· 2016-12-26 · b) Two tangents and 4 normals can be drawn to an ellipse from a point. c) Two tangents and 4 normals can be drawn to an hyperbola from a point. d) Two tangents

www.Padasalai.Net

Padasalai Centum Question Paper Page -1- Prepared by P.Kabilan (PG Maths)

Padasalai.net Special – Centum Coaching Team Question Paper

(2016-17)

Register Number:

PART- III

MATHEMATICS (English Versions)

Time Allowed: 3 hours] [Maximum Marks: 200

-------------------------------------------------------------------------------------------------------------------------------------------------

Instructions: (1) Check the question paper for fairness of printing. If there is any lack of Fairness, inform the Hall Supervisor immediately.

(2) Use Blue or Black ink to write and pencil to draw diagrams. -------------------------------------------------------------------------------------------------------------------------------------------------

PART- A 40x1=40 Note: (i) All Questions are compulsory

(ii) Choose the most suitable answer from the given four alternatives and write the option code and the corresponding answer.

-------------------------------------------------------------------------------------------------------------------------------------------------

1. The line 5x - 2y + 4k = 0 is a tangent to 4x2 - y2 = 36 then k is

1) 9

4 2)

3

2 3)

4

9 4)

16

81

2. If the normal to the curve x2/3 + y2/3 = a2/3 makes an angle with the x-axis then the slope of the normal is

1) -tan 2) cot 3) -cot 4) tan

3. If u = f

x

ythen

y

uy

x

ux

is equal to

1) 0 2) 1 3) 2u 4) u

4. If in a Poisson distribution P(X = 0) = k, then the variance is

1) log k

1 2) log k 3) e 4)

k

1

5. The rank of the diagonal matrix is

1) 0 2)2 3)3 4)5

6. If x 2 + y 2 = 1, then the value of iyx

iyx

1

1 is

1) x –iy 2) 2x 3) -2iy 4) x + iy

7. Var (4X + 3) is

1)7 2)16 Var(X) 3)19 4)0

A

www.Padasalai.Net www.TrbTnpsc.com

http://www.trbtnpsc.com/2014/12/half-yearly-exam-key-answer-for-12th.html

www.Padasalai.Net


8. The vertex of the parabola x2 = 8y -1

1)

0,

8

1 2)

0,

8

1 3)

8

1,0 4)

8

1,0

9. If the magnitude of moment about the point kj

of a force kjai

acting through the

point ji

is 8 then the value of a is

1) 1 2) 2 3) 3 4) 4

10. A particular integral of (D2 - 4D +4)y = e2x is

1) xex 2

2

2 2) x xe 2 3) x xe 2 4) xe

x 2

2

11. The differential equation obtained by eliminating a and b from y = ae3x + be-3x is

1) 02

2

aydx

yd 2) 09

2

2

ydx

yd 3) 09

2

2

dx

dy

dx

yd 4) 09

2

2

xdx

yd

12. Which of the following is correct ?

1) The set of all 2x2 real matrices forms a group under matrix multiplication.

2) An element of a group can have more than one inverse.

3) If every element of a group is its own inverse, then the group is abelian.

4) (a * b )-1= a -1* b -1, for all a, b G.

13. Volume of solid obtained by revolving the area of the ellipse 12

2

2

2

b

y

a

x about major and

minor axes are in the ratio

1) b2 : a2 2) a2 : b2 3) a : b 4) b : a

14. Every homogeneous system(linear)

1) is always consistent 2) has only trivial solution

3) has infinitely many solution 4) need not be consistent

15. Which of the following is incorrect?

1) Multiplying a complex number by i is equivalent to rotating the number counter

clockwise about the origin through an angle 90 .

2) Multiplying a complex number by - i is equivalent to rotating the number clockwise

about the origin through an angle 90 .

3) Dividing a complex number by i is equivalent to rotating the number counter

clockwise about the origin through an angle 90 .

4) Dividing a complex number by i is equivalent to rotating the number clockwise about

the origin through an angle 90

16. If the gradient of a curve changes from positive just before P to negative just after then “P”

is a

1) minimum point 2) maximum point 3) inflection point 4) discontinuous point



www.Padasalai.Net


17. The curved surface area of a sphere of radius 5, intercepted between two parallel planes of distance 2 and 4 from the centre is

1) 20 2) 40 3)10 4) 30

18. The order of -i in the multiplicative group of 4th roots of unity is

1) 4 2) 3 3) 2 4) 1

19. The curve 22 )2()1( xxy is not defined for

1) 1x 2) 2x 3) 2x 4) 1x

20. The order and degree of the differential equation 22 )"()"(' yxyy are

1) 1, 1 2) 1, 2 3) 2, 1 4) 2,2

21. The solution of dy

dx+ mx = 0 , where m < 0 is

1) x = cemy 2) x = ce-my 3) x = my + c 4) x = c

22. If is a cube root of unity then the value of (1 - + 2 )4+ (1 + - 2 )4 is

1) 0 2) 32 3) -16 4) -32

23. Which of the following is not true?

1) Negation of a negation of a statement is the statement itself.

