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47. The condition that the roots of x3+3px2+3qx+r=0 may be in A.P is

x3+3px2+3qx+r=0H = A.P LO> x==.1. 2p3+r=3pq 2. p3r=q3 3. 2q3+r2=3pqr 4. 3p+3q+r=0

47. The condition that the roots of x3px2+qxr=0 may be in G.P is

x3px2+qxr=0H = G.P LO> x==.

1. p

3

=q

3

r 2. q

3

=p

3

r 3. pq=r 4. pqr=147. If the roots of kx318x236x+8=0 are in H.P then k =

kx318x236x+8=0H = H.P LO> k =1. 45 2. 81 3. 26 4. 17

47. If the roots of x3kx2+14x8=0 are in G.P then k =

x3kx2+14x8=0H = G.P LO> k =1. 3 2. 7 3. 4 4. 0

47. If the roots of 2x33x2+kx+6=0 are in A.P then k =

2x33x2+kx+6=0H =A.P LO>k =1. 3 2. 5 3. 7 4. 11

48. If,,the roots of x33x+7=0 then++=

x33x+7=0H = ,,J~` ++=1. 0 2. 3 3. 7 4. 1

48. If,,are the roots of x3+2x1=0 then1 1 1

+ + =

x3+2x1=0H = ,,J~`1 1 1

+ + =

1. 0 2. 3 3. 7 4. 2

48. If 1,-2,3 are the roots of x32x2+ax+6 = 0 then a =

x32x2+ax+6 = 0H = 1,-2,3J~` a =1. 4 2. 3/2 3. 7/4 4. 5

48. If,,are the roots of 2x35x2+3x1=0 then1 1 1

+ + =

2x35x2+3x1=0H = ,,J~` 1 1 1

+ + =

1. 5 2. 3 3. 7 4. 0

48. If,,are the roots of x3+x2+x+1=0 then ()2+()2+()2=x3+x2+x+1=0H = ,,J~` ()2+()2+()2=1. 2 2. 2 3. 4 4. 4

49. The roots of 4x313x213x+4=0 are H =1. 1,4,1/4 2. 1,2,1/2 3. 1,4,1/4 4. 1,2,1/2

49. The roots of x410x3+26x210x+1=0 are H =1. 322, 23 2. 232, 23 3. 322, 32 4. 1,2,3,4

49. The roots of 6x65x544x4+44x2+5x6=0 H =1. 1,1,2,2,3,3 2. 1,-1,-2,-1/2,3, 1/3 3. 1,2,3,4,5,6 4. 1,1,2,1/2,3,1/3

49. The roots of 6x45x338x25x+6=0 are H =1. 2,1/2,3,1/3 2. 2,-1/2,3,1/3 3. 1,-1,2,-2 4. 1,-1,3,1/3

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49. The roots of x55x4+9x39x2+5X1=0 are H =

1. 2,1/2,3,1/3 2.1 3 3 5

1, ,2 2

i 3. 1,-1,-2,-1/2,3 4. 1,1,2,2,3

50.2 4 6

1 3 5+ + + =

1. e 2. e2 3. 2e 4. 1/e

50.3 5 7 9

2 4 6 8+ + + + =

1. e 2. 2e 3. e1 4. e/2

50.3 5 7

11 2 3

+ + + + =

1. e 2. 2e 3. 3e 4. 4e

50.4 7 10

12 3 4

+ + + + =

1. e 2. 2e 3. e-2 4. e+2

50.

2 2

1 1 1 1 1 11 12 4 6 3 5 7

+ + + + + + + + = 1. 0 2. 1 3. e 4. 1/e

51.

3 33 1 3 1 3

4 3 4 5 4

+ + +

1. log3 2. log4 3. log7 4. log 7

51.

3 51 1 1 1 1

22 3 2 5 2

+ + + =

1. log3 2. log 4 3. log2 4. log5

51.

3 52 1 2 1 2

23 3 3 5 3

+ + + =

1. log 3 2. log 4 3. log 2 4. log 5

51. 4 5 71 1 1 1

3 3 5.3 7.3+ + + + =

1. log2 2. log2 3. 2 log2 4. log(1/2)

51. 1+ 2 4 61 1 1

3.2 5.2 7.2+ + + =

1. log2 2. log3 3. log2 4. log3

52. If( )( ) 222 1

1 11 1

x A Bx c

x xx x += +

+ + then B =

1. 3/2 2. 1/2 3. 2/3 4. 2/3

52. If( )

2

3 2

1

1

x A Bx c

x x x x

+ += +

+ +then sin1A/c=

1./2 2./3 3./4 4./6

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52. If2

2 3

5 2

1

A Bx x

x x x x

++ =

+ +then B =

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

52. If( )( ) 22

1 1

1 21 2

ax x

x x xx x x

=

+ + + + then a =

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

52. If( )( ) 222 1

1 11 1

x A Bx C

x xx x

+ += +

+ + then A+B+C =

1. 1/4 2. 3 3. 1/2 4. 4

53.31 2

0 1 2

2. 3. .1

n

n

C CC Cn

C C C C + + ++ =

1.( )1

2

n n +2.

