1SRI CHAITANYA DAY-SCHOLARS EDUCATIONAL INSTITUTIONS , VJASubject : Maths Important questions

1. I f numbers of the form 34n 2 + 26n 3 + 1, where n is a positigve integer , are dividedby 17, thenthe set of al possible remainders is1) {1} 2) {0, 1} 3) {0, 1, 7} 4) {1, 7}

3. The number of ways in which five persons A, B, C, D, E can be seated in a r ing sothat A sits between B and C is1) 120 2) 24 3) 4 4) 9

4. I f 4100log10log 10x then x =

1) 100 2) 4100 3) 10log 4 4) 10log 2

6. I f , , are the roots of 3 22 3 3 0x x x then 3 33

1 1 1

1) 13 2) 18 3) 44 4) 47

7. I : I f 3 3 3 3x y z xyz then x yxz yz Az

I I : I f u = (x y) ( y z) (z x) then x y zu u u B

I I I : I f u = f(r ), r 2 = x2 + y2 + z2 then 2 2 2

2 2 2 '' 'u u u Cf r f r

x y z r

The ascending order of A, B, C is1) B, A, C 2) B, C, A 3) A, B, C 4) C, B, A

9.

3 3 3

2 1 2 11.3 3.5 .......2 2 2n

n nLim

n n n

1) 0 2) 2 3) 13 4)

23

16. P is the point of intersection of the lines ax + by a = 0 and bx ay + b = 0. A circlewith centre (1, 0) passes through P. I f the tangent to this circle at P meets x- axis atthe point (k, 0) then k =

1) 1 2) 1 3) 2 22ab

a b 4) 2 22ab

a b

Model EAMCET - 2005

218. In the quadr ilateral of the adjacent figure, AC = x, BD = y. Then 2xy cos =

1) 2 2 2 2b d a c 2) 2 2 2 2b a c d

B C

D A

d

c

b

a

3) 2 2 2 2a c b d 4) 2 2 2 2a d b c

19. The maximum distance between two points of a unit cube is

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

20. Let A = (0, 10), B = (20, 20) be two points in the XY plane and let P = (x , 0) be amovin point on x a-axis. The value of x so that PA + PB is minimum is1) 0 2) 10 3) 15 4) 20

21. The equation 2 2cos 6 sin 92r r

(in polar coordinates) represents

1) a circle 2) a straight line

3) a pair of lines 4) a circle and a straight line

23. The angle made by the complex number 1001

3 i with positive real axis is

1) 1200 2) 2400 3) 1500 4) 600

28. I f a, b, c are in G.P. and Tan1a, Tan1b, Tan1c are in A. P. then1) a = b = c = 0 2) a= b = c 3) a= b = c, or 1b 4) ca = 1

29. The number of elements in the complete set of solut ions of the equationSin1 x = 2 Tan1x is1) 2 2) 3 3) 5 4) Infinity

31. A straight pole L subtends a r ight angle at a point A of anothe pole at a distance of30 m from L. The angle of elevation of the top of L at A is 600. Then the length ofthe pole L in metres is

1) 20 3 2) 40 3 3) 40

3 4) 60 3

34. f is a function with per iod a and g is a function with per iod b. then the functionf[f(x)]1) is not periodic 2) has period a3) has period b 4) has period ab

36. A r ight circlar cylindr ical container closed on both sides is to contain a fixed vol-ume of oil. I f r is the radius of its base and h its height then the overall sur face areaof the container is minimum when

1) 43

h r 2) h = 2r 3) h = 4r 4) h = 3r

339. 20040 1 tandx

x

1) 4

2) 2

3) 4) 0

44. The condition for the line 1x ya b

to touch the hyperbola xy = c2 is

1) 4c2 = ab 2) c2 = ab 3) 2c2 = ab 4) c2 = 2ab

46. Thevalues of x for which f(x) = 1xx

is an increasign function belong to the

interval

1) 1, 2) 0, 3) , 1 4) 1,

49. Three circles of equal radius r touch one another . The radius of the circle touch-ing all the three given circles internally so that all of them are inside it is

1) 2 3 r 2) 2 3 r 3) 2 3 3r

4) 2 3 3r

51. A and B are two events of a random exper iment such that P(A) = 13 and P(B) = 34 .

Then the range of P A B is

1) 1 12,3 13

2) 5 2,

12 3

3) 1 2,3 3

4) 1 5,3 12

52. ,a b are the position vectors of A and B respectively where ,a a b b . I f AB isdivided internally by P and externally by Q in the sameratio 2 : 3 and if OP and OQare prependicular then

1) 2 29 4a b 2) 2 24 9a b 3) 4a = 3b 4) 9a = 4b

53. The lines 2 2 21y mx a m and 2 2 21y nx a n form a rhobmbus but not asquare when1) m2 = n2 2) m 1 3) mn = 1 4) mn 1

55. The equation 2 2 2 2 22 3 4 8 12 0x y xy y x y xy y represents

1) two pairs of straight lines through the origin2) a pair of straight lines and a circle

3) a pair of straight lines and a parabola4) a set of four lines forming a square

456. Given 2 2 2 , , ,a b c a b b c c a are factors of the determinant

22 2

22 2

22 2

a a b c bc

b b c a ca

c c a b ab

,

the remaining factor is1) ab + bc + ca 2) a + b + c 3) 2(a + b + c) 4) 2(ab + bc + ca)

57. I f , ,a b c are non-zero noncoplanar vectors of which no two of them are collinear

then the simplified form of . . .a a b c a b c a a c a b is

1) a 2) 2 a 3) 0 4) a b c a

58. I f ,a xi y j zk 2 3 6b i j k and . 35ab then the vector a such that a isleast is

1) 10 15 30

7i j k 2)

10 15 307

i j k

3) 10 15 30i j k 4) 10 15 30i j k

62. x + ky + 3z = 0, 3x + ky 2z = 0, 2x + 3y 4z = 0. I f the above system of equationshas a non-zero solution then x : y : z =1) 5 : 2 : 6 2) 15 : 2 : 6 3) 15 : 2 : 6 4) 5 : 2 : 6

64. I f 2 3x xf x

x

then

f x f y f z k

x y x z y z y x z x z y xyz

where

k =1) 6 2) 12 3) 18 4) 24

65. A = (2, 3, 4), B = (4, 1, 2). The maximum area of the tr iangle which can beinscr ibed in thesemicircle having AB as diameter in sq. units is1) 28 2) 56 3) 16 4) 14

70. I f A is a 3 x 3 matr ix such that |A| = 5 then det [(AT)1] =

1) 5 2) 5 3) 15 4)

15

Model EAMCET - 2003

3. In a ABC, if 3 4AB i j

and 5BC i j

then te length of the altitude through C is

1) 85 2) 1 3)