2) If the last column of its truth table contains only T then it is tautology.

3) If the last column of its truth table contains only F then it is contradiction.

4) If p and q are any two statements then qp is a tautology.

24. If X is a continuous random variable then P(X a) =

1) P(Xa) 3) P(X>a) 4) 1-P(X a-1)

25. If A is a scalar matrix with scalar k≠0, of order 3, then A-1 is

1) Ik

2

1 2) I

k3

1 3) I

k

1 4) kI

26. If s = t3 - 4t2 + 7, the velocity when the acceleration is zero is

1) sec/3

32m 2) sec/

3

16m

3) sec/

3

16m 4) sec/

3

32m

27. If qp

, and qp

are vectors of magnitude then the magnitude of qp

is

1) 2 2) 3 3) 2 4) 1

28. The true statements of the following are

a) Two tangents and 3 normals can be drawn to a parabola from a point.

b) Two tangents and 4 normals can be drawn to an ellipse from a point.

c) Two tangents and 4 normals can be drawn to an hyperbola from a point.

d) Two tangents and 4 normals can be drawn to an rectangular hyperbola from a point.

1) a, b, c and d 2) a, b only 3) c, d only 4) a, b and c

29. If I is unit matrix of order n, where k≠0 is a constant, then adj(kI)=

1) kn(adj I) 2) k(adj I) 3) k2(adj I)) 4) kn-1(adj I)



www.Padasalai.Net


30. If the projection of a

on b

and projection of b

on a

are equal then the angle between

a

+ b

and a

- b

is

1)2

2)

3

3)

4

4)

3

2

31. The shortest distance of the point (2 , 10 , 1) from the plane ⃗⃗ [ kji

43 ]= 262 is

1) 262 2) 26 3)2 4) 26

1

32. The polar form of the complex number (i 25)3 is

1) cos 2

+ i sin

2

2) cos + i sin 3) cos - i sin 4) cos

2

- i sin

2

33. dxexx

26

0

is

1) 7

2

6 2)

62

6 3) 62 6 4) 62 7

34. The shortest distance between the lines 4

3

3

2

2

1

zyx and 5

5

4

4

3

2

zyx is

1) 3

2 2)

6

1 3)

3

2 4)

62

1

35. The point on the curve y = 2x2 -6x – 4 at which the tangent is parallel to the x–axis is

1)

2

17,

2

5 2)

2

17,

2

5 3)

2

17,

2

5 4)

2

17,

2

3

36. The vector equation of a sphere whose centre is origin and radius ‘a’ is

1) ar

2) acr

3) ar

4) ar

37. Which of the following is a tautology?

1) p q 2) pq 3) p ~p 4) p ~p

38. The random variable X follows normal distribution f(x) = c 25)100(21

2 x

e . Then the value

of ‘c’ is

1) 2 2) 2

1 3) 5 2 4)

25

1

39. The area of the triangle formed by the tangent at any point on the rectangular hyperbola

xy = 72 and its asymptotes is

1) 36 2)18 3)72 4)144

40. The value of dxx

0

4sin is

1)16

3 2)

16

3 3) 0 4)

8

3



www.Padasalai.Net


-------------------------------------------------------------------------------------------------------------------------------------------------

PART- B 10x6=60 Note: (i) Answer any ten questions. (ii) Question No. 55 is compulsory and Choose any nine questions from the remaining. -------------------------------------------------------------------------------------------------------------------------------------------------

41. Solve the following non-homogeneous equations of three unknowns. 10633;8422;42 zyxzyxzyx by using determinant method.

42. Find the inverse of the following matrix:

121

022

113

A

43. (i) Find the vectors whose length 5 and which are perpendicular to the vectors

kjia 43 and kjib 256

(ii) Find the angle between the line kjikjir 23 and the plane

.1 jir

44. If ,...2211

iBAibaibaibann

prove that

(i) 222222

2

2

2

1

2

1... BAbababa

nn

(ii) ZkA

Bk

a

b

a

b

a

b

n

n

,tantan....tantan11

2

21

1

11

45. If sinsinsin0coscoscos , prove that

02cos2cos2cos and 02sin2sin2sin

46. (i) Find the critical numbers of xx 453

(ii) Evaluate: x

x e

x2

lim

47. Find the equation of the tangent and normal to the curves 542 xxy at 2x

48. Use differentials to find out approximate value of .633

49. Find the volume of the solid that result when the region enclosed by the given curve

22

2 axxay is revolved about x - axis, a>0.

50. Solve 2adx

dyxy

51. Use the truth table to determine whether the statement qpqP ~~ is a

tautology.