( )1

2

n n 3.

( ) ( )1 1

2

n n +4.

( )2

2

n n +

53. 31 2

0

2 3 4 1

nC CC C

Cn

+ + + + =

+

1.

1

2 11

n

n

+ +

2.2 11

n

n+

3. 21

n

n +4. 1

1n +

53. 2 3 11 202 2 . 2 . 2

2 3 1

n nCC CCn

++ + + =+

1.1

1n + 2.4

1

n

n +3.

13 1

1

n

n

+ +

4.

14 1

1

n

n

+ +

53.1 1 1

1 1 3 3 5 5n n n+ + +

1.2

1

n

n +2.

12n

n

3.

12n

n

+

4.

2

2

n

n +

53. 3.Co+7.C1+11.C2+ ---- + (4n+3) Cn=1. (3n+2)2n 2. (2n+3)3n 3. (2n+3)2n 4. (3n+2)3n

54. The sum of the coefficients of x32and x17in

15

4

3

1x

x

is15

4

3

1x

x

=~} x32and x17Q}H !`O

1. 15 2. 0 3. 15 4. 1

54. If the coefficient of x7in

11

2 1ax

bx

is equal to the coefficient of x7in11

2

1ax

bx

then ab=11

2 1axbx

=~} x7

Q}HO "

11

2

1ax

bx

=~} x7

Q}HO =#$= J~` ab=1. 0 2. 1 3. 1 4. 2

54. If the coefficient of x in

5

2 kx

x

+ is 270 then k =5

2 kxx

+ %~} xQ}HO &'( J~` k =

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

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54. If the coefficient of x7and x8in 23

nx + are equal then n =

23

nx + %~} x7, x8 Q}H =#$O J~` n =

1. 45 2. 55 3. 35 4. 27

54. If the coefficient sof (2r+1)th and (4r+5)th term in the expansion of (1+x)10are equal then r=

(1+x)10%~} (2r+1)th=)(4r+5)th*+, Q}H=#$O J~` r=

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

55. There are 10 straight lines in a plane no two of which are parallel and no three are concurrent.

The point of intersection are joined, then the number of fresh lines formed are

-H`Ox /( ~01~2 3 4~O56 =#O`~OH+7. 3=56 J$8H H=9. : ~2 2O56$

;O+7=9`< 3~56 H?` ~2 O2@1. 630 2. 615 3. 730 4. 60055. There are two parallel lines, one having 10 points and the other having five points. The number

of triangles formed with vertices as these points is

4~O56 =#O`~ ~2A*B -H +,x C+7 /( ;O+7=9"!~?H +,xA*B D ;O+7=9 H=9. E ;O+7=9 F~GQQ IK [email protected]. 225 2. 100 3. 325 4. 125

55. The maximum number of points of intersection formed by 4 circles and 4 straight lines is

M =N`G" M ~01~2 2O5OH?O> 3~56Q)8P 2O56$ ;O+7=9 O2@.

1. 26 2. 50 3. 56 4. 72

55. There are 10 parallel lines intersected by a family of 5 parallel lines. The numbers parallelogram

thus formed is

10=#O`~ ~2 !~?H D =#O`~ ~22O5O H?GR~. SO+7 $O5 3~56=#O`~ `~T [email protected]. 225 2. 450 3. 730 4. 600

55. In a plane there are 10 points, no three are in the same straight line except 4 points which are

collinear then the number of straight lines so formed is-H `Ox /( ;O+7=9 M ;O+7=9 ~U#%VW$ !GXY 3=56 ;O+7=9 -H ~2A*B LO56=9.

J~` !GXY`< 3~56 ~01~2 [email protected]. 39 2. 41 3. 45 4. 40

56. The number of different matrices that can be formed with elements 0,1,2 or 3 each matrix having

4 elements is

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("/"& +, Z =H`< %;$R M =H =#IH O2@1. 324 2. 244 3. 344 4. 44

56. The number of quadratic expression with the coefficients drawn from the set {0,1,2,3} is

{0,1,2,3}%I $O5 [\H?$R %= Q}HQ Q =~]=#^ O2@.