195 4)

265

58. 2 2 2 25 3 2 1 5 3 2 1 5 3 2 1 5 3 2 1 =1) 176 2) 22 3) 44 4) 88

11. A sum of money is rounded offto the nearest rupee. The probability that the er roroccured in rounding off is at least 15 paise is

1) 7

10 2) 71

100 3) 29

100 4) 7

20

12. Five currency notes of different denominations are distr ibuted at random amongfour persons. The probability that a par ticular person gets three currency notes is

1) 133256 2)

45512 3)

45256 4)

135512

21. The smallest difference possible between the slopes of two perpendicular lines in aplane is1) 2 2) 2 3) 1 4) 4

25. The value of p for which both the r oots of t he equat ion4x2 20px + (25p2 + 15p 66) = 0 are less than 2 lies in the interval1) (1, 2) 2) , 1 2, 3) 2, 4) , 1

28. The expansion of (1 + 4x + x2)1/2 in ascending powers of x is valid if1) 3 2 5x 2) 2 5x

3) 1x 4) 2 1x

48. sin0 log sinbxxLim ax =

1) 1 2) a

b 3) 2

2

a

b4)

ba

49. 21 2 3 4 ...... 2

1nnLim

n

=

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

56. The length of t he chor d j oining the points 4 cos , 4sin and 0 04 120 , 4sin 120Cos of the circle x2 + y2 = 16 is

1)4 2) 4 3 3) 5 4) 6

59. The graph of y = ax2 + bx + c passes through the points (0, 2), (1, 6) and symmetr icabout the line 2x = 5. Then a + b + c =1) 2 2) 8 3) 2 4) 6

661. Length of the tangent at one ver tex of the hyperbola 9x2 16y = 144 between theasymptotes is1) 6 2) 4 3) 8 4) 3

64. Equation of the curve in xy plane whose normal at any point (x, y) cuts x-axis at(x + 2, 0) is1) 2 2y x C 2) 2 2y x C 3) 2 4y x C 4) 2 4y x C

69. I f sin 2 2dx K

x Cosx Sinx Cosx

. In sin 22

x Cosx CSinx Cosx

then K =

1) 12 2)

15 3)

13 4)

14

73. I f x = log t, y = tn then n

n

d ydx

=

1) nny 2) 1nny 3) y n 4) 1y n

78. In ABC, if the internal bisector of angle A meets BC in D and if ADC thenSin =

1) 2B CSin 2) 2

B CCos 3) 2C BSin 4) 2

ACos C

Maths Revision Test 9-3-043. In ABC two sides a = 6 and b =3 and cos(A B) = 4/5 then the area of the tr iangle

in square units is1) 7 2) 9 3) 12 4) 10

17. In a ABC value ofa = m2 + n2, b = m2 n2, c =2mn then ex-radius r 1 =

1) 2 2

2m n

2) 2 2

2m n

3) m n m 4) mn

32. In a ABC if cos A tanC

a c

then sin (B + C) =

1) cos A. cos C 2) Cos B. cos C 3) cos A. cos B 4) Sin B sin C

62. The velocity of a par ticle moving in a straight line is propor tional to the squareroot of the displacement then the par ticle moves with1) Variable acceleration

2) Constant acceleration3) Acceleraton proportional to velocity

4) Acceleration proportional to displacement

763. The equation of the motion of a par ticle P(x, y) is given by x = 4 + cos t and y = 5 +b sin t then its velocity at time t is1) 4 2) 5 3) b 4) 9

79. A metal sphere is dissolving in a liquid such that it always remains spher ical. I f therate of dissolving the sphere us always K times its sur face area, then the rate ofchange in the radius of the sphere is1) 4K 2) 3K 3) 2K 4) K

80. A is a fixed point on acircle O and radius r. A par ticle P star ts at A and moveswith a nagular velocity of 4 radians / sec. I f PM is perpendicular to OA then rateof increase of the area of the tr iangle OPM when POM is 600 is1) r2 2) r2 3) 2r2 4) 2r2

Maths 2nd year rev test - 4 (28-3-04)4. I f P is a point o nthe circum ference of an equililateral tr iangle ABC of side a,then

PA2 + PB2+ PC2 =1) a2 2) 2a2 3) 3a2 4) 4a2

60. I f 7

33

1

6.7 6 1f x dx

then f(x) equals to

1) 432

x 2) 432

x c 3) 18x2 4) 18x2 + C

61. I f g(x) = 40

cosx

t dt , then g(x + ) equals

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

LTC AIEEE Unit -3 (24-2-04)

1. I f y = 2 31

1 x x x then 2

2

d ydx

= .............. at x = 0

1) 1 2) 1 3) 0 3) 1/4

2. I f x = cos t, y = log te then at t = 2

the value of

22

2 ...........d y dydx dx

1) 1 2) 0 3) 4) 2

4

8. I f y2 = ex/2 then the value of 2

321 ........

d d yydx dx

1) ex 2) 12

xe 3) 14

xe 4) 18

xe

811. I f f(x) = (2x)n then the value of

0

1!

rn

r

fr

1) 2n 2) 12n 3) 4

n 4) 2n

15. I f f(x) = tan x then f (n)(0) 42 42 0 0 ........nn nC f n C f

1) 2

2) 2n

3) sin 2n

4) 0

17. I f x2y = 1 the value of x12y10 = ..........1) 10! 2) 11! 3) 12! 4) ( 10!)

22. A point P is on y = x3 and the abscissa 2 of P is measured with an er ror of 0.1 thenthe er ror in the slope of tangent at P is ............

1) 15 2)

25 3)

45 4)

65

27. I f 1 2sin sin a and 1 2cos cos b then

1) 2 2 4a b 2) 2 2 4a b 3) 2 2 3a b 4) 2 2 2a b

28. I f 1 2and are two values lying in [0, 2 ] for which tan = then 1 2tan . tan2 2

is

equal to1) zero 2) 1 3) 2 4) 1

38. I f sin x = cos2x then cos2x(1 + cos2x) is always equal to

1) 2 2) 1 3) 12 4)

12

41. The numer ical value of 2 4 8tan 2 tan 4 tan 8 tan

3 3 3 3

is equal to

1) 5 3 2) 3) 5 3 4) 53

43. The minimum value of 27cosx + 81sinx is equal to

1) 2

3 3 2) 1

3 3 3) 2

9 3 4) None

46. I f cot2x = cot(xy). cot(xz) then cot 2x is equal to

1) 1 tan tan2x y 2) 1 cot cot2

y z

3) 1 sin sin2y z 4) 1 tan cot2

x y

949. The minimum value of the expression sin sin sin . Where , , are realnumber satisfy is

1) positive 2) zero 3) negative 4) 3

51. I f the image of the poin (2, 1) by a line mir ror be (2, 1) then the equation of theline mir ror is .........1) y = x 2) x = 2y 3) y = 2x 4) y + x = 5