52. Show that the set of all non-zero complex numbers is an abelian group under the usual

multiplication of complex numbers.

53. Marks in an aptitude test given to 800 students of a school was found to be normally

distributed. 10% of the students scored below 40 marks and 10% of the students scored

above 90 marks. Find the number of students scored between 40 and 90



www.Padasalai.Net


54. (i) The difference between the mean and the variance of a Binomial distribution is 1 and

the difference between their squares is 11. Find n.

(ii) If the probability of a defective fuse from a manufacturing unit is 2% in a box of 200

fuses find the probability that exactly 4 fuses are defective and more than 3 fuses

are defective .0183.04 e 55. (a) Find the equation of the plane passing through the intersection of the planes

3482 zyx and 010453 zyx and perpendicular to the plane 0423 zyx

(OR)

(b) Show that the locus of a point which moves so that the difference of its distances from

the points (5,0) and (-5,0) is 8 is .144169 22 yx

-------------------------------------------------------------------------------------------------------------------------------------------------

PART- C 10x10=100 Note: (i) Answer any ten questions. (ii) Question No. 70 is compulsory and Choose any nine questions from the remaining. -------------------------------------------------------------------------------------------------------------------------------------------------

56. Investigate for what values of , the simultaneous equations

zyxzyxzyx 2,1032,6 have

(i) no solution

(ii) a unique solution and

(iii) an infinite number of solutions. (by using Rank Method)

57. If kjckibkjia 3,52,32 Verify that cbabcacba ..

58. Altitudes of a triangle are concurrent – prove by vector method.

59. If show that

60. The girder of a railway bridge is in the parabolic form with span 100ft. and the highest point

on the arch is 10ft, above the bridge. Find the height of the bridge at 10ft, to the left or right

from the midpoint of the bridge.

61. Find the eccentricity, centre, foci, vertices for the following ellipse and draw the diagram:

068168422

yxyx

62. Find the equation of the rectangular hyperbola which has for one of its asymptotes the line

052 yx and passes through the points (6,0) and (-3,0).

63. Let P be a point on the curve 3

xy and suppose that the tangent line at P intersects the

curve again at Q. Prove that the slope at Q is four times the slope at P.

64. If veuw 2 where y

xu and ,log xyv find

x

w

and y

w

65. Find the perimeter of the circle with radius “a”.

66. Find the cubic polynomial in x which attains its maximum value 4 and minimum value 0 at

x = -1 and 1 respectively



www.Padasalai.Net


67. Solve: 011 dyyxedxe yxyx given that ,1y where 0x

68. Show that the nth roots of unity form an abelian group of finite order with usual

multiplication.

69. The probability density function of a random variable X is

elsewhere

xexkxf

x

,0

0,,,1

Find (i) k (ii) P ( X >10 )

70. (a) A ladder 10m long rests against a vertical wall. If the bottom of the ladder slides away

from the wall at a rate of 1 m/sec how fast is the top of the ladder sliding down the wall

when the bottom of the ladder is 6m from the wall?

(OR)

(b) Find the area between the line 1 xy and the curve .12 xy

******************************

Prepared by

P.Kabilan, M.sc.,M.Ed., (PG Asst in Maths)

E R K Higher Secondary School

Harur – Salem main Road

Dharmapuri(Dt)-636 905

……………………………………………………………………………………………………………………………………………

Answer Scripts Send :

P.Kabilan, M.sc.,M.Ed., (PG Asst in Maths)

Erumiyampatti(vill), Kokkarapatti(Po),

Pappireddipatti(Tk), Dharmapuri(Dt)-636 905

Contact:

Mobile No: 9942361438

E.Mail Id: [email protected]

******************************



mailto:[email protected]


Padasalai.Net’s Centum Coaching Team

http://www.trbtnpsc.com/2014/10/how-to-get-centum-in-12th-and-10th.html

ாணவர்கள் செய் வவண்டிது என்ன?

1. Click Here & Enter Your Details (Students Only) 2. நது ாடசால யலதத்தில் யமங்கப்டும் சிப்பு யிாத்தால ிரிண்ட்

எடுத்து யிடுமுல ாட்கில் முழுலநனா, முலனா ததர்வு எழுதி யிாத்தாள் தனாரித்து யமங்கின ஆசிரினருக்கு அனுப்ி லயக்க தயண்டும்.

3. A4 Size (Or) Legal Size உள் துணிக்கயர்கள் இபண்டு யாங்கிக்ககாள் தயண்டும். ஒரு தாில் யிாத்தாள் தனாரித்த ஆசிரினர் முகயரிலன “கறுர்” குதினில் குிப்ிட்டு அதில் தங்கள் யிலடத்தால லயக்க தயண்டும்.

