Olympia Academy

NEET/JEE Main/IIT Foundation Courses Tirupattur, Vellore-D.t

Olympia Academy

II-50% - ONE MARK - REVISION EXAM - 2016 A

MATHEMATICS

CLASS : XII MARKS : 100

[ CHAP – 5,6,7,8,10 B.B & C.B ] TIME : 1.00 hrs

I. Choose the correct answer : 100 x 1 = 100

1. The gradient of the curve y = -2x³ +3x + 5 at x = 2 is

1) -20 2) 27 3) -16 4) -21

2. The velocity v of a particle moving along a straight line when at a distance x from the origin is

given by a + bv²= x² where a and b are constants. Then the acceleration is

3. The slope of the normal to the curve y = 3x² at the point whose x coordinate is 2 is

4. The equation of the normal to the curve

at the point

1) 3

= 27t - 80 2) 5

= 27 t -80 3) 3

= 27 t + 80 4)

5. The parametric equation of the curve x^2/3 + y^2/3 = a^2/3 are

1) x = a sin³ q , y = a cos³ q 2) x = a cos³q , y = a sin³ q

3) x = a³ sin q , y = a³ cos q 4) x = a³ cos q , y = a³sin q

6. What is the surface area of a sphere when the volume is increasing at the same rate as its radius?

1) 1 2)

3) 4

7. If y = 6x - x³and x increases at the rate of 5 units per second, the rate of change of slope when x = 3 is

1) -90 units/sec 2)90 units/sec 3)180 units/sec 4)-180 units/sec

8. The angle between the parabolas y² = x and x² = y at the origin is

9. The value of ‘a’ so that the curves y = 3e^x and y =

intersect orthogonally is

1) -1 2) 1 3)

4) 3

10. The Rolle’s constant for the function y = x² on [ -2, 2] is

2) 0 3) 2 4) -2

11. The value of ‘c’ of Lagranges Mean Value Theorem for f (x) =

when a = 1 and b = 4 is

12. If f (a) = 2; f ' (a) = 1 ; g (a) = -1 ; g ' (a) = 2, then the value of

1) 5 2) -5 3) 3 4) -3

13. The function f (x) = x² is decreasing in

1) ( -

) 2) ( -

, 0 ) 3) ( 0,

) 4) ( -2,

)

14. The least possible perimeter of a rectangle of area 100 m² is

1. 10 2. 20 3. 40 4. 60

15. Which of the following curves is concave down?

1) y = - x ² 2) y = x ² 3) y = e ^x 4) y = x² + 2x - 3

16. If u = x ^y then

is equal to

1) yx^y-1 2) u log x 3) u log y 4) xy^x-1

17. The curve y²(x-2) = x²(1+x) has

1) an asymptote parallel to x-axis 2) an asymptote parallel to y-axis

3) asymptotes parallel to both axes 4) no asymptotes

18. If u = log

, then

1) 0 2) u 3) 2 u 4) u^-1

19. An asymptote to the curve y² (a + 2x) = x² (3a - x) is

1) x = 3a 2) x = -

3) x =

4) x = 0

20. If u = f

then

is equal to

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

21. If u = sin ^{- 1}

and f = sinu, then f is a homogeneous function of degree

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

22. If u =

, then

2) u 3)

4) - u

23. Identify the true statements in the following:

(i) If a curve is symmetrical about the origin, then it is symmetrical about both axes.

(ii) If a curve is symmetrical about both the axes, then it is symmetrical about the origin.

(iii) A curve f (x, y) = 0 is symmetrical about the line y = x if f (x, y) = f (y, x).

(iv) For the curve f (x, y) = 0, if f (x, y) = f (-y, - x), then it is symmetrical about the origin.

1. (ii), (iii) 2. (i), (iv) 3. (i), (iii) 4. (ii), (iv)

24. The percentage error in the 11^th root of the number 28 is approximately _________ times the

percentage error in 28.

3) 11 4) 28

25. The curve 9y² = x²(4-x²) is symmetrical about

1. y-axis 2. x-axis 3. y = x 4. both the axes

26. The value of

is 1)

3) 0 4)

27. The value of

is 1)

2) 0 3)

28. The value of

29. The value of

3. 0 4.