52. The real value of a for which the value of m satisfying the equation (n2 1)m2 (2a 3)m + a = 0 gives the sloe of a line parallelto the x-axis is1) 3/2 2) 0 3 )1 4) 1

56. A family of lines is given by 1 1 0x x y , being the parameter . Theline belonging to this family at the maximum distance from the point (1, 4) is ........1) 4x y + 1 = 0 2) 33x + 12y + 7 = 0 3) 12x + 33y = 7 4) x + y 5 = 0

Unit-3 ( 20-2-04)

1. The value of 1

2 2 1

6

4 3sin 2 snxx

Lim x Cos x

is

1) 1 2) 1e

3) e 4) e

2. Let 2 2 2

3

1 2 .......n

nLimn

and 3 2 3 2 3 2

4

1 1 2 2 .........n

n nLim

n

then

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

3. 1

2 sin2

01 x

xLim Tan x

1) e 2) e1 3) e 4) 1e

4.

2

1 1 2 2 3 ........ 1lim

nn nn n n n nn

nm

m mLim

m

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

7. The pr incipal valueof 11 9 9

10 102Cos Cos Sin

1) 2320

2) 1720

3) 720

4) 2720

10

12. I f one ofthe roots of the equation 2 2 1 2 0x i x i is 2 i then the other rootof the equation is1) i 2) 2 + i 3) i 4) 2i

29. I f

10 10 114 5

11 11 126 7 2

12 12 138 9 4

m

m

m

C C CC C CC C C

= 0 then m =

1) 4 2) 5 3) 6 4) 7

38. The general solution of 3 1 3 1 sin 2Cosx x is

1) 2 4 12x n

2) 2 12 4

x n

3) 2 4 12x n

4) 2 12 4

x n

39. I f a square matr ix,the element a column are 2,5k+1, 3 and the cofactors of an-other column are 1 5k, 2, 4k 2 then k =1) 1/6 2) 1/6 3) 1/4 4) 1/4

45. A double ordinate of the parabola y2 = 8px is of length 16p. The angle subtends byit at the ver tex of the parabola is1) / 4 2) / 2 3) 4) / 3

47. The equation 1ax by represents

1) pair of lines 2) circle 3) parabola 4) Ellipse49. I f (a 2)x2 + ay2 = 4 represents a rectangular hyperbola then a =

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

69. Thevlueof 1 11 1 112 4 8 ..........1 11 1 1 1/ 273 9

is

1) 0 2) 1/3 3) 2/3 4) 1/2

75. The value of 10

20

0r

r

C is

1) 220 2) 219 3) 219 + 12

20C10 4) 221 1

78. I f , are roots of the equation6x2+11x + 3 = 0 then

1) Both Cos1 and Cos1 are real 2) Both Cosec1 and Cosec1 are real

3) Both Cot1 and Cot1 are real 4) None

11

79. The value of Tan1 2sin 1

cos2

is

1) 12 2) 2 2

3) 1 4

4) 14

80. The number of dostr ict real roots of

in os0

S x C x CosxCosx Sinx CosxCosx Cosx Sinx

inthe inter nal

4 4x

is

1) 0 2) 3) 1 4) 3Revision programme(18-2-04)

7. In a ABC if a + b = 3c,then Cos A + Cos B = ...........1) 3 Cos C 2) 3 Sin C 3) 3 Cos(A B) 4) 3 3 Cos C

8. In ABC , if A = 180 b a = 2, ab = 4 then the tr iangle is ..........1) Acute angled 2)right angled 3) obtuse angled 4) Isoscees

11. The area of a circle is A1 and the area of the regular pentagoniscr ibed in the circleis A2. Then A1 : A2 = ...........

1) 5 10Cos 2)

2 sec5 10

3) 2 sec5 10

co

4) 3 sec5 5

co

16. In a ABC 1 2 35 2 6 3 2 2r r r r then A = ...........

1) 300 2) 600 3) 0122

24)

0172

28. The equation of the common tangent to the curves y2 = 8x and xy = 1 is...........1) 3y = 9x + 2 2) y = 2x + 1 3) 2y = x + 8 4) y = x + 2

32. A tangent is drawn at the point 3 3 cos , Sin , 0 2

of an ellipse

2 2

127 1x y

,

the least value of the sum of the interscepts on the coordinate axes by this tagent isattained at 0 = .......

1) 6

2) 3

3) 8

4) 4

40. I f the ellipse 2 2

14 1x y

meets the ellipse

2 2

2 11x y

a , a > 1 in n points, the n = .......

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

12

1. The points P(1, 3, 4), Q(1, 6, 10), R( 7, 4, 7) and S form a Rhyombus, the S = ........(17-2-04)

1) (1, 1, 5) 2) (1, 1, 5) 3) (1, 5, 1) 4) (5, 1, 1)

Revision Test (23-2-04)

1. 1

min0

1 nml t t dt then

1) , 1, 12

1 1

n

m n m n

nl lm m

2) , 1, 1

21 1

n

m n m n

nl lm m

3) , , 12

1 1

n

m n m n

ml lm m

4) , 1, 2

21 1m n m n

nl lm m

3. I f f(y) = ey, g(y) = y, y > 0 and F(t) = 1

0

f t y g y dy then

1) F(t) = te1 2) F(t) = 1 et(1 + t)3) F(t) = et (1 + t) 4) F(t) = tet

33. A wheel is rotated so that the angle of rotation is propor tioal to the square of time.The first revolution was per formed by the wheel for 8 sec. Then the angular veloc-ity in 32 sec after the wheel star ted is .............(rad / sec)

1) 2

2) 3) 32

4) 2

34. Two cars started from a place, one moving due east and other due north with equalspeed V. Thenthe rate at which they where being separated from each other is .....

1) 2V

2) 2V

3) 12V 4) 2V

40. A charge following through a conductor begining with time t = 0 is given by Q = 2t2+ 3t + 1. Then the currnt intensity at the end of the fifth second is .........1) 32A 2) 1/32 A 3) 1/ 23 A 4) 23A

12. I f a Sin 540 + b Cos 720 = 2 5 + 4, then a b = ......... 22-2-04

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

Daily Test - 17 (27-2-03)15. The number of ways in which we can put n distinct things in two identical boxes so

that no box is empty is1) 2n 2 2) 2n 1 3) 2n 1 1 4) None

18. Three men have 4 shir ts 5 pants and 6 caps. The number of ways they can wearthem is1) 15p3 2) 4

3.53.63 3) 4p3.5p3.

