Plus Two/ HSE/ 12th Std/ +2 Model Question Paper : Maths www.dhsekerala.gov.in

Board : Higher Secondary Education, Government Of Kerala
Exam : HSE Mathematics(Commerce)
Document type : Question Paper
Website : dhsekerala.gov.in

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DHSE Kerala Mathematics Model Question Paper

MODEL EXAMINATION 2011-12
Maximum Score 80
Time : 2 hrs
HSE I (Including cool off time 15minutes)

Related : HSE Higher Secondary Education Kerala Botany Question Paper : www.pdfquestion.in/6003.html

General Instructions

** You are not allowed to write answers or discuss anything with others during cool off time.
** Cool off time is for familiarizing questions and planning answers.

** All questions are compulsory and only internal choice is allowed.
** When you select a question all sub questions must be answered from the same question itself.

Model Questions

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 .
11.(i)Find the slope of the line passing through the points (3,-2) and (-1,4)
(ii) Consider the straight line 3x-4y+12=0.Reduce it to the slope – intercept
12. Consider the ellipse 4×2+9y2=36
(i) Find the eccentricity (ii) Find the latus rectum. (1+1)
13. Let A (2,1,3) , B( 1,2,1) and C(3,3,2) be the vertices of a triangle

Two cards are drawn simultaneously from a well shuffled deck of 52 cards Let X denotes the number of aces.
(i)Find the probability distribution of X 2
(ii)Find the mean and variance of X

14. (i) If 6 5 7 11 11 11 P A = P B = P A U B = find P (A/B) 1
(ii) A die is thrown twice and the sum of the numbers appearing is observed to be 6.What is the conditional probability that the number4 has appeared at least once? 2

(iii)A candidate has to reach the examination centre in time. Probability of him going by bus or scooter or by other means of transport are 3 1 3 10 10 5 respectively. The probability that he will be late is 1 4 and 1 3 respectively, if he travels by bus or scooter. But he reaches in time if he uses any other mode of transport. He reached late at the centre. Find the probability that he travelled by bus. 3

15. Categorize the following 2
Walkie-Talkie, Telephone, Keyboard to CPU, TV broadcasting, Intercom
16. Identify the name given to the person who leads the system development team. Write any four qualities of him. 3
17. Write any two fact-finding techniques. In which stage of system development it is used? 3
18. What are the two methods for opening files? Write the syntax also. 2
19. Write and explain the usage of any three error handling functions in C++. 3
20. Compare any two guided communication channels used for long range communication. 3
21. Consider P and Q are two relations. Then explain the following 5
a. P U Q
b. P ? Q
c. P – Q
d. Q – P
e. P x Q