30. The value of

4) 0

31. The area of the region bounded by the graph of y = sinx and y = cosx between x = 0 and

x =

3) 2

4) 2

32. The area bounded by the parabola y² = x and its latus rectum is

33. The volume, when the curve y =

from x = 0 to x = 4 is rotated about x- axis is

1) 100

34. Volume of solid obtained by revolving the area of the ellipse

about major and minor axes are in the ratio

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

35. The length of the arc of the curve x^2/3 + y^2/3 = 4 is

1) 48 2) 24 3) 12 4) 96

36. 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

37. The value of

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

38. The value of

3. 0 4.

39. The area bounded by the line y = x, the x-axis, the ordinates x = 1, x = 2 is

40. The area between the ellipse

and its auxillary circle is

b(a - b) 2) 2

a (a - b) 3)

a (a - b) 4) 2

b ( a - b)

41. The integrating factor of

1) log x 2) x² 3) e^x 4) x

42. The integrating factor of dx + xdy = e^-y sec² y dy is

1) e^x 2) e^-x 3) e^y 4) e^-y

43. The solution of

+ mx = 0 , where m < 0 is

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

44. The differential equation

1. of order 2 and degree 1 2. of order 1 and degree 2

3. of order 1 and degree 6 4. of order 1 and degree 3

45. The differential equation of all circles with centre at the origin is

1) x dy + y dx = 0 2) x dy - y dx = 0 3) x dx + y dy = 0 4) x dx - y dy = 0

46. The complementary function of (D² + 1 ) y = e^2x is

1) (Ax + B)e^x 2) A cos x +B sinx 3) (Ax + B)e^{2 x} 4) (Ax + B)e^-x

47. The differential equation of the family of lines y = mx is

= m 2) y dx - xdy = 0 3)

4) ydx + xdy = 0

48. The degree of the differential equation c=

, where c is a constant is

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

49. The differential equation satisfied by all the straight lines in xy-plane is

= a constant 2.

3. y+

= 0 4.

50. The differential equation obtained by eliminating a and b from y = ae^3x + be^-3x is

51. If f ^¢(x) =

and f (1) = 2, then f (x) is

52. The particular integral of (3D² + D-14)y = 13e^2x is

1) 26xe^2x 2)13xe^2x 3) xe^2x 4)

53. The particular integral of the differential equation f (D) y = e^ax , where f (D) = (D-a) g(D),

g(a) ¹0 is

1) me^ax 2)

3) g(a)e^ax 4)

54. If cos x is an integrating factor of the differential equation

+ Py = Q , then P =

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

55. The integrating factor of

1) e^x 2) log x 3)

4) e^-x

56. A random variable X has the following probability distribution

X	0	1	2	3	4	5
P(X=x)		2a	3a	4a	5a

Then P(1

4) is

57. X is a discrete random variable which takes the values 0, 1, 2 and P(X=0) =

P(X=1) =

, then the value of P(X =2 ) is

58. Given E(X+ c) = 8 and E(X-c) = 12 then the value of c is

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

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

1) 2 2) 4 3) 6 4) 8

60. Var (4X + 3) is

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

61. The mean of a binomial distribution is 5 and its its standard deviation is 2. Then the value

of n and p are

62. In 16 throws of a die getting an even number is considered a success. Then the variance of

the successes is

1. 4 2. 6 3. 2 4. 256

63. If 2 cards are drawn from a well shuffled pack of 52 cards, the probability that

they are of the same colours without replacement, is

64. If a random variable X follows Poisson distribution such that E(X² ) = 30, then the variance of the distribution is

1. 6 2. 5 3. 30 4. 25

65. For a Poisson distribution with parameter

=0.25 the value of the 2^nd moment about the origin is

1)0.25 2)0.3125 3)0.0625 4)0.025

66. If

is a p.d. f. of a normal distribution with mean

, then

1. 1 2. 0.5 3. 0 4. 0.25

67. If

is a p.d. f. of a normal variate X and X ~ N(

), then

1. undefined 2. 1 3. 0.5 4. -0.5

68. The marks secured by 400 students in a Mathematics test were normally distributed with mean 65. If 120 students got more marks above 85, the number of students securing marks between 45 and 65 is