1. 27 2. 36 3. 48 4. 6456. The number of ways in which can three letters be posted in four letter boxes so that all the letters

are not posted in the same letter box are

JxR L`~G$ -HA*>_ !abO5c Z L`~G$ MA*>_ !d %+,G [email protected]. 43 2. 434 3. 343 4. 34

56. The number of ways in which 5 rings of different type can be put in 4 fingers is

%;$R ~H D LOQ~G$ M !01eab A*> %+,GO2@

1. 54 2. 45 3.5p4 4. 24

56. Four dice are rolled. The number of possible out comes in which at least one die shows 2 is

M fgH$ %\)$*956 HhO -H fgHA*B *\Oiij =k JxR %+, O2@.

1. 1296 2. 625 3. 615 4. 671

57. Three dice are rolled, the probability of that the sum of the numbers on them is 6

=_zH# îOz` "\q^ JOH "Ò 6J!O$%& %'(6 )& *'%+, (& )6'*- .& %('(.

57. Three dice are rolled. The probability of that exactly two of the numbers are equal is.

=_ zH# ^/0Oz`1 /O_O\ q^ 23H JOH 4O_1!O5=7`%& %6*')%6 )& %%-')%6 (& *%')%6 .& 8+')%6

57. Three dice are rolled, the probability that the sum of the numbers on them is 16 is

=_ zH# ^/0Oz`1 "\ q^ JOH "9Ò %6

:1 !O5=7`%& %'(6 )& *'%+, (& )6'*% .& %('(.57. Two dice are thrown the probability of getting sum of the numbers on them is 10 is

/O_ zH# î;! "\q^ JOH "9Ò %+ J1!O5 =7`%& %'8 )& %'%) (& %'6 .& *'(6

57. Two dice are thrown the probability of getting a doublet is

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/O_ zH # ^i;! "\q^ 23H JOH 4O_1 !O5 =7`%& %'(6 )& %'8 (& %'6 .& %'.

58. If P(A) = 2/5, P(AB) = 3/10 (J/9`1& then P(B/A) =1) 1/3 2) 3/5 3) 3/4 4) 1/4

58. If P(E1) = 1/4, P(E2/E1) = 1/2, P(E1/E2) = 1/4 (J/9`1&then P(E1/ 2E ) =1) 1/3 2) 1/4 3) 2/3 4) 3/458. If P(A) = 0.3, P(B) = 0.6, P(B/A) = 0.5 (J/9`1&then P(AUB) =

1) 0.50 2) 0.65 3) 0.75 4) 0.85

58. If P( A ) = 0.7, P(B) = 0.7, P(B/A) = 0.5 (J/9`1& then P(A/B) =1) 2/3 2) 3/4 3) 4/174) 3/14

58. If P(A) = 0.3, P(B) = 0.6, P(B/A) = 0.5 (J/9`1&then P(A/B) =1) 1/2 2) 1/3 3) 1/4 4) 2/3

59. In a bn!"a# $%t&b't!n, n = 400, P = 1/5 then t% %tan$a&$ $eat!n %

^ q5 ?#O@A n = 400, P = 1/5 J/9`1 ^BC DH=qE #O$1) 102 2) 1/800 3) 4 4) 859. In a bn!"a# $%t&b't!n, "ean = 20, a&an*e =15 then P =^ q5?#O@A =^==9= 20F q!7G =15 J/9`1 P =1)1/3 2) 1/8 3) 1/2 4) 1/4

59. If a bn!"a# $%t&b't!n hae +a&a"ete&% 9, 1/3 then P ( = 4) =

^ q5?#O@A >/q` 9, 1/3J/9`1 P ( = 4) =1) 448/2187 2) 224/1186 3) 112/1046 4) 94/886