6p3 4) 180

13

28. Find 15C2 + 2.(15C3) + 3. 15C4 + .......... + 14. 15C15 = ........1) 14. 215 + 1 2) 13. 214 + 1 3) 14. 215 1 4) 13. 214 + 1

39. I f the sum of coefficients in (1 + x + x2)n is 243 then sum of coefficients in(2 + 3x x2)n is ........1) 256 2) 1024 3) 512 4) 2048

DAILY TEST-16 26-02-03

4). The middle term in the expantion of (1+4x+ 6x2+4x3+x4)6 is.....1) 6c3 x

3 2) 4c2 x2 3) 10c5x

5 4) 24c12x12

5) (11+ 2 30 )n=I+F ,where I,n are positive integers 0

14

16) The co efficient of x19 in (x+1)(x+4)(x+9)(x+16)...........(x+400) is 1) 2870 2) 210 3) 4001 4) 1900

17) The sum of the rational terms in the expantion of

10152 3

is

1) 32 2)42 3) 41 4) 38

18) The range of x for which the expantion 1 1

2 1 3x x

is valid is

1) (2,-2) 2) 1 1,

2 2

3) 2 2,

3 3

4)1 1,

3 3

19) if 1x and 20 1 221 .......

1 2x

a a x a xx x

then

1) 3 2) 4 3) 5 4) 6

20) If the mode coefficient of x2 in the expantion 2 2

1 11 x a x

is 246. Then a=

1) 12 2)

13 3)

14 4)

16

33) If 0 1 21 .........

( 1)( 2)........( ) 1 2nA AA A

x x x x n x x x x n

then g=

1) 5 2) -5 3) 3 4) -345) A bag contains 3 black, 4 white and 2 red balls, all the balls being different . The number of selec-tions of at most 6 balls containing balls of all the colors is 1) 26x4! 2) (26-1)4! 3) (25 -1)4! 4) (42) 4!54) There are n things of which r are identical and the rest are all different. The number of ways of arranging the things round a circle is

1) (n-1)! (r-1)! 2) ( 1)

!n

r

3) (n-1)!r 4)

( 1)!!

n

r

68) If 1x and f(x) =x+x2+x3+........ .g(x) = x-x2+x3-........... then (fog)(x) =

1) x 2) 1x

3) 2

21x

x4)

2

2

1xx

70) :f R A such that f(x) =2

2

11

x x

x x

is an ontofunction than A=

1)1 ,33

2) 1 ,13

3) 1,3 4) R-1 ,33

72) f(x) =sin2 2x+cos22x and g(x) =sec2x-tan2 x are such that f(x) =g(x) then they are defind on

1) 2) R 3) R- / (2 1) ,2x x n n z

4) 0, 2

15

28-11-04

1) If 1

(1 )(1 2 )(1 3 ) 1 1 2 1 3a b c

x x x x x x

then 1 3 5a b c

1) 13 2)

16 3)

115 4)

15

9) The coefficient of x53 in the expantion 100

0100

mc

m (x-3)100-m 2m is :

1) 47

100c 2) 53100c 3) 53100c 4) 53100c

11) If in the expantion of (1+x)n , the co efficients of 14th ,15th and 16th terms are in A.P , then n= 1) 23 2) 32 3) 34 4) 1or3

31) If ( )

( )

( ) , { (1 )}1

f ax

x

f a

ef x I xg x x dxe

and

( )

2( )

{ (1 )}f a

f aI g x x dx

then 21

II

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

37) / 4 2

2/ 4

sec1

x

x

e x dxe

1) 0 2) 2 3) e 4) e-2

38) If [x] denotes the greatest integer function less than or equal to x then 0

2x

dxe

1) log2 2) e2 3) 0 4) e-2

40) x x dx

, where 0 is;

1) 2 2

2

2) 2 2

2

3) 3 3

3

4)4 4

4

47)

2

02

0

[ ]

{ }

x dx

x dx

(where [x]=Fractional part of x)=

1) 0 2) 1 3) 2 4) 358) The radius of a centre of three circles described on the three sides 4x-7y+10=0,x+y-5=0 and 7x+4y-15=o of triangle as diameters is 1) (-1,-2) 2) (-1.2) 3) (1,-2) 4) (1,2)60) The radius of a circle having the lines x2+y2-2x+6y=0 as its normals and having size just sufficient to contain the circle x(x-4) +y(y-3)=0 is

1) 15 2) 152 3) 5 4) 7

65) A,B are conjucate points w.r.t two circle x2+y2+-2x+3y-4=0,x2+y2+2x-3y-6=0.Then the line 2x- 3y-1=0 divides AB in the ratio. 1) 1:2 internally 2) 29:37 internally 3) 29 : 37 internally 4) 1:1 internally

16

15-11-04

4) If f: 0, 2

(0, ) be a function defined by y=sin 2x

, then f is:

1) Injective 2) surjactive 3) bijection 4) only a function8) Let g(x) =sinx+cosx, g(x)= x2-1. thus g{f(x)} is invertible for x :

1) 02

2) 2

3) ,4 4

4) 0, 2

5) Let g(x)=1+x-[x] and f(x) =

1, 00, 01, 0

x

x

x

then for all x, f {g(x)}=

1) x 2) 1 3) f(x) 4) g(x)10) Range of the function f(x) =4x+2x+ 4x + 2 x+3 is :

1)3 ,4

2)3 ,4

3) (7, ) 4) 7,

11) If log2 x+log2 y>6, then the least value of (x+y) is: 1) 4 2) 8 3) 16 4) 32

12) If x=9 is a root of the eqation log (X2+15a2)- log (a-2)= log8

2ax

a

then the other root is:

1) 3 2) 12 3) 15 4) 2016) 12-22+32-42+ 52-62+........+(2n-1)2-(2n)2

1) 212 n n 2) 21 ( )

2n n

3) 21 ( 1)2

n n 4) 21 ( 1)2

n n

19) suppose a,b,c are in A.P and 2, 2 2,a b c a re in G.P (a

17

22) The first term of an infinite geometric progression is x and its sum is 5. Then 1) 0 10x 2) 0 10x 3) 10 10x 4) 10x

23) If a

b ,bc

,c

a are in H.P then

1) a2b,c2a,b2c 2) a2b,b2c,c2a 3)a2b,b2c,c2a are in G.P 4) a2b,c2a, b2c are in G.P25) The sum of (33-23)+(53-43)+(73-63)+.......... to 10 brackets is 1) 4960 2) 4860 3) 5060 4) 56028) is an imaginary cube root of unity . If 2 4(1 ) (1 )m m ,then least positive integral value of m is 1)6 2)5 3) 4 5) 3

29) If z=x-iy and z1/3 =p+iq, then 2 2

x yp q

p q

is equal to

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

30) Let z, be complex numbers such that 0z i and arg z = , Then arg z equals

1) 4

2) 2

3) 34

4) 54

35) If 1, a1,a2,a3,......, an-1 be the nth roots of unity and be a non real complex cube root of unity then

for n =3m+1, the value of 1 2 1( )( ).......( )na a a

1) 0 2) 1 3) 1 4) 21

36) If n = Cos 2 2n nx i Sin ,

1n

n

x

1) -1 2) 1 3) 12 4) 2

i

39. A point on the line x = 3 from which the tangents drawn to the circle x2 + y2 = 8 are at right anglesis :

1) 3, 7 2) 3, 23 3) 3, 3 4) ( 3, 0 )46. If the points A(1, 4) and B are symmetrical about the tangent to the circle x2 + y2 -x + y = 0 at the

origin then coordincates of B are

1) (1, 2 ) 2) 2,1 3) (4, 1) 4) 1, 247. Two circles, each of radius 5, have a common tangent at (1, 1) whose equation is 3x + 4y -7 = 0.