1)120 2)20 3)80 4)160

69. The random variable X follows normal distribution f(x) = c

. Then the value of ‘c’ is

3) 5

70. In a Poisson distribution if P(X = 2) =P(X=3) then the value of its parameter

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

71. Let ‘h' be the height of the tank. Then the rate of change of pressure ‘p’ of the tank with respect to height is

72. Food pockets were dropped from an helicopter during the flood and distance fallen in ‘t’ seconds is given by

(g = 9.8 m/

). Then the speed of the food pocket after it has fallen for ‘2’ seconds is

1. 19.6 m/sec 2. 9.8 m/sec 3. -19.6 m/sec 4. -9.8 m/sec

73. A continuous graph y = f (x) is such that

. Then

has a

1. vertical tangent y =

2. horizontal tangent x =

3. vertical tangent x =

4. horizontal tangent y =

74. The point that separates the convex part of a continuous curve from the concave part is

1. the maximum point 2. the minimum point

3. the inflection point 4. critical point

75. Which of the following statement is incorrect?

1. Initial velocity means velocity at t = 0

2. Initial acceleration means acceleration at t = 0

3. If the motion is upward, at the maximum height, the velocity is not zero

4. If the motion is horizontal, v = 0 when the particle comes to rest

76. In the law of mean, the value

satisfies the condition

77. If

is a differentiable function of x and y ; x and y are differentiable functions of ‘t’ then

78. The differential on y of the function

4. 0

79. The differential of

80. The curve

has

1. only one loop between x=0 and x=1

2. two loops between x=-1 and x=0

3. two loops between x=-1 and 0; 0 and 1

4. no loop

81. The x-intercept of the curve

2. 6, 0 3.

82. The curve

is symmetrical about

1. x-axis only 2. y-axis only 3. both the axes 4. both the axes and origin

83. If f(x) is even function

1. 0 2. 2

4. -2

84.

85. The surface area obtained by revolving the area bounded by the curve y= f(x), the two ordinates x=a, x=b and x-axis, about x-axis is

3. 2

4.2

86. If

, then

87. The arc length of the curve y = f(x) from x=a to x=b is

3. 2

4.2

88.

1. -

3. -

4. 2

89. The order and degree of the differential equation

are

1. 2, 1 2. 1, 2 3. 1, 1 4. 2,2

90. The order and degree of the differential equation

are

1. 1, 1 2. 1, 2 3. 2, 1 4. 0, 1

91. The order and degree of the differential equation

are

1. 2, 1 2. 1, 2 3. 2,

4. 2,2

92. The order and degree of the differential equation

are

1. 1, 1 2. 1, 2 3. 2, 1 4. 2,2

93. The solution of a linear differential equation

where P and Q are functions of x is

94. The solution of a linear differential equation

where P and Q are functions of y is

95. A continuous random variable takes

1. only a finite number of values

2. all possible values between certain given limits

3. infinite number of values

4. a finite or countable number of values

96. A continuous random variable X has probability density function ‘f(x)’ then

97. Which of the following is or are correct regarding normal distribution curve ?

a. symmetrical about the line X =

(mean)

b. Mean = median = mode

c. unimodal

d. Points of inflection are at X =

1. a, b only 2. b,d only 3. a.b,c only 4. all

98. For a standard normal distribution the mean and variance are

3. 0, 1 4. 1, 1

99. If X is a continuous random variable then which of the following is incorrect ?

100. Which of the following is not true regarding the normal distribution?

1. skewness is zero. 2. mean = median = mode

3. the points of inflection are at X =

4. maximum height of the curve is

RKV MATRIC HIGHER SECONDARY SCHOOL – JEDARPALAYAM

II-50% - ONE MARK - REVISION EXAM - 2016

MATHEMATICS

CLASS : XII MARKS : 100

DATE : 05.11.16 [ CHAP – 5,6,7,8 & 10 B.B.& C.B ] TIME : 1.00 hrs

I. Choose the correct answer : 100 x 1 = 100

1. x = 2 ,y; y = -2x³ +3x + 5 vd;w tistiuapd; rha;t[

1) -20 2) 27 3) -16 4) -21

2. MjpapypUe;J xU neh;f;nfhl;oy; x bjhiytpy; efUk; g[s;spapd; jpirntfk; v vdt[k; a +bv² = x²vdt[k; bfhLf;fg;gl;Ls;sJ/ ,';F a kw;Wk; b khwpypfs;/ mjd; KLf;fk; MdJ

