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MATHEMATICS

SECTION – I Single Correct Choice Type

This section contains 9 single correct choice type questions. Each question has 4 choices: (a), (b), (c) and (d) for its answer, out of which ONLY ONE is correct.

1. If xbcb −− 2, and ab − are in H.P., then

−

−

2,

2xbxa and

−

2xc are in

(a) A.P. (b) G.P. (c) H.P. (d) none of these

2. A function f : ++ →QQ is defined such that)(

)()(2)()(yxf

xyfxyxyfyfxf+

=++ , then ( )1f

is equal to (a) 1 (b) 0 (c) 2 (d) none of these 3. The number of seven digit integers, with sum of the digits equal to 10 and formed by using

the digits 1, 2 and 3 only, is (a) 55 (b) 66 (c) 77 (d) 88 4. In a complex plane the points A and B are at iz 251 −= and .12 iz += If )(zP moves such

that |,|2|| 21 zzzz −=− then the maximum area of PAB∆ is (a) 5 (b) 1/3 (c) 25/3 (d) 50/3

5. If in a ∆ABC, 2coscos2cos =++ CBA , then a, b, c are in (a) A.P. (b) H.P. (c) G.P. (d) A.G.P.

6. A function ∫ ∫θ θ

+=θ2 2sin

0

cos

0

)()()( dxxfdxxfg is defined in the interval

ππ−

2,

2 where )(xf

is an increasing function, )(θg is increasing in the interval

(a)

π− 0,

2 (b)

π

−π

−4

,2

(c)

π

2,0 (d)

π− 0,

4

7. ∫∞ −

0

//

dxx

ee xbax

, ( )0≠ab is equal to

(a) ba / (b) 2/x (c) ab (d) none of these

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8. If ||ln cx

xy = (where c is an arbitrary constant) is the general solution of the differential

equation

φ+=

yx

xy

dxdy , then the function

φ

yx is

(a) 2

2

yx (b) 2

2

yx

−

(c) 2

2

xy (d) 2

2

xy

−

9. If A is a skew symmetric matrix, then 1))(( −+−= AIAIB is (where I is an identity matrix of

same order as of A) (a) idempotent matrix (b) symmetric matrix (c) orthogonal matrix (d) none of these

SECTION − II

Multiple Correct Choice Type This section contains 4 multiple correct choice type questions. Each question has

4 choices: (a), (b), (c) and (d) for its answer, out of which ONE OR MORE is/ are correct.

10. If a, b, c, d are in A.P. and ∫ −=2

04)( dxxf where

dbxdxcxxcxbx

caxbxaxxf

+−++−++−+++

= 1)( , then the

common difference of the A.P. may be (a) 1 (b) –1 (c) 2 (d) 4 11. Let 1z and 2z be two complex numbers such that izz 20164 2

21 +=− . If α and β are roots of

0212 =+++ Mzxzx (where M is complex number) and ( ) 282 =β−α , then

(a) maximum value of M is 417 + (b) maximum value of M is 415 +

(c) minimum value of M is 417 − (d) minimum value of M is 415 −

12. The system of equations ,rqczbyax −=++ prazcybx −=++ and qpbzaycx −=++ is

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(a) consistent if rqp == (b) inconsistent if ,cba == and rqp ,, are distinct (c) consistent if cba ,, are distinct and 0≠++ cba (d) all of above 13. If the tangents of the angles A and B of a triangle ABC satisfy the equation

,022 =+− abxcabx then

(a) baA =tan (b)

abB =tan

(c) 0cos =C (d) 2sinsinsin 222 =++ CBA

SECTION − III Reasoning Type

This section contains 3 reasoning type questions. Each question contains Statement-1 and Statement-2. Each question has 4 choices (a), (b), (c) and (d), out of which ONLY ONE is correct.

Directions: Read the following questions and choose (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for

Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for

Statement-1. (C) Statement-1 is True, Statement-2 is False. (D) Statement-1 is False, Statement-2 is True.

14. Statement-1 : ( ) ][sin 1 xxf −= and ( ) ][cos 1 xxg −= are identical functions (where [.] denotes greatest integer function)

Statement-2 : Identical functions have the same domain. (a) A (b) B (c) C (d) D

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15. Statement-1 : Let A, B, C are three independent events and ( ) ( ) ( )61,

31,

21

=== CPBPAP ,

then ( )181

=CBAP .

Statement-2 : If A, B, C are 3 independent events then CBA ,, are also independent. (a) A (b) B (c) C (d) D

16. Statement-1 : There exist no triangle ABC which has the property that 53cos =A and

31tantan =− CB .

Statement-2 : In a triangle ABC; CBACBA tantantantantantan =++ . (a) A (b) B (c) C (d) D

SECTION−IV Matrix−Match Type

This section contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled 1, 2, 3, 4 and 5. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the following example:

If the correct matches are A – 1, 4 and 5; B – 2 and 3; C – 1 and 2; and D – 4 and 5; then the correct darkening of bubbles will look like the following.

A 1 2 3 4

1 2 3 4

1 2 3 4

1 2 3 4

B

C

D

1 2 3 4

5

5

5

5

5

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1. Column I Column II

(A) The solution set of ,21||log100 =+ yx

4log||loglog 1001010 =− xy is

1. }2,2{

(B) The solution set of ( ) yx 22

2 log21log4 =+ and yx 2

22 loglog ≥ is

2. {1, 1}

(C) The solution set of 0loglog 24 =− yx and 045 22 =+− yx is

3. {–10, 20}

(D) The solution set of the equation 044123162 22 =+−+− yyxx is

4. {4, 2}

5.

320,

310

2. If zyx ,, are unit vectors such that ,azyx =++ ,)( bzyx

=×× ,)( czyx

=×× 23· =xa ,

47· =ya , aa ˆ2=

, then match the following column–I with column–II

Column–I Column–II (A) =x 1. c4−

(B) =y 2. )(34 bc

−

(C) =z 3. )843(31 cba

++

(D) =++ zyx 323

4. )43( ca +

5. ( )bc

−32