Then their centres are:1) (4, -5), (-2, 3) 2) (4, -3), (-2,5) 3) (4, 5) (-2, -3) 4) (4, 0) (0, 3)

50. If every member of family (2x-3y-5) + (3 4 7) 0x y is normal to a circle of area 154 sq.units, then the equation of this circle is:1) (x-1)2 + (y+1)2 = 49 2) (x-1)2 + (y-1)2 = 493) (x-1)2 + (y-2)2 = 25 4) (x-3)2 + (y-1)2 = 25

53. Centre of circle whose normals are x2 -2xy-3x + 6y = 0 is:

1) 33,2

2) 33,2

3) 3 ,32

4) 33,2

18

54. The length of tangents from any point on 15(x2 + y2 ) + 9x + 12y = 0 to the circles 25 (x2 + y2 ) +

15x +20y+5 = 0 50 (x2 + y2 ) + 30x + 40y +52 = 0 are in:

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

57) Let , a b and c be non-zero vectors such that 1 = c a3a b c b . If is the acuteangle between the vectors b and c , then Sin equals :

1) 13 2)

23

3) 23 4)

2 23

62. A function y = f(x0 has a second order derivative f11(x) = 6 (x-1). If its graph passes through thepoint (2,1) and at that point the tangent to the graph is y = 3x -5, then the function is :1) (x - 1)2 2) (x - 1)3 3) (x +1)3 4) (x+1)2

63. Angle of intersection of the curves x2 = 5 - 4y and y = x2 at the point in the first quardant is :

1) 2

2) 3

3) 4

4) 6

64. If the area of triangle formed by the positive x - axis and the normal and the tangent to the circle

x2 + y2 = a2 at the point ,2 2a a

is 2 units, then a =

1) 1 2) 2 3) 3 4) 472. The velocity of a rectilinear motion of a body is proportional to the square root of the distance

covered . Then the acceleration of the body is:1) Twice its velocity 2) Half the velocity3) 2 times the velocity 4) Constant

Specilal Batch Eamcet Cumulative 04-10-047. If the origin is shifted to (1, ) the co-ordinates of a point (3, ) changes to ( , )

then ( , ) =1) (1, 1) 2) (1, 0) 3) (0, 1) 4) (0, 2)

8. If axes are rotated through an angle and the point (Cos + Sin , Cos -Sin ) has new co-ordinates (p,q) then p+q =1) 2 Cos2 2) 2 Sin 2 3) Cos 2 4) Sin 2

15. If m1 , m2 are the roots of t2 - 7t + 12 = 0 then the area pf triangle formed by y = m1 x, y = m2 x

and y = 2 is _____ square units1) 1/3 2) 2/3 3) 1 4) 2

16. The equation of the straight line through the intersection of the lines x+3y+4 = 0 and 3x + y + 4 =0 and parallel to the angular bisector of the lines x - 2 = 0 and y + 5 = 01) x + y + 2 = 0 2) x + y = 0 3) x - y - 2 = 0 4) 3x - 2y = 0

Eamcet Date : 17-10-04

2. If the circle x2 +y2 + 2 2 x + 2 y + 6 = 0 represents a real circle then the least positiveintegral value of is1) 1 2) 2 3) 3 4) 4

19

9. If the common points of xy (3x + 6y - 4) ( x + 2y +5 ) = 0 are concyclic then the value of is1) 3 2)6 3) 2 4) 4

12. A circle passes through the points (1,2) (4, 3) and centre lies on x = y then its centre is

1) (3, 3) 2) (4, 4) 3) (6, 6) 4) 5 5, 2 2

13. A circle is inscribed and circumscribed to the square formed by the lines xy(x2 - a2) = 0 then thedifference of the radii of the circles is

1) a 2 1 2) a 2 12 3) 2 1a 4) a 2 12

14. If 2 21 + x Cos + y Sin - 4 = 02 x y has centre , and radius then the maximumvalue of where is parameter is

1) 4 2) 3 3) 3 2 4) 2 315. If the equation of the circle having 2x + y = 6 and 3x + 2y = 4 as diameters and radius 10 is

x2 + y2 + ax + by + c = 0 then1) a < b b > c 3) a < b > c 4) c < a > b

18. If A (1, 2), B(3, -3), C(5, 7 ) ans if the sum of the square of the distances of a point P to A, B, Cis constant and locus of P is a circle then its centre is1) (0, 0) 2) (3, 2 ) 3) (2, 3 ) 4) (1, 4)

27. If A = {1, 2, 3, 4, }, B = {1, 2, 3, 4, 5, 6} the number of functions of the type :f A B , f(x) =y and x < y where , y Bx A is

1) 6 5C 2) 6

5P 3) 56 4) 5!

41. If 1f xx

= 2 21

xx

then the value of f(2) =

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

43. If 3x-1 = x+2f x , : { 2} {3}f R R is __ function

1) one one 2) onto 3) bijection 4) Only function

44. If f(x) = - 1 + - 2x x then f : R R is1) only function 2) one-one 3) onto 4) bijection

46. The domain of the function f(x) = 2

2

416x

x

is the set A then the number of integral values i A is

1) 3 2) 4 3) 5 4) 6

47. The domain of = x- xf x where [] is G.I.F is1) R 2) 0, only 3) , 0 4) R - {0} only

50. If A and B are the domains if the function f(x) =log x and g(x) =log x then___1) A B 2) B A 3) A=B 4) A B R

20

57. The angle between the abscisa and the tangent to the parabolay y= x2+4x-17 at the point

5 -3, 2 4

M

is

1) 119

Tan 2) Tan-1 9 3) 119

Tan 4) -Cot -1 9

64. The function 2 = x ax-xf x , a>o

1) Increases in 300,4

2) Decreases in 3 ,4a

a

3) Decreases in 30,4a

4) Increases in 3 ,4a

a

74. The function 2 2 + 3x x is an increasing function when x belongs to the interval

1) 1, 2) (2, ) 3) (3, ) 4) (4, )80. The sum of two non-zero number is 6. The minimum value of the sum of the sum of their recipro-

cals is

1) 34 2)