3. y = 3x² vd;w tistiuf;F x ,d; Maj;bjhiyt[ 2 vdf; bfhz;Ls;s g[s;spapy; br';nfhl;od; rha;thdJ 1)

vDk; tistiuf;F g[s;sp

vd;w g[s;spapy; br';nfhl;od; rkd;ghL

1) 3

= 27t - 80 2) 5

= 27 t -80 3) 3

= 27 t + 80 4)

vDk; tistiuapd; Jiz myFr; rkd;ghLfs;

a) x = a sin³ q , y = a cos³ q c) x = a cos³q , y = a sin³ q

b) x = a³ sin q , y = a³ cos q d) x = a³ cos q , y = a³sin q

6. xU nfhsj;jpd; fd mst[ kw;Wk; Muj;jpy; Vw;gLk; khWtPj';fs; vz;zstpy; rkkhf ,Uf;Fk; nghJ nfhsj;jpd; tisgug;g[

1) 1 2)

3) 4

7. y = 6x - x³ nkYk; x MdJ tpdhof;F 5 myFfs; tPjj;jpy; mjpfhpf;fpd;wJ/

x = 3 vDk; nghJ mjd; rha;tpd; khWtPjk;

1) -90 myFfs;/tpdho 3) 90 myFfs;/tpdho

3) 180 myFfs;/tpdho 4) -180 myFfs;/tpdho

8. y² = x kw;Wk; x² = y vd;w gutisa';fSf;fpilna Mjpapy; mika[k; nfhzk;

9. y = 3e^x kw;Wk; y =

vd;Dk; tistiufs; br';Fj;jhf btl;of; bfhs;fpd;wd vdpy; ‘a’ ,d; kjpg;g[ 1) -1 2)1 3)

4) 3

10. y = x² vd;w rhh;gpw;F [ -2, 2] ,y; nuhypd; khwpyp

2) 0 3) 2 4) -2

11. a = 1 kw;Wk; b = 4 vdf; bfhz;L. f (x) =

vd;w rhh;gpw;F byf;uh";rpapd; ,ilkjpg;g[j; njw;wj;jpd;go mika[k; ‘c’ ,d; kjpg;g[

12. f (a) = 2; f ' (a) = 1 ; g (a) = -1 ; g ' (a) = 2 vdpy;

,d; kjpg;g[

1) 5 2) -5 3) 3 4) -3

13/ f (x) = x² vd;w rhh;g[ ,w';Fk; ,ilbtsp

1) ( -

) 2) ( -

, 0 ) 3) ( 0,

) 4) ( -2,

)

14. 100 kP ² gug;g[ bfhz;Ls;s brt;tfj;jpd; kPr;rpW Rw;wst[

1. 10 2. 20 3. 40 4. 60

15. gpd;tUk; tistiufSs; vJ fPH;nehf;fp FHpt[ bgw;Ws;sJ>

1) y = - x ² 2) y = x ² 3) y = e ^x 4) y = x² + 2x - 3

16. u = x ^y vdpy;

f;Fr; rkkhdJ

1) yx ^y-1 2) u log x 3) u log y 4) xy ^x-1

17. y ² ( x - 2 ) = x² ( 1 + x ) vd;w tistiuf;F

1) x - mr;Rf;F ,izahd xU bjhiyj; bjhLnfhL cz;L

2) y - mr;Rf;F ,izahd xU bjhiyj; bjhLnfhL cz;L

3) ,U mr;RfSf;Fk; ,izahd bjhiyj; bjhLnfhLfs; cz;L

4) bjhiyj; bjhLnfhLfs; ,y;iy

18. u = log

vdpy;

vd;gJ

1) 0 2) u 3) 2u 4) u^-1

19. y² (a + 2x) = x² (3a - x) vd;w tistiuapd; bjhiyj; bjhLnfhL

1) x = 3a 2) x = -a/2 3) x = a/2 4) x = 0

20. u = f

vdpy;.