59. In a bn!"a# $%t&b't!n n = 20, - = 0.75 then "ean =

^ q5?#O@A n = 20, - = 0.75J/9`1 =^==9$%& * )& %* (& %+ .& )+

59. In a bn!"a# $%t&b't!n , n+ = 5, n+- = 4 then n =^ q5?#O@A n+= 5, n+- = 4 J/9`1 n =1) 9 2) 20 3) 25 4) 125

60. A &an$!" a&ab#e ha% the f!##!n $%t&b't!n

2H ^7zH E#/I 9H q5?K#O L DHO^1YZ "[YO$

1) 4/3 2) 2/3 3) 8/3 4) 16/3

66. The area bounded by y =x, y = x2is

: = , : = 2% @A W/0X_ D>^1YZ "[Y O$ 1) 1/3 2) 8/3 3) 1/2 4) 4/3

66. Area enclosed by y2= 4ax, x

2= 4by is

y

2

= 4ax, x

2

= 4by @A W/0X_ D>^1YZ "[Y O$ 1) 16/3 ab 2) 3/3 ab 3) 4/3 ab 4) 2/3 ab

66. Area enclosed by y2= 4x, x

2= 2y is

y2= 4x, x

2= 2y@A W/0X_ D>^1YZ "[YO$

1) 1/3 2) 8/3 3) 1/2 4) 4/3

67. If x = ct, y = c/t then yzat t = 1/2

= *t, : = */tJ/9`1 t = 1/2 =^] :21) 16 2) 16/C 3) C/16 4) C

67. x = t2, y = t3(J/9`1&then y21) 3/2 2) 3/4t 3) 3/2t 4) 3t/2

67. x = 2/t2, y = t

3 1(J/9`1& then y2=

1) 15t2 2) 15 / 16t2 3) 15 t

7/ 16 4) 16 t

2

67. x = cos; ;sin;,y = sin; < ;cos then y2 =

1) cosec3; 2) sec; 3) tan3; 4) cos3;

; ; ; ;67. x = acos3;,y = sin3;then y2at; /4

= a*!%3;, : = %n3;J/9`1 ; = /4=^] :2=1) 3a 2) 1 3) 42 4) 42

42 122 3a 3a

68. The degree of the differential equation y3+ 2y41+ y1= cos x is

y3+ 2y41+ y1= cos x9H `/0MVG$

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

68. The degree of [2 + y21]3/2= a y2is (9H `/0MVG&

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

68. The degree of y3+ 5 y22= x

3log y2is (9H `/0MVG&

1) 1 2) 2 3) 3 4) does not exists ==!R`O HN^$68. The degree of 3y = 7x y1+ 5/y1is(9H `/0MVG&

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

68. The degree of the differential equation of the family of all parabolas whose axis is x axis is

JHO /=O aTOPO 9HJ=H !qH/0bCH `/0MVG$%& % )& ) (& ( .& .

69. Integrating factor of sin x dy +y cos x = sin 2x is(9H !=H#HN/0bOHO&

dx1) cos x 2) sin x 3) sin x 4) cos x

69. Integration factor of x cos x dy + ( x sin x + cos x) y = 1 is(9H !=H#HN/0bOHO&

dx

1) x cos x 2) x sin x 3) x sec x 4) x cosec x

69. Integrating factor of ydx xdy + 3x2y2exdx = 0% (9H !=H#

HN/0bOHO&1) 1/y2 2) 1/x2 3) 1/xy 4) 1/x2y2

69. Integrating factor of dy - 2 y = (x +1)3is

dx x + 1

1) cos x 2) log sec x 3) sec x 4) (x +1)-2

69. Integration factor of (x + 2y3) dy = y

2is

dx

1) e1/y 2) e

1/y 3) y 4) 1/y

70. The equation of the circle touching both axes lying in the first quadrant and having the radius 3 is"c/0dO ( HefF "9^\ ^O@A 4Ogh /O_

JHN# !IOE =7` !qH/0bO$1) x

2+ y2 6x 6y +9 = 0 2) x

2+ y2+ 10 = 10y +25 = 0

3) x2+y2+ 2x + 2y +1 = 0 4) x

2+y2 4x + 4y +4 = 0

70. If x2+ y2 4x +6y + K = 0 touches x axes then K =

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x2+ y2 4x +6y + K = 0 =7Ò < JHO# !X7I;! =

1) 9 2) 4 3) 2 4) 3

70. If x2+ y2+ 6x + 2ky + 25 = 0 touches y axes then K =

x2+ y2+ 6x + 2ky + 25 = 0 =7Ò: < JHO# !X7I;! =

1)+ 3 2) + 4 3) + 5 4) + 170. The equation of the circle with centre (2,3) and touching x axis is

3HODÔ Q)F(& HefF < JHO# !X7IOE1 =7`!qH/0b=9$

1) x2+ y2 4x 6y +4 = 0 2) x

2+ y2+ 6x 8y + 16 = 0

3) x2+ y2 8x 6y +21 = 0 4) x

2+ y2 24x 10 y + 144 = 0

70. The equation of the circle with centre ( 3, 4) and touching y axis is

3HODÔ (

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71. If (x1, y1) is the pole of the line lx + my + n = 0 with respect to circle

( < ?)2

(: < @)2 = &

2 then 1< ? = :1< @

l

"( < ?)2

(: < @)2 = &

2 =7`O ^7j # ": n = 0 9H

^7=O (1, :1)J/9`11< ? = :1< @

l "