4. நற்தாரு கயரில் நாணயர்கள் தங்கள் சுனமுகயரிலன ”கறுர்” எனும் இடத்தில் எழுதி அதற்கு ததலயனா அயில் ஸ்டாம்ப்கலமம் ஒட்டின ிகு, அக்கயலபமம் யிலடத்தாள் எழுதி அனுப்பும் கயருக்குள்ததன லயத்து அனுப் தயண்டும்.

5. ஒன்றுக்கும் தநற்ட்ட நாணயர்கள் இலணந்து யிலடத்தால அனுப்ிால் கநாத்தநாக ஒதப கயரில் அனுப்ாம். ஆால் ஒரு கயரில் மூன்று யிலடத்தாள்களுக்கு தநல் இருக்கக்கூடாது.

6. ஆசிரினர்கள் தங்கள் யிலடத்தால திருத்தின ிகு தங்கள் சுனயிாசநிட்ட கயரில் (Return Cover) லயத்து தங்களுக்கு யிலபயில் திருப்ி அனுப்புயார்.

7. தங்கள் யிலடத்தால உரின ஆசிரினருக்கு அனுப்ி லயத்த தததினிிருந்து 3 யாபங்களுக்குள் தங்களுக்கு நீ கிலடக்காயிடில் இங்கு தபப்ட்டுள் ”புகார் திவு டியத்தில்” தங்கள் யியபத்லத திவு கசய்னவும். Click Here for Complaint Box!

8. Slow Learners நீது நட்டும் கயம் கசலுத்தாநல் நீத்தின் நிகுந்த நாணயர்களுக்கும் உதவும் தாக்கில், நாணயர்கின் ன் கருதி, இச்தசலயனில் தங்கல இலணத்துக்ககாண்டுள் ாடசால ஆசிரினர் குழுயில, நாணயர்கள் நிகுந்த ணிவுடன் கதாடர்பு ககாண்டு திருத்தப்ட்ட யிலடத்தாள் குித்த தங்கள் சந்ததகங்கலமம், ஆதாசலகலமம் அலதசி மூநாக காம்.

இவ்வினாத்தாளுக்கான விடைகடை எழுதி அனுப்ப வவண்டி முகவரி-

P.Kabilan, M.sc.,M.Ed., (PG Asst in Maths), Erumiyampatti(vill), Kokkarapatti(Po), Pappireddipatti(Tk), Dharmapuri(Dt)-636 905 Mobile No: 9942361438 If any doubt, Please contact our Padasalai’s Centum Coaching Team Co-ordinator: Mr. S. Ravi kumar, B.Sc., B.Ed., Headmaster., GHS, PasmarPenta,, Vellore Dt: CellNo: 9994453649

Useful Links:

1. All Other Subject Question Papers Download - Click Here 2. Centum Coaching Team Instructions - Click Here 3. Centum Coaching Team Teacher's Registration Form - Click Here 4. Centum Coaching Team Student's Registration Form - Click Here
http://www.padasalai.net/2014/10/centum-coaching-team-registration-form_6.htmlhttp://www.padasalai.net/2014/10/centum-coaching-team-registration-form_6.htmlhttp://www.padasalai.net/2014/10/centum-coaching-team-registration-form_6.htmlhttp://goo.gl/forms/JwqijySiDrhttp://www.trbtnpsc.com/2014/10/how-to-get-centum-in-12th-and-10th.htmlhttp://www.trbtnpsc.com/2014/10/how-to-get-centum-in-12th-and-10th.htmlhttp://www.trbtnpsc.com/2014/10/how-to-get-centum-in-12th-and-10th.htmlhttp://www.trbtnpsc.com/2014/10/how-to-get-centum-in-12th-and-10th.htmlhttp://www.padasalai.net/2014/10/padasalais-centum-coaching-team.htmlhttp://www.padasalai.net/2014/10/padasalais-centum-coaching-team.htmlhttp://www.padasalai.net/2014/10/padasalais-centum-coaching-team.htmlhttp://www.padasalai.net/2014/10/padasalais-centum-coaching-team.htmlhttp://www.padasalai.net/2014/10/centum-coaching-team-registration-form.htmlhttp://www.padasalai.net/2014/10/centum-coaching-team-registration-form.htmlhttp://www.padasalai.net/2014/10/centum-coaching-team-registration-form.htmlhttp://www.padasalai.net/2014/10/centum-coaching-team-registration-form_6.htmlhttp://www.padasalai.net/2014/10/centum-coaching-team-registration-form_6.htmlhttp://www.padasalai.net/2014/10/centum-coaching-team-registration-form_6.htmlhttp://www.padasalai.net/2014/10/centum-coaching-team-registration-form_6.html

Documents

· 2016-12-26 · b) Two tangents and 4 normals can be drawn to an ellipse from a point. c) Two tangents and 4 normals can be drawn to an hyperbola from a point. d) Two tangents