,d; kjpg;g[

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

21. u = sin ^{- 1}

kw;Wk; f = sin u vdpy;. rkgoj;jhd rhh;g[ f ,d;go

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

22. u =

vdpy;

2) u 3)

4) - u

23/ gpd;tUtdtw;Ws; rhpahd Tw;Wfs;:

1) xU tistiu Mjpia bghWj;J rkr;rPh; bgw;wpUg;gpd; mJ ,U

mr;Rfisg; bghWj;JK; rkr;rPh; bgw;wpUf;Fk;/

2) xU tistiu ,U mr;Rfisg; bghWj;J rkr;rPh; bgw;wpUg;gpd; mJ

Mjpiag; bghWj;Jk; rkr;rPh; bgw;wpUf;Fk;/

3) f (x , y) = 0 vd;w tistiu y = x vd;w nfhl;ilg; bghWj;J rkr;rPh;

bgw;Ws;sJ vdpy; f (x , y) = f ( y , x)

4) f (x , y) = 0 vd;w tistiuf;F f (x , y) = f (-y , -x ) cz;ikahapd; mJ

Mjpiag; bghWj;J rkr;rPh; bgw;wpUf;Fk;/

1) (ii), (iii) 2) (i), (iv) 3) (i), (iii) 4)(ii), (iv)

24. 28 ,d; 11 Mk; go rjtpfpjg; gpiH njhuhakhf 28 ,d; rjtpfpjg; gpiHiag; nghy; _____ kl';fhFk;/

3) 11 4) 28

25. 9y² = x²(4-x²) vd;w tistiu vjw;F rkr;rPh;>

1) y -mr;R 2) x -mr;R 3) y = x 4) ,U mr;Rfs;

26.

,d; kjpg;g[ 1)

3)0 4)

27.

,d; kjpg;g[ 1)

2) 0 3)

28.

,d; kjpg;g[ 1)

29.

,d; kjpg;g[ 1.

3. 0 4.

30.

,d; kjpg;g[ 1)

4) 0

31. x = 0 ,ypUe;J x =

tiuapyhd y = sinx kw;Wk; y = cos x vd;w tistiufspd; ,ilg;gl;l gug;g[

3) 2

4) 2

32. gutis y² = x f;Fk; mjd; brt;tfyj;jpw;Fk; ,ilg;gl;l gug;g[

33. y =

vd;w tistiu x = 0 tpypUe;J x = 4 tiu x- mr;ir mr;rhf

itj;Jr; RHw;wg;gLk; jplg;bghUspd; fd mst[

1) 100

34.

vd;w ePs;tl;lj;jpd; gug;ig bel;lr;R. Fw;wr;R ,tw;iw bghWj;Jr; RHw;wg;gLk; jplg;bghUspd; fd mst[fspd; tpfpjk;

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

35. x^2/3 + y^2/3 = 4 vd;w tistiuapd; tpy;ypd; ePsk;

1) 48 2) 24 3) 12 4) 96

36/ Muk; 5 cs;s nfhsj;ij js';fs; ikaj;jpypUe;J 2 kw;Wk; 4 J}uj;jpy; btl;Lk; ,U ,izahd js';fSf;F ,ilg;gl;l gFjpapd; tisg;gug;g[

1) 20

2) 40

3)10

4) 30

37.

,d; kjpg;g[

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

38.

,d; kjpg;g[

3. 0 4.

39. y = x vd;w nfhl;ow;Fk; x- mr;R. nfhLfs; x = 1 kw;Wk; x = 2 Mfpatw;wpw;Fk; ,ilg;gl;l mu';fj;jpd; gug;g[

40.

vd;w ePs; tl;lj;jpw;Fk; mjd; Jiz tl;lj;jpw;Fk; ,ilg;gl;l gug;g[

b(a - b) 2) 2

a (a - b) 3)

a (a - b) 4) 2

b ( a - b)

41.

vd;w tiff;bfGr; rkd;ghl;od; bjhiff; fhuzp

1) log x 2) x² 3) e^x 4) x

42. dx + xdy = e^-y sec² y dy ,d; bjhiff; fhuzp

1) e^x 2) e^-x 3) e^y 4) e^-y

43. m < 0, Mf ,Ug;gpd;

