1312 NP Tam+Eng Mathematics AAAA

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!1312NPMathematics!

PART - III

Pou? / MATHEMATICS

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/ Tamil & English Versions)

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Time Allowed : 2.30 Hours ]

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Instructions :

: 90

[Maximum Marks : 90

(1)

A??zx ???UP?? \???P¡§ ?v??Q E??u? G??u??a

\????zxU ?P?????. Aa_¡§?v?? S??¡ã?¡§¡è?, A??U

PsP?o¡§????h? Eh?i??Pz ?u??UP??.

(2)

}?? A??x P?¡§? ??¡ã?? ?mk¡Â? G?x?u?S?,

Ai¡ÂP?ik?u?S? ????kzu ¡Â?sk?. ?h[P? ????u?S

???]? ????kzu??.

(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 underline and pencil to draw diagrams.

?Sv &

S?¡§? :

Note :

I / PART - I

(i)

A??zx ???UP?US? ??h??UP??.

(ii)

?P?kUP¡§?mk?? ???? ??hP?? ?P?? H???h?

??h??z ¡Âu???ukzxU S?¡Àmkh? ??h¡ã???? ¡Â\?zx

G?u??.

(i)

All questions are compulsory.

(ii)

Choose the most appropriate answer from the given four alternatives and

write the option code and the corresponding answer.

20x1=20

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1.

2

C? 11 &B? ?i¡ë? \u?Qu¡§ ¡è?? ¡Âu??????P

¡è????¡§ ¡Â??? __________ ?h[P?S?.

28

28

C? \u?Qu¡§

1

1

(4)

28

11

th

The percentage error in the 11 root of the number 28 is approximately __________

times the percentage error in 28.

2.

(1)

11

(2)

28

(3)

(1)

11

(2)

28

(3)

4x2?y2=36

1

28

9

81

4

(2)

(3)

4

16

9

2

2

The line 5x?2y+4k=0 is a tangent to 4x ?y =36, then k is :

3.

1

11

US 5x?2y+4k=0 G?? ¡ÂP?k J? ?u?k¡ÂP?k G?? k C? ?v¡§? :

(1)

(1)

(4)

9

4

(2)

81

16

(3)

4

9

(4)

2

3

(4)

2

3

???UP??¡§ ????zx S???Q? J??? ?¡§?i ¡ë?[P??, ¦Ø2 C? ???\.

(C[S ¦Ø G??x (1)1/3 -? P?¡§??s ¡ë??)

(1) 2

(2) 1

(3) 4

(4) 3

2

In the multiplicative group of cube root of unity, the order of ¦Ø is : [¦Ø is a complex cube

root of unity]

(1) 2

(2) 1

(3) 4

(4) 3

4.

???? g(x) BQ? \???P? ???x?i? C?h?v¡§? ?v¡ã?

?????UP¡§?mh?? ¡Â??? A???? G??, ???x ?i? C?h?v¡§?

?v¡ã? G?u S?¡§¡èmh {??¡ã? Ax ??U??g]¡ã? C?h ?v¡§? ?v??P

???? ?

f(x)

(1)

f 9(x)=0

(2)

g9(x)=0

(3)

g(x)

G??x J? \??a\???

G??x J? \??a\???

(4) f(x)

If f(x) and g(x) are two functions as defined in Generalized law of mean then Lagrange¡¯s

law of mean is a particular case of Generalised law of mean for :

(1) f 9(x)=0

(2) g9(x)=0

(3) g(x) is an identity function

(4) f(x) is an identity function

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3

5.

?x?iy

?u? P???Sv¡ã? A???u??

1312 (NP)

?ix+y

A???? P?? ?Sv :

(1)

¡ë???? P?? ?Sv

(2)

|??P?? P?? ?Sv

(3)

?u? P?? ?Sv

(4)

C?sh?? P?? ?Sv

If ?x?iy lies in the first quadrant, then ?ix+y lies in the :

6.

(1)

third quadrant

(2)

fourth quadrant

(3)

first quadrant

(4)

second quadrant

¡è????????? Gx ???????S? ?

(1)

p¡Å(~p)

(2)

p¡Ä(~p)

(3)

p¡Åq

(4)

p¡Äq

(3)

p¡Åq

(4)

p¡Äq

G??