65 3)

23 4)

32

Eamcet5. In a square ABCD, G1 = (2,4) is centroid by triangle ACD G2 = (4,4) is centroid of triangle ABC

then its area is1) 18 2) 18 3) 6 2 4) 5 2

8. In triangle ABC, centroid G = (4, 5) and orthocentre H = (3, 6) then distance between orthocentreand circumcentre is

1) 12 2)

32 3) 2 2 4) None

10. A = (3, 5) ; B = (7, 1); P = (6, 2) then the point Q which is collinear with A, B and P such that thelengths AP, AB, and AQ are in H.P is1) (9, -1) 2) ((-9, 1) 3) (7, 2) 4) None

11. In a triangle ABC, the internal angular bisector of angle A divides BC at D where A = (3, 2) D =(7, 10/3) and incentre is (6, 3) then excentre opposite to A is1) (9, 4) 2) (4, 9) 3) (-9, 7) 4) nONE

15. Let P = (1, 1) ; Q = (3, 2) R is a point on x - axis such that PR + RQ is minimum then its minimumvalue is1) 13 2) 2 13 3) 4 13 4) None

18. A= (3,4) B=(3,6) C=(7,4) are the vertices of triangle ABC where circumstencentre is (5,5) thenA

1) 450 2) 600 3) 900 4) None20. The locus of center of the circle which touches x-ax is and cuts off an interept odf length 10 units

from y-axis is1) x2 - y2 = 25 2) y2 - x2 = 25 3) x2 + y2 = 25 4) 2x2 - y2 = 25

21

21. A variable line passes through a fixed point A (1, 2) the locus of foot of perpendicular from A to itis a circle with radius is

1) 5 2) 5

23) 2 5 4) 3 5

28. 064 32 16 4 2 1

15 - 4

x x x x x

xLt

Cosx Sinx

=

1) (log 2)3 2) -8 (log 2)3 3) -12 (log 2)3 4) -96 (log 2)3

35. 2 n0

( / 2). Cos (x/2 ) ..... Cos (x/2 )x nLt Lt Cos x

1) 0 2) 1 3) 1/2 4) Sinx

x

62. If tan x tan y = a and x + y = 2b, then tan x and tan y are the roots of the equation1) x2 + x (1+a) tan 2b + a = 0 2) x2 + x (1-a) tan 2b + a = 03) x2 - x (1+a) tan 2b + a = 0 4) x2 - x (1-a) tan 2b + a = 0

DATE : 30/12/031. If /y x + /x y = 6 then dy/dx

1) 17

17x y

x y

2) 17

17x y

x y 3)

1717

y xx y 4)

1717

y xx y

8. f(x) is differentiable at x = a and ( ) 0f a then 1

1af

=

1) 21 /f a f a 2) 21 /f a f a

3) 21f a f a 4) 21f a f a10. Suppose f ; R-----> R is a function f(1) = 2, f(2) = 6 and f(x+y) = f(x) -kxy 2y2 for all x, y R

then1) f1(x) = f(x) 2) f1 (nx) f1 3) f1(nx) f(x) 4) f(nx) f1(x)

11. If f(x) is differentiable function such that ( f (x) )n = f (nx) x then f(x) f1 (nx)1) f(x) f(nx) 2) f1 (nx) f1 ( ) 3) f1 (nx) f (x) 4) f (nx) f1 (x)

12. If I(x) is the inverse function of f (x) and f1 (x) = 21

1 x then g1 (x) =

1) 1 + x 2 2) 21 [ ( )]g x 3) 21

1 [ ( )]g x 4) 1/1+x2

DAILY TEST-14 24-02-031. If m,n,p,q are consecutive integers then the value of im+in+ip+iq is

1) 1 2) 4 3) 0 4) None

3. If i reZ then ize

1) sinrre 2) sinre 3) rCose 4) rCosre

22

4. The value of the expression 2 2 21 1 1 1 1 11 1 2 2 ........ n n

where is an imaginary cube root of unity is

1) 2 2

3n n

2) 2 2

3n n

3) 2 1

3n n

4) None

IC ENGINEERING MATHS DATE: 21-03-200327. If , are the roots of (x-a) (x-b) = 10 then the roots of the equation (x- ) (x- )+10 = 0 are

1) a, b 2) a+b, a-b 3) a+10, b+10 4) a-10, b-10

31. If 2a2 = 5 +4 , 22 5 4, ( ) then the value of =______

1) -2 2) 98

3) 418 4)

418

32. If the roots of 5x2+ ( ) (2 1) 0x are the reciprocals o the roots of 2 2x 5 0X then ( , ) ___ 1) (1,1) 2) (1,-1) 3) (-1,-1) 4) (2,5)

33. If the equation (a2-5a+6)x2 + (a2-3a+2)x + (2a-4)=0 is an identity in x then a must be ____1) 3 2) 1/2 3) 2 4) -2

06-04-043) If (5,12) and (-9,12) are the foci of the hyperbola passing through the origin then its eccentricity is

1) 12 2) 2 3) 7 4)

17

22. Eqaton of the directries of the hyperbola xy=4 are1) 2 2X y =0 2) 2 2 0X y 3) 2 2 0X y 4) 2 2 0X y

24. pole of the line X+Y+2=0 w.r.fo xy =1 is1) (-1,-1) 2) (1,1) 3) (1,-1) 4) (-1,1)

25. If the eqation x2- 4y+ 4x-8y=k 1 is represent a hyperbola then1) k=0 2) k>0 or k

23

35.If the eccentricity of a hyperbola is 32 then the eccentricity of its conjugate hyperbola is

1) 35 2)

35

3) 23 4)

23

45. A practicle moves in a line with velocity given by 1ds

sdt

. The time takes by the practical to

cover a distance of 9 meters is1) 1 2) loge 10 3) log10e 4) 2log210

53. The particular solution of log dydx

=3x+4y and y(0)= 0 is

1) e3x+3e-4y=4 2) 4e3x+3e-4y=7 3) 4e3x-e-4y=3 4) 3e3x+4e4y=7AIEEE-UNIT-7 09-03-04

5. The number of ways of selecting atleast one and atmost n from 2n+1 distinct objects is 255 then n=1) 2 2) 3 3) 4 4) 5

7. Mr. A has 6 books & Mr B has 5 books . All the books are different. The number of ways in whichthey can exchange keeping their original numbers as it is1) 462 2) 461 3) 460 4) 459

8. The number of ways in which 7 different toys may be given away to 3 children so that each getsatleast 2 toys is1) 420 2) 510 3) 630 4) 720