+ mx = 0 ,d; jPh;t[

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

44.

vd;w tiff;bfGtpd;

1) thpir 2 kw;Wk; go 1 2) thpir 1 kw;Wk; go 2

3) thpir 1 kw;Wk; go 6 4) thpir 1 kw;Wk; go 3

45/ Mjpg;g[s;spia ikakhff; bfhz;l tl;l';fspd; bjhFg;gpd; tiff;bfGr;

rkd;ghL

1) x dy + y dx = 0 2) x dy - y dx = 0 3) x dx + y dy = 0 4) x dx - y dy = 0

46. (D² + 1 ) y = e^2x ,d; epug;g[r; rhh;g[

1) (Ax + B)e^x 2) A cos x +B sinx 3) (Ax + B)e^{2 x} 4) (Ax + B)e^-x

47. y = mx vd;w neh;f;nfhLfspd; bjhFg;gpd; tiff;bfGr; rkd;ghL

= m 2) y dx - xdy = 0 3)

4) ydx + xdy = 0

48. c =

vd;w tiff;bfGr; rkd;ghl;od; go

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

49. xy- jsj;jpYs;s vy;yh neh;f;nfhLfspd; bjhFg;gpd; tiff; bfGr; rkd;ghL

= xU khwpyp 2.

3. y+

= 0 4.

50. y = ae^3x + be^-3x vd;w rkd;ghl;oy; a iaa[k; b iaa[k; ePf;fpf; fpilf;Fk;

tiff;bfGr; rkd;ghL

51. f ^¢(x) =

kw;Wk; f (1) = 2 vdpy; f (x) vd;gJ

52. (3D² + D-14)y = 13e^2x ,d; rpwg;g[r; jPh;t[

1) 26xe^2x 2)13xe^2x 3) xe^2x 4) x²/2e^2x

53. f (D) = (D-a) g(D) , g(a) ¹0 vdpy; tiff;bfGr; rkd;ghL f (D) y = e^ax ,d;

rpwg;g[j; jPh;t[

1) me^ax 2)

3) g(a)e^ax 4)

54.

+Py = Q vd;w tiff;bfGr; rkd;ghl;od; bjhiff; fhuzp cos x

vdpy;. P ,d; kjpg;g[

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

55.

,d; bjhiff; fhuzp

1) e^x 2) log x 3)

4) e^-x

56. X vd;w rktha;g;g[ khwpapd; epfH;jft[g; guty; gpd;tUkhW:

X	0	1	2	3	4	5
P(x = X)	1/4	2a	3a	4a	5a	1/4

P(1£ x £ 4) ,d; kjpg;g[

57. X vd;w xU jdpepiy rktha;g;g[ khwp 0 , 1 , 2 vd;w kjpg;g[fisf; bfhs;fpwJ/ nkYk; P (X= 0) =

, vdpy; P (X = 1) =

, vdpy; P(X = 2 ) ,d; kjpg;g[

58. E(X+ c) = 8 kw;Wk; E (x-c) = 12 vdpy; c ,d; kjpg;g[

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

59. X vd;w rktha;g;g[ khwpapd; gutw;go 4 nkYk; ruhrhp 2 vdpy; E(X²) ,d;

kjpg;g[

1) 2 2) 4 3) 6 4) 8

60. Var (4X + 3) ,d; kjpg;g[

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

61. xU <UWg;g[g; gutypd; ruhrhp 5 nkYk; jpl;ltpyf;fk; 2 vdpy; n kw;Wk;

p ,d; kjp;gg[fs;

62. xU gfilia 16 Kiwfs; tPRk; nghJ. ,ul;ilg;gil vz; fpilg;gJ btw;wpahFk; vdpy; btw;wpapd; gutw;go

1)4 2)6 3)2 4)256

63. ed;F fiyf;fg;gl;l 52 rPl;Lfs; bfhz;l rPl;Lf;fl;oypUe;J 2 rPl;Lfs; vLf;fg;gLfpd;wd/ ,uz;Lk; xnu epwj;jpy; ,Uf;f epfH;jft[

