There are two urns ,the first urn contains 8green and 12 blue balls
Related : HSE Higher Secondary Education Kerala Sociology Model Question Paper : www.pdfquestion.in/6017.html
1) The first urn [ 1+5 ] 2) The second urn
2. A card is drawn from a pack of cards. Find the probability of getting
a) a king b) a card of heart [ 2 ]
3 a ) I f E ( X ) = 10 then E(3X+ 2 ) =———–
b) Three unbiasded coins are tossed . The random variable X is defined as
the number of tails in the three tosses of a coin .Find :
1 ) Probability distribution of X . [ 1 + 4 ] 2 ) E ( X )
4 .a) Write any two properties of frequency distribution.
b) The probability distribution is X -2 -1 0 1 2
P(x) 1/12 1/3 2/12 1/4 2/12 Find 1) F (x ) 2) P ( X < 1 ) [ 2 + 3 ] 3) P ( -1<X < 2)
5 . A four digit number is formed of the integers 0,2,3 and 6 . In how many
1) it is divisible by 5. [ 4 ] 2 ) it is divisible by 2.
6. Find n such that 3 .n c = ( n-1 ) c
7 . Represent the following by o histogram :
8 . a) For a negatively skewed distribution :
[ 1) Mode < Median , 2) Mean > Median , 3)Mean < Mode , 4 ) None of these]
b) If the first four central moments of a distribution are 0 , 5 , -10 , and 30.
Find the measure of skewness and measure of kurtosis – [ 1 + 3 ]
9 . Calculate median for the following frequency distribution :
10 .a) Histogram can be used to estimate ———–
[ 1) mean , 2) median , 3 ) mode , 4 ) variance ]
b ) The average mark of 100 students was found to be 76.27. It was later
discovered that marks 87 and 54were mistakenly entered as 78 and 68.What is the
11. a ) Mean deviation is minimum when deviations are taken from ——–
[ 1) mean , 2) median , 3) mode , 4 ) zero ]
b ) The scores of two batsmen A and B in six innings during a certain
Examine which of the two batsmen is more consistent in scoring . [ 1 + 5 ]
12 .Choose the correct answer :
a ) To measure the inequalities in the distribution of income , we use ———–
[1) Frequency curve 2 ) Ogive 3 ) Lorenze curve ,4) Scatter diagram ]
b )The following frequency table presents the income in hundred earned by
13. Marks of 30 students in statistics are as follows :
31, 10, 48, 46, 45, 32, 28, 36, 31, 25, 22, 23, 24, 5, 6, 17, 30, 25, 26, 2, 8, 23 22, 40.
29, 21, 19, 16, 38,41. Classify the data by taking the width of the class as 10. [ 5 ]
14. Write down the domain and range in the set A ={ 1, 2, 4, 5, 7, 8, 11 }
15. If log 2 =0.3010 , and log3= 0.4771 , find 1) log 16 ; 2) log 12 [2 ]
16. If A ={ 1,2,3} ,B = { 3.4.5 }, C = { 1,3,5 } Prove that A-(B U C ) = ( A-B ) n
17 . Find two numbers of which sum is 30 and difference is 4. [ 2 ]
18 a ) We want to test the life time of electric bulbs and blood groups of
b) You are asked to collect information regarding annual result of SSLC
Maths :
1. Consider U={1,2,3,4,5,6,7,8} ,A={2,4,6,8} and B={2,4,8}
(i) FindAI and BI (ii) Also find (AUB)I (iii)Verify that (AUB)I =AInBI
(iv) If X and Y are two sets such that n(x) =17 ,n(Y) =23 and n(XUY) =38
2.(a) Given A={1,2,3} and B={4,5} ,find
(i) AXB (ii) the number of relations from A to B
(iii)Represent AXB and BXA graphically (1+1+2)
(b) Let f(x) =x2 and g(x) = 2x+1 be two real valued fuctions .Then find
(i) (f+g)x (ii) (f-g)x (iii) (fg)x (iv) f g x (1+1+1+1)
3. (i)Find the radius of the circle in which the central angle of 600 intercepts
(ii) Prove sin2p6 +cos2 p 3 – tan2p4 = -1 2 (2+2)
4. Consider the statement P(n) : “9n -1 is a multiple of 8” where n – N
(i) Is P(1) is true – (ii) If P(k) is true then prove that P(k+1) is true.
(iii) Is the statetment true for all ‘n’- justify your answer. (1+2+1)
5. (i)Express 1 -i in a+ib form (ii) Express 1 -i in polar form. (2+3)
6. (i)Solve the inequality 2(2x+3) – 10 < 6(x -2) where x is a real number.
(ii) Solve graphically x -2y = 4, 3x + 4y = 12, x = 0, y = 0 (2+4)
7. Consider the expansion of ( + )6
(i) Write the general term (ii) Find the middle term (1+3)
8. (a) (i) ) In how many different ways can the letters of the word
(ii) Find if n-1P3 :nP4=1:9 (3+3)
(b) (i) If nC8 = nC2 then find nC3 and nC4
(ii) In how many ways can a team of 3 boys and 3 girls be selected
9. (i) Find the 10th term of the sequence -4,-1,2,……………
(ii) Find the sum of all natural numbers between 100 and 1000 which are
10. (i) Find the value of x in which the numbers – 7 , x , -72 are in G.P.
(ii) The sum of three consecutive terms of a G.P is 26 and their product is 216