E(X2)

Which of the following is a tautology ?

(1)

7.

p¡Å(~p)

(2)

p¡Ä(~p)

G?? \????¡§? ???¡ã? ?????i

?v¡§? :

4

(1)

(3)

X

6

(2)

8

¡Â??? \??\?

2

2

(4)

C?

4

Variance of the random variable X is 4. Its mean is 2. Then E(X2) is :

(1)

¡ú

8.

6

(2)

¡ú

(1)

yz -

u??

(2)

xz -

u??

¡ú

i ???? k

xy - u??

¡ú

2

(4)

4

G?? \????k S?¡§?x :

¡ú

¡ú

(4)

(3)

¡ú

r = s i ?t k

(3)

8

???P?? C?nUS? ¡Â|?U¡ÂP?k

¡ú

r = s i ? t k is the equation of :

(1)

yz - plane

(2)

xz - plane

(3)

a straight line joining the points i and k

(4)

xy - plane

¡ú

¡ú

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1312 (NP)

4

1

9.

y = x3

G?? ??????US R?UP?q? T??P?? Gx ??????x ?

(1)

??????US J? ???? ????¡§ ??? E??x. ¡Â??? A¡§???¡ã?

y99 Q?hUP?x

(2)

??????US J??US ¡Â???? ???? ????¡§ ???P? E??x

(3)

??????US ???? ????¡§ ??? Q?h??x

(4)

??????US J? ???? ????¡§ ??? E??x. ¡Â??? A¡§???¡ã?

y99=0 BS?

1

Which one of the following statements is true about the curve y = x 3 ?

10.

(1)

The curve has a point of inflection in which y99 does not exist

(2)

The curve has more than one point of inflection

(3)

The curve has no point of inflection

(4)

The curve has a point of inflection in which y99=0

???? z3=2+4i G??,

G??? J? B?P? u?zv? :

z 1=1+2i, z 2=1?3i

z 1z 2z 3, 2z 1z 2z 3

(1)

C? \??UP ?U¡ÂP?nzv? ???¡§???P?

(2)

J¡Â? ¡ÂP?h????

(3)

?\[¡ÂP?n ?U¡ÂP?nzv? ???¡§???P?

(4)

\??UP ?U¡ÂP?nzv? ???¡§???P?

????

?7z 1z 2z 3

If z 1 =1+2i, z 2 =1?3i and z 3 =2+4i then, the points on the Argand diagram

representing z1z2z3, 2z1z2z3, ?7z1z2z3 are :

(1)

Vertices of an isosceles triangle

(2)

Collinear

(3)

Vertices of a right angled triangle

(4)

Vertices of an equilateral triangle

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11.

1312 (NP)

\??izu?? ¡Â|??a \????kP?? ?u?S¡§¡è? ¦Ñ(A) G??x ???P??

GsoU?P?? ?h S?????x G?? ?u?S¡§???x :

(1)

???¡§??h??? w??P? ?mk¡Â? ?????US?

(2)

w??P? ?????UP?x

(3)

???¡§??hz w?? ?mk¡Â? ?????US?

(4)

???¡§??hz w?? ???? GsoU?P??? ???¡§??h??? w??P?

?????US?

In the homogeneous system ¦Ñ(A) is less than the number of unknowns, then the system

has :

12.

(1)

only non-trivial solutions

(2)

no solution

(3)

only trivial solution

(4)

trivial solution and infinitely many non-trivial solutions

y=cx?c2

G??u??¡§ ???xz w???P¡§ ???? ??PU?P? \????k :

(1)

y9=c

(2)

(y9) 2+xy9+y=0

(3)

(y9)2?xy9+y=0

(4)

y99=0

y=cx?c2 is the general solution of the differential equation :

13.

(1)

y9=c

(2)

(y9) 2+xy9+y=0

(3)

(y9)2?xy9+y=0

(4)

y99=0

y9+(y99) 2 =x(x+y99) 2

G?? ??PU?P?a \????mi? ???\ ???? ?i

???¡Â? :

(1)

1, 2

(2)

1, 1

(3)

2, 2

(4)

2, 1

The order and degree of the differential equation y9+(y99)2=x(x+y99)2 are :

(1)

1, 2

(2)

1, 1

(3)

A

2, 2

(4)

[

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2, 1

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