First Terminal Examination - June 2017
Grade:12 BIO/IT / Mathematics
(SET – B) / Max. Marks:100
Date: 13-06-2017 / Time: 3 Hrs
General Instructions:
1. All questions are compulsory.
2. Question paper consists of 3 sections – Section A , Section B,SectionC and Section D.
3. Questions in Section A carry 1 mark each
4. Questions in Section B carry 2 marks each
5. Questions in Section C carry 4 marks each
6. Questions in Section D carry 6 marks each
Section- A
1. Describe the set {x∈N :x is a perfect square, 10<x<20} in roster form
2. Find the range of the function f(x) = x-53-x.
3. Find the value of cot(-15π4).
4. Write the multiplicative inverse of –i.
Section – B
5. If 1+i1-im= 1,then find the least positive integral value of m.
6. Solve x2+x√2 +1 = 0.
7. In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French.How many speak atleast one of these two languages.
8. Find the domain and range of the function defined by f(x) = 19-x2.
9. Set A ={January,February,April,August,November.December}; Set B = {28,29,30,31}.Write the relation R given by R= {(a,b)∈A X B, a month has b number of days}. Write a subset of a relation R connected with independence day.
10. Find the values of other 5 trigonometric functions when sec x =√2, x lies in the fourth quadrant.
11. Prove that sec(270- A)sec (90- A) – tan(270-A)tan (90+A) +1 = 0.
12. If U ={a,e,i ,o,u} ,A= { a,e,i },B ={e, o,u} and C ={a,i.u} then; verify that A-(B∩C)= (A-B)U(A-C).
Section – C
13. Solve (i) 4x-102 ≤ 5x-122 , x∈R
(ii) x-43 - 22x+34 -3, x∈R.
14. Solve the following inequality graphically
5x+4y≤ 20, x≥1, y≥2 .
15. If f(x) = y = ax-bcx-a , then prove that f(y)= x.
16. If f(x) = x-1x+1 ,x ≠-1, then show that f(f(x)) = -1 x.
17. Show that sin (600) tan(-690)+sec(840)cot(-945) = 3/2.
18. Show that tan 70= 2 tan 50 + tan 20.
19. Verify the following results
(i) AU(B∩C) = (AUB)∩(AUC)
(ii) A∩(BUC) =(A∩B)U(A∩C) where A={a,e,i,o,u}, B={x: x is a letter of the word JINGARO},and C ={x: x is a letter of the word PROBABILITY}.
20. Given set aN= {ax:x∈N, a is a constant natural number}.Describe the set 4N∩6N.
21. Find the general solution of sin x+ sin 2x+ sin 3x = 0.
22. Find sin(x/ 2) , cos(x/2) and tan(x/2) if tan x = -4/3,where x lies in the second quadrant.
23. If z1= 2-i, z2=1+I , find z1 +z2+1z1-z2+1.
Section – C
24. In a group of 84 persons each plays atleast one game out of 3 viz. tennis,badminton and cricket; 28 of them play cricket , 40 play tennis and 48 play badminton.If 6 play both cricket and badminton and 4 play tennis and badminton and no one plays all the three games .Find the number of persons who play cricket but not tennis.
25. Solve the following system of inequalities graphically
x+2y≤10, x+y ≥ 1,x-y≤0, x ≥0, y ≥0.
26. (i)Convert 2+6√3i5+√3i into polar form.
(ii)Write the multiplicative inverse of (2 +3i)(1-2i) in the form a+ib.
27. Let U={ x∈N: x≤8}, A={ x∈N:5<x2<50}and C={ x∈N:x is a prime number less than 10}. Draw a venn diagram to show the relationship between the given sets .Hence list the elements of the following sets.
(i)A1 (ii) B1 (iii)A –B (iv) A∩ B1 (v) Is A –B= A∩ B1.
28. Find the domain and range of
(i) the relation R given by R = {(x,y): y= x+ 6x ; where x,y ∈ N and x<6 }
(ii) the real valued function f(x) = x2-9x-3.
29.Prove that (i) cos9x-cos5xsin17x-sin3x =-sin2xcos10 x .
(ii)(cos x + cos y)2+ (sin x + sin y)2 = 4 cos2x-y2.
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