64. xU rktha;g;g[ khwp X gha;!hd; gutiyg; gpd;gw;WfpwJ/ nkYk; E(X²) = 30 vdpy; gutypd; gutw;go

1)6 2)5 3)30 4)25

65. gha;!hd; gutypd; gz;gsit

=0.25 vdpy; ,uz;lhtJ tpyf;fg; bgUf;Fj; bjhif

1)0.25 2)0.3125 3)0.0625 4)0.025

66. xU ,ay;epiyg; gutypd; epfH;jft[ mlh;j;jpr; rhh;g[ f (x) ,d; ruhrhp

m vdpy;

,d; kjpg;g[

1)1 2)0.5 3)0 4)0.25

67. xU ,ay;epiy khwp X ,d; epfH;jft[ mlh;j;jpr; rhh;g[ f(x) kw;Wk;

X~N(m , s²) vdpy;

1) tiuaWf;f KoahjJ 2)1 3) 0.5 4) -0.5

68. 400 khzth;fs; vGjpa fzpjj; njh;tpd; kjpg;bgz;fs; ,ay;epiyg; gutiy xj;jpUf;fpwJ/ ,jd; ruhrhp 65. nkYk; 120 khzth;fs; 85 kjpg;bgz;fSf;F nky; bgw;wpUg;gpd;. kjpg;bgz;fs; 45 ,ypUe;J 65 f;Fs; bgWk; khzth;fspd; vz;zpf;if

1)120 2)20 3)80 4)160

69. xU rktha;g;g[ khwp X , ,ay;epiyg; guty; f(x)=c

I gpd;gw;WfpwJ vdpy; c ,d; kjpg;g[

3) 5

70. xU gha;!hd; gutypy; P(X = 2) = P(X =3) vdpy;. gz;gsit

,d; kjpg;g[

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

71/ xU ePu;j; bjhl;oapd; cauk;

vd;f/ mj;bjhl;oapd; mGj;jk;

MdJ cauj;ijg; bghWj;J khWk; tPjk;

72/ bts;sg; bgUf;fj;jpd; nghJ K:yk; ,lg;gl;l czt[g; bghUl;fs;

tpdhoapy; fle;j J}uk;

tpdho²) vdpy; mJ nghlg;gl;l 2?tpdhofSf;Fg; gpd; mg;bghUspd; ntfk;/

1/ 19/6 kP

tpdho 2/ 9/8 kP

tpdho

3/ ?19/6 kP

tpdho 4/ ?9/8 kP

tpdho

73/ bjhlu;r;rpahd tistiu

MdJ

vd;w g[s;spapy;

vDk;nghJ

vdpy;

f;F

vd;w epiyf;Fj;jhd bjhLnfhL cz;L

vd;w fpilkl;l bjhLnfhL cz;L

vd;w epiyf;Fj;jhd bjhLnfhL cz;L

vd;w fpilkl;l bjhLnfhL cz;L

74/ xU bjhlu;r;rpahd tistiuapy; FHpt[ gFjpapypUe;J Ftpt[ gFjpahf khw;wk; bgWk; g[s;sp

1/ bgUk g[s;sp 2/ rpWk g[s;sp

3/ tist[ khw;Wg; g[s;sp 4/ khWepiyg;g[s;sp

75. fPH;f;fhQqk; Tw;wpy; vJ rupay;y>

1 bjhlf;f jpirntfk; vd;gJ

tpYs;s jpirntfk;

2 bjhlf;f KLf;fk; vd;gJ

tpYs;s KLf;fk;

3 xU Jfs; br';Fj;jhfr; brd;W mjpfgl;r cauk; mila[k; nghJ mjd;

jpirntfk; g{r;rpaky;y

4/ xU JfshdJ fpilkl;l ,af;fj;jpy; njf;f epiyf;F tUk; neuj;jpy;

76/ ,ilkjpg;g[ tpjpapd;go

tpd; kjpg;g[ ve;j epge;jidia epiwt[ bra;a ntz;Lk;/

77/

vd;gJ x kw;Wk; y ,y; tifaplj;jf;f rhu;g[/ nkYk;

kw;Wk;

vd;git

My; Md tifaplj;jf;f rhu;g[fs; vdpy;

78.

vdpy;

,d; tifaPL

4. 0

79.