9. n parallel lines intersect another set of 5 parallel lines and 150 parallelo grams are formed. Then n=1) 4 2) 5 3) 6 4) 10

21. A parallelogram is cut by two sets of 3 lines and 4 lines parallel to the sides , respectively thenumber of parallelograms thus formed is1) 100 2) 120 3) 150 4) 70

34. If z be any complex number such that 3 2 3 2 4z z then the locus of z is1) a circle 2) An elipse 3) a line segment 4) none of these

56. Length of shortest distance between the lines x=y=z and x+y=2,z-x =2 is ......

1) 2 2) 3 3) 12 4) 5

AIEE -MATHS-UNIT-5 (02-03-04)3. The points on the curve y-cos(x+y)- 2 2x at which the tangents are parallel to the line

x+2y=0 are

1) 3,0 ,0

2 2

2) ,0 ,02 2

3)30, ,0

2 2

4) 3,0 0,

2 2

4. From a pont A on the curve x=3y2-2y+7, subnormal and subtangent are drawn . if they measure 1unit each then distance of A from (11,-3) is1) 5 2) 3 3) 7 4) 1

11. If the tangent at P on the curve x2y3= a5 meets the coordinate axes at A and B then AP: PB=1) 2:3 2) 3:2 3) -2:3 4) -3:2

17. If y=z 2

2 1

x

o

t

t dt then the rate of change of y w.r.t x when x= 1 is

24

1) 2 2) 12 3)

12 4) -1

18. A stick of length a cms rests against a vertical wall and the horizantal floor. If the foot of the stickslides with a constant velocity of b cm/s then the mgnitued of the velocity of the middle point of thestick when it is equally inclined with the floor and the walls is

1) 2b

cm/s 2) 2b

3) 2ab

4) None

23. A variable triangle is inscribed in a circle of radius R. If the rate of change of a side is 2 R timesthe rate of change of the opposite angle than that angle is1) / 6 2) / 4 3) / 3 4) / 2

25. A point P is moving with angular velocity of 5 rad/sec on the circumference of a circle with center Oand radius 3 cm. If M is foot of the prependicular of p on the dia meter such that angle POM=300then the velocity at M is

1) 152 cm/sec 2)

152

cm/sec 3) 72 cm/sec 4)

72

cm/sec

45. If the bisector of the A makes an angle with BC then sin =

1) cos 2B C

2) sin 2B C

3) sin 2B A

4) sin 2C A

DAILY TEST (15-02-03)

2. The most general solutions 11

sin cos 22 2 2x x

are

1) 4n

2) 2 4

n

3) 4n

4) ( 1) 4

nn

3. The number of solutions of the equations tanx +tan2x+tan3x= tanx tan2x tan3x in the interval 0,1) 7 2) 5 3) 4 5) 6

4. If (sinx + cosx) (1+sin 2x) = 2 2 then general solutions of x=...........

1) ( 1) ;4nn n z

2) 2 ;4n n z

3) 2 ;4

n n z

4) 4n

9. If , , , are roots of tan 3 tan 34

then that value of tan +tan +tan +tan =___

1) 1/3 2) 1/6 3) 1/ 3 4) 0

13. The general solutions of the equation tan tan 2 2 0

tan 2 tanx x

x x is

1) n 2) 3n

3) 6n

4) (3 1) 3

n

16. the general solution of the equation cosx cos6x=-1 is given by ____

1) 2 1 2n

2) n 3) 2 1n 4) 2

n

18. If sinx+siny=0=cosx+cosy then x=

1) 2n y 2) 4n y 3) 2 1n y 4) 4 1n y

25

21. By the suitable translation of axes if the equation xy+3x-y+2=o has changed to XY=d then1) d=ab+c 2) d= c-ab 3) d= ab-c 4) a+b+c=d

22. By the translation of axes if 2xy+3x-y+2=0 has transformed to 2XY+K=0 then K=1) 10 2) 7/2 3) -7/2 4) 2/7

24. By shifting the origin to a suitable point if the equation (x-2)2+3(x-2)(y+1)+(y+1)2 +3(x-5)+2(y-1)+6=0 is transformed to x2+3xy+y2 +3x+2y=k then k=1)27 2) -27 3) -6 4) 7

25. By the suitable translation of the axes if 2 22 4

116 25

x y x y is transformed to

2 22 2

x y x ya b

=1 then a+b = _____

1) 41 2) 19 3) 9 4) 4

32. If the line joining A(1,1) B1 32,

3

is rotated through an angle 150 in anti clock wise direction

.If B goes to C then C=

1)(2,1) 2) (1,2) 3) 2 21 ,1

3 3

4) 2 21 ,13 3

37. Mirrors reflection of (2,3) in the line y=x is reflect again in y=0 , then the coordinates of resultingpoint is1) (2,3) 2) (2,-3) 3) (-3,-2) 4) (-3,2)

REVISION TEST -4 -MATHS (28-02-04)

2. If the 2 2X Y =1

tanyx

ae then

dydx =

1) x yx y 2)

x yx y 3)

x ya

x y

4) x y

ax y

7. If x=sec -cos , y=sec10 -cos10 and (x2+4)

2dydx

= k(y

2+4) then k=

1) 10 2) 1

10 3) 100 4) 1

1009. Let f(x) = (ax+b) cosx +(cx+d) sin x and f1(x) = x cos x be an identity in x then

1) a=1 2) b=1 3) c=2 4) d=1

10. If f(x)= cos cos cos .........cos2 4 8 2nnx x x xlt

then f1(x) at x= 2

is

1) 0 2) 24

3) 4

4) 24

13. If xn+m yn-m = ( ax2+2hx +by2)n ey/x then dydx =

1) x

y 2) yx

3) x

y

4) y

x

26

20. If sin(x+y) +cos(2x+2y) = log (3x+3y) then dydx =

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

23. If y=1 1 1

1 1 1n m p m m n p n m p n px x x x x x

then

dydx =

1) 0 2) 1 3) -1 4) 3

27. The derivative of tan-13

2 4

4 41 6

x x

x x

w.r to Tan-1 2

2

2 11 2x x

x

at x=0 is

1) 2 2) 14 3)

12 4) 4

29. If 2x yf

=

( ) ( )2

f x f y,x y R and f1(0)=-1, f(0)=1 then f(3)=

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

35. If 2cos = 2 2 2 2 and 2cos y= 2 2 2 3 then

1) x=y 2) 2x=3y 3) 3x=y 4) 3x=2y37. Tan 700-Tan 500 -Tan 200 +Tan 100=

1) 4 cot 200 2) 4 cos 400 3) 4 cot 600 4) 4 cot 800

43. If 1

9 cos 12 sinx x

then for all real x

1) the greatest positive value of is 1

15 2) the greatest negative value of is 1

15

3) 1

15 4)

