01_maths

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Space for rough work

MATHEMATICS

1. For the equationcxbxax

111 , if the product of the roots is zero, then the sum of the

roots is

(a) 0 (b)cb

ab2 (c)

cb

bc2 (d)

cb

bc2

2. The point on the st. line 112xy which is nearest to the circle

050832)(16 22

yxyx is

(a) 2,

2

9 (b) 2,

2

9 (c) 2,

2

9 (d) none of these

3.15

7

35

35nnn

is a

(a) positive integer for all n N (b) positive odd integer

(c) positive even integer (d) prime integer

4. Two vectors a

and b

of equal magnitude 5 originating from a point and directs respectively

towards north-east and north-west. Then the magnitude of ba

is

(a) 23 (b) 32 (c) 52 (d) 25

5. If the area of the triangle formed by the points izzz, and iz on the complex plane is 18,

then the value of ||z is

(a) 6 (b) 9 (c) 23 (d) 32

6. If the term independent ofxin the expansion of

10

2x

kx is 405, then k is equal to

(a) 1 (b) 2 (c) 3 (d) none of these

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7. The equation of the plane containing the two lines

31

1

2

1 zyxand

3

1

1

2

2

zyxis

(a) 0758 zyx (b) 0758 zyx

(c) 0758 zyx (d) none of these

8. In a certain test, there are n questions. In this test in2 students gave wrong answers to at least

i questions; where ,1....,2,1 ni n. If the total number of wrong answers given is 2047, then

n is equal to

(a) 10 (b) 11 (c) 12 (d) 13

9. 7x touches the circle ,0126422

yxyx then the co-ordinates of the point of

contact are

(a) (7, 3) (b) (7, 4) (c) (7, 8) (d) (7, 2)

10. Ifx

xxf

1

1log)( and ,

31

3)(

2

3

x

xxxg then ))(( xgf is equal to

(a) )(xf (b) )(3 xf (c)3))(( xf (d) )3( xf

11. If in a3

, AABC andAD is a median, then

(a) bcbcAD 2222 (b) bcbcAD 2224

(c) bcbcAD

222

6 (d) none of these

12. The equation 021xe

x has

(a) one real root (b) two real roots

(c) three real roots (d) infinite real roots

13. If the capital letters denote the cofactor of the corresponding small letters in the determinant

,

333

222

111

cba

cba

cba

then the value of

333

222

111

'

CBA

CBA

CBA

is

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(a) (b) 2 (c) 2 (d) 0

14. The vector ,c

directed along the internal bisector of the angle between the vectors

kjia

447 and kjib

22 with 65|| c

, is

(a) )27(3

5kji

(b) )255(3

5kji

(c) )27(3

5kji

(d) )255(3

5kji

15. If ,)( nAn then n },,,,:),,{( xzzyyxzyxzyx

(a) 3n (b)2)1(nn (c) )2(2 nn (d) nnn 23 23

16. If PQ is a double ordinate of the hyperbola 12

2

2

2

b

y

a

x such that OPQ is an equilateral

triangle, Obeing the centre of the hyperbola. Then the eccentricity e of the hyperbola satisfies

(a)3

21 e (b)

3

2e (c)

2

3e (d)

3

2e

17. If ,11

c

P

b

P

a

P rn

r

n

r

n

then)(

2

cba

bis equal to

(a) 1 (b) 2 (c) 2

1 (d) none of these

18. If ,)!(!

!

rnr

nCrn then the sum of the series r

rnnnnCCCC

1

3

2

2

1

1 ....1 is equal to

(a) rrn C (b) r

rn C1 (c) 1rrn C (d) none of these

19. For a 3 3 matrixA, if detA = 4, then det (AdjA) equals

(a) 4 (b) 4 (c) 16 (d) 64

20. Let Iyx, and suppose that a relation onI is defined by yRx if ,yx then

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(a) R is not symmetric (b) R is an equivalence relation

(c) R is reflexive and symmetric (d) R is symmetric and transitive

21. If cba ,, are in A.P., cmba ,, are in G.P. then cbma ,, 2 are in

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

22. Suppose values taken by a variableX are such that bxa i where ix denotes the value ofX

in the ith case for .,....2,1 ni Then

(a) bXVara )( (b)22 )( bXVara

(c) )(4

2

XVara

(d) )()( 2 XVarab

23. Let )()()( yfxfyxf and )()2(sin1)( xgxxf where )(xg is continuous. Then )(' xf

is equal to

(a) )0()( gxf (b) )0()(2 gxf (c) )0(2g (d) none of these

24. If 2)( xxf when 1x and 14)( xxf when ,1x then

(a) )(xf is continuous at 1x (b) 4)(1xfLt

x

(c) )(xf is discontinuous at 0x (d) none of these

25. The area bounded by the curve ,2xy the normal at (1, 1) and x-axis is

(a)

3

4 (b)

3

2 (c)

3

1 (d) none of these

26. If we consider only the principal values of the inverse trigonometric functions, then the value

of17

4sin

25

1costan 11 is

(a)3

29 (b)

3

29 (c)

29

3 (d)

29

3

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27. Letn

S be the sum of first n terms of an A.P. with non-zero common difference. If

1

21

n

nn

S

S is

independent of 1n , the ratio of the first term and common difference is

(a)3

1 (b)

2

1 (c)

4

1 (d) none of these

28. The general solution of the equation 02tan

2tan

2tan

tan

x

x

x

xis

(a) n (b)3

n

(c)

3

)13( n (d) Znn ;

3

)12(

29.1)2( xx

dxx

(a) cxx 1tan12 1 (b) cxx 1tan212 1

(c) cxx 1tan412 1 (d) none of these

30. If )(')( xx and ,2)1( then )3( is equal to

(a) 2e (b)2

2e (c) 23e (d)3

2e

31. If the function

2for2

2for2

)2()(

2

x

xx

AxAxxf , is continuous at ,2x then

(a) 0A (b) 1A (c) 1A (d) none of these

32. If cosecA + ,2

11cotA then Atan is

(a)22

21 (b)

16

15 (c)

117

44 (d)

43

117

33. The solution of22xydyyxdyydxx dx is

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(a) )1(1 22 yCx (b) )1(1 22 yCx

(c) )1(1 33

yCx (d) )1(1 33

yCx

34. If 1E denote the event of coming sum 6 in throwing of two dice and 2E be the event of

coming 2 in any one of the two, then )/( 12 EEP is

(a)5

1 (b)

5

4 (c)

5

3 (d)

5

2

35. If 11a and 1,23

341 na

aa

n

nn and if ,lim aan

nthen the value of a is

(a) 2 (b) 2 (c) 2 (d) none of these

36. Equation of the directrix of the parabola whose focus is (0, 0) and the tangent at the vertex is

01yx is

(a) 0yx (b) 01yx (c) 02yx (d) 01yx

37.23 )1( xx

dxis equal to

(a) cxx

x33/1

3/1

1

1

1log3 (b) c

xx

x33

3

1

11log3

(c) cxx

x33

3

1

11

log3 (d) none of these

38. If mean = (3 medianmode) k, then value of k is

(a) 1 (b) 2 (c)2

1 (d)

2

3

39.2/5

...33221

n

nnLtn

is equal to

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(a) 0 (b) 1 (c)

2

5 (d)

1

0

dxxx

40. The equation 0,022 ccycxbyax represents a pair of st. lines if

(a) 0ba (b) 0cb (c) 0ac (d) 0cba

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