,d; tifaPL

80.

vd;w tistiu

kw;Wk;

f;fpilna xU fz;zp bgw;Ws;sJ

kw;Wk;

f;fpilna ,U fz;zpfis bgw;Ws;sJ

kw;Wk;

kw;Wk; 1 fSf;fpilna ,U fz;zpfs; bgw;Ws;sJ/

4/ fz;zpfs; VJk; bgwtpy;iy/

81.

vd;w tistiuapy;

btl;Lj;Jz;L.

2. 0, 6 3/

82.

vd;w tistiu vjidg; bghWj;J rkr;rPu; bgw;Ws;sJ/

-mr;ir kl;Lk; 2/

mr;ir kl;Lk;

3. ,U mr;Rf;fis 4/ ,U mr;Rf;fs; kw;Wk; Mjpia

83/

Xu; ,ul;ilg;gilr; rhu;bgdpy;

1/ 0 2/

84/

85/

vd;w tistiu

Mfpa nfhLfs;

mr;R Mfpatw;why; milg;gLk; gug;gpid

-mr;irg; bghWj;J RHw;wpdhy; Vw;gLk; jplg;bghUspd; tisgug;g[

86/

vdpy;

87/

vd;w tistiuf;F

apypUe;J

tiu cs;s tpy;ypd; ePsk;/

88/

1. -

3. -

4) 2

89.

vd;w tiff;bfGr; rkd;ghl;od; tupir kw;Wk; go

90/

vd;w tiff;bfGr; rkd;ghl;od; tupir kw;Wk; go

91/

vd;w tiff;bfGr; rkd;ghl;od; tupir kw;Wk; go

92/

vd;w tiff;bfGr; rkd;ghl;od; tupir kw;Wk; go

93/

vd;w neupa tiff;bfGr; rkd;ghl;oy;

kw;Wk;

Mfpait

,d; rhu;g[fshf ,Ug;gpd;/ jPu;t[

94/

vd;w neupa tiff;bfGr; rkd;ghl;oy; P kw;Wk;

Mfpait

,d; rhu;g[fshf ,Ug;gpd;. jPu;t[

95. xU bjhlh; rktha;g;g[ khwp

1. Kot[w;w fzj;jpd; kjpg;g[fisg; bgWfpwJ.

2. Fwpg;gpl;l xU ,ilbtspapYs;s vy;yh kjpg;g[fisa[k; bgWfpwJ

3. vz;zpyl';fh kjpg;g[fisg; bgWfpwJ/

4. xU Kot[w;w my;yJ vz;zplj;jf;f kjpg;g[fisg; bgWfpwJ/

96. xU bjhlh; rktha;g;g[ khwp X ,d; epfH;jft[ mlh;j;jpr; rhh;g[ ‘f(x)’ vdpy;

97. ,ay;epiyg; gutiyg; bghWj;J gpd;tUtdtw;Ws; vit my;yJ vJ rhp ?

a. X =

(ruhrhp) vd;w nfhl;ow;Fr; rkr;rPuhdJ b. ruhrhp = ,ilepiy mst[ = KfL

c. xU Kfl;Lg; guty; d. X =

tpy; tist[ khw;Wg;g[s;spfs; cs;sd/

1. a, b kl;Lk; 2. b,d kl;Lk; 3. a.b,c kl;Lk; 4.midj;Jk;

98. jpl;l ,ay;epiyg; gutypd; ruhrhpa[k; gutw;goa[k;

3. 0, 1 4. 1, 1

99. X xU bjhlh; rktha;g;g[ khwp vdpy; vJ jtW>

100. ,ay;epiyg; gutypd; nghJ fPnH bfhLf;fg;gl;l Tw;wpy; vJ rhpahdjy;y>

1. nfhl;lf;bfG g[{r;rpakhFk;/ 2. ruhrhp = ,ilepiy mst[ = KfL

3. tist[ khw;Wg;g[s;spfs; X =

4. tistiuapd; kPg;bgU cauk;

MATHS HUNTERS

Thursday, 19 April 2018

Olympia Academy

NEET/JEE Main/IIT Foundation Courses Tirupattur, Vellore-D.t

Olympia Academy

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