1 1 15 15

53. Period of Tan ......1.2 3.4 5.6x x x

(x

27

63. The axes are rotated through certain angle and the equation 3 2x y changes to x=k then k

1) 1 2) 12 3)

12

4) 0

72. The equyation of the base of an isosceles triangle is 3 3x y with one of the vertex (1,2) theequation aa side though the vertex1) 3 3 2x y 2) 3 1 2 3x y

3) 3 1 2 3x y 4) 3 1 2 3x y 74. A line through (0,0) having slope = 2 meets two lines 2x+y=3 and 4x+2y+1=0 at p and q then

op:pq=1) 6:1 2) 3:1 3) 3:2 4) 2:1

HYDERABAD (17-03-04)14. If the lines joining the origin tot he points of intersection of the circle (x-h)2+(y-k)2=c2 and the line

1x yh k are at right angles then h2+k2=

1) c2 2) c2/2 3) 2c2 4) 4c250. Given that the equation Z2 +(P+iq)Z +r+is=0 where p,q,r,s are non zero ,has real roots then

1) pqr=r2+p2s 2) prs = q2+r2p 3) qrs=p2+s2q 4) pqs=s2+q2r

51. The arguement of sin 65

+i61 cos5

is

1) 6 / 5 2) 5 / 6 3) 9 /10 4) 2 / 552. common roots of the equations Z3 +2Z2+2Z+1=0 and Z1985+Z100+1=0 are

1) 2, 2) 21, , 3) 21, , 4) 2,

55. If 23e

then 2 4321 ........

1) -1 2) 1 5

2i

3) 1 4) 1 5

2i

72.In a ABC ,a=13 cm ,b=12 cm and c=5cm then the distance of A from BC is1) 450 2) 750 3) 600 4) 18

REVISION UNIT TEST 1 TO5AIEEE (16-03-2004)

3. If 0 sinlim

sin( )exx x

x, where a,b,c R {0} , exists and has non -zero value , then

1) a+c=b 2) b+c=a 3) a+b=c 4) None of these

4. If f(x) = x,x is rational =1-x,x is irational and lim ( )x a

f x

exists and has non -zero value , then1) 0 2) 1 3) 2 4) More than 2

5. Let f(x) = 0

1sin ,x

t dtt then the number of points of discontinuity of f(x) in (0, ) is

1) 0 2) 1 3) 2 4) None of this10. Let f: RR be a function defined by f(x) =max {x,x3}. The set of all points where f(x) is not

differentiable is1) {-1,1} 2) {-1,0} 3) {0,1} 4) {-1,0,1}

28

14. Let f(x) =maximum {sin x,cos x} X R . Minimum value of f(x) is1) 1- 2 2) -1 3) 1/ 2 4) 1/ 2

16. The minimum value of 12x+5y+6 satisfying the relation x2+ y2 =4 is1) 7 2) -20 3) 0 4) None of these

17. The difference between the least and the greatest value of the function

20

( ) cos cos 2x

f x t t dt in the intervel [0,2 ]is k . Then k=1) 1 2) 3 3) 5 4) None of these

18. The value of x for which the function f(x) = 2

2 2

0

1x t

t e

dt has externum is

1) -2 2) 0 3) 1 4) 220. The value of n for which the area of the triangle included between the axes and tangent to the

curve xny = bm is consant ,is1) 1/2 2) 1 3) 3/2 4) 2

27. If f( )= sin + cos , R , then

1) f( )[0,2] 2) ( ) [0, 2]f 3) ( ) [0,1]f 4) ( ) [1, 2]f 30. The no.of all possible tradis (a,b,c) sow that a+b cos 2x+c sin2 x=0 for all x is

1) 0 2) 1 3) 3 4) 33. The period of the function Cos(sin nx) is

1) 2n

2)

n

3) 2n

4) 4n

40. If 10

11

1sin ( ) 5

ix

,then 10

2

1i

ix

1) 0 2) 5 3) 10 4) 1541. The principal value of cos-1 (cos5) is

1) 5 2) 5 3) 5 4) 2 5 47. For a ABC , if cotA. CotB.Cot C>0, then the nature of the triangle is

1) Acte angled 2) Right angled 3) Obtuse angled 4) None of these52. Let f: RR be a function given by f(x+y)+ f(x-y) =2f(x). f(y) for all x,yR and f(0) 0 . then f(x)

is1) an even function 2) an odd function 3) neither even nor odd 4) None of these

60. If a,b,c are three consecutive odd numbers then the line ax-by+c=0 passes through a fixed pointhaving coordinates1) (2,3) 2) (-1,2) 3) (0,1) 4) (1,2)

63. The straight line ax+by+c=0 where abc 0 will pass through the first quadrant if1) ac>0,bc>o 2) ac>0 and bc>0 3) bc>0 and or ac>0 4) ac

29

REVISION PROGRAMME(07/02/04)

2 Let y=e2x; then 2

2

d ydx

2

2

d xdy

=.........

1) 1 2) e-2x 3) 2e-2x 4) -2e-2xWEEKEND(24-11-02)

6. S={3,5,7,11,13,17,19,23}, x=p/q where p,q S .The number of X such that x1 is

1) circle 2) ellipse0 3) straight line 4) pair of lines30. axis of a parabola is X-axis and and vertex is the origin . If the relative error of ordinate of any point

on the parabola is k times the relative error of its abscissa then k=.......1) 1/2 2) 1 3) 2 4) 4

57. In a right angled triangle ,the length of hypotenuse is h and intradius is r. The ratio of the area ofincircle and area of incircle and area of triangle is

1) 2r

h r

2) 2r

h r

3) 2

2 2

r

h r

4) r

h r

80. The base of an issoceless trriangle is x+4y-65=0 and the vertex formed by the equal sides is (2,3)then the centrod is1) (5,15) 2) (4,11) 3) (3,7) 4) (5,7)

REVISION PROGRAMME (09/02/04)3. The image of the line L=x+3y-5=0 w.r.t (0,0) is..........

1) x+3y-5=0 2) x-3y-5=0 3) x+3y+5=0 4) x-3y+5=0

26. The no.of real soltions of the equation 1 1 1

27 12 2 8x x x

is

1) 0 2)1 3) 4) None39. If P,Q are the roots of X2-2x+A=0 and r,s are the roots of x2-18x+B=0. If P

30

64.2

1

[2 1]x dx where [x] indicates greatest integer function of x

1) 72 2)

52 3) 7 4)9

80. The value of / 2

0

log tan x

dx =p / 2

0

log nsi x

dx=q / 2

0

log nse x

dx = r then p,q,r in decreasingorder1) pqr 2) rqp 3) rpq 4) prq

SPECIAL BATCH ASSIGN MENTS SURDS

9. If 012 3)