1) < &2 2) &

2 3) < &

2 4) &

2

#? " @ n # ? " @ n " ? n @ l # " n

72. The number of common tangents to the circles x2+y2=4, x2+y28x+12=0

=N`G ab Q L=l5 ~m~2 O2@. 1. 1 2. 2 3. 3 4. 4

72. The two circles x2+y2+2ax+2by+c=0 and x

2+y2+2bx+2ay+c=0 have three real common tangents then

x2+y2+2ax+2by+c=0 , x2+y2+2bx+2ay+c=0=N`Gab Q L=l5~m~2 =56 J~`1. (a+b)2=2c 2. (a b)2=2c 3. a+b+c=0 4. a=b+c

72. The number of common tangents to the circles x2+y24x+2y4=0, x2+y2+2x6y+6=0

=N`Gab Q L=l5 ~m~2 O2@1. 1 2. 2 3. 3 4. 4

72. Only one common tangent can be drawn to the circles x2+y22x4y20=0, (x+3)2+(y+1)2=p2

then p=

x2+y22x4y20=0, (x+3)2+(y+1)2=p2=N`Gab L=l5 ~m~2-HXY =#`! LO>p=1. 20 2. 16 3. 49 4. 10

72. If the circles x2+y26x8y+c=0, x2+y2=9 have three common tangents then c =

x2+y26x8y+c=0, x2+y2=9=N`Gab L=l5 ~m~2 nZo J~`c =

1. 18 2. 19 3. 20 4. 21

73. The radical axis of the co-axal system having the limiting points (2,1) (-5,-6) is

(2,1) (-5,-6)J=p ;O+7=9Q Q qHr =N` ~}Y

H =HrO1. x+y+4=0 2. 3x+y 10=0 3. x y 1=0 4. 4x 2y 5 = 0

73. If (0,0) is one limiting point of a co-axal system of circles whose radical axis is x+y=1 then the

other limiting point is

qHr =N` ~}Y -H J=p ;O+7=9 s("(t=HrO x+y=1J~` 4~O56= J=p ;O+7=9.1. (1,1) 2. (-1,-1) 3. (1,-1) 4. (-1,1)

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73. If (1,2) is a limiting point of the co-axal system of circles containing the circle x2+y2+x 5y+9=0

then the equation of the radical axis of

qHr =N`~}Y -H =NÒ x2+y2+x 5y+9=0-HJ=p ;O+7=9 s/"&t J~` +,x =HrO1. x+3y+9=0 2. 3x y+4=0 3. x+9y 4=0 4. 3x y 1 = 0

73. Origin is a limiting point of a co axal system of which x

2

+y

2

6x 8y +1=0 is a member. Theother limiting point is

qHr =N`~}Y -H =NÒ x2+y2 6x 8y +1=0-HJ=p ;O+7=9s("(tJ~` 4~O56= J=p ;O+7=91. (-2,-4) 2. (3/25, 4/25) 3. (3/25, 4/25) 4. (4/25, 3/25)

73. If (2,1) is a limiting point of the co axial system of which x2+y26x4y3=0 is a member then

the other limiting point is

qHr =N`~}Y -H =NÒ x2+y26x4y3=0-HJ=p ;O+7=9 s&"/t J~` 4~O56= J=p ;O+7=91. (-5,-6) 2. (5,6) 3. (3,5) 4. (-8,-13)

74. PSQ is the focal chord of the parabola y2=4ax where S is the focus then1 1

SP SQ+ =

y2=4ax*~G=#xHY PSQG;@" SG; J~`1 1

SP SQ+ =

1. a 2. 1/a 3. 2a 4. 2/a

74. The latus rectum of a parabola whose focal chord is PSQ such that SP=3, SQ=2 is

*~G=#xHY PSQG;@" SP=3, SQ=2 SG; J~` :*~G=O H G;OuO fv56=9.

1. 24/5 2. 12/5 3. 6/5 4. 3/5

74. If the point t is one extremity of a focal chord of the parabola y2=4ax then the length of the chord

is

y2=4ax*~G=#xHY tG;@ H -H JQO J~` :@ fv56=9.

1. a 2. at 3. a(t+1/t) 4. a(t+1/t)2

74. The length of the focal chord of the parabola y2=4ax which makes an angle with its axes is

y2=4ax*~G=O H JHrO `< H

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75. The eccentricity of the ellipse whose latus rectum is equal to half of its minor axes is

y~z=NÒ G;OuO fv56=9" q^{HrO fv56=9QO LO> +,x LÒ+7`.

1. 3/5 2. 2/3 3. 1/2 4.7

4

75. The eccentricity of the ellipse whose major axes is double the minor axes isy~z=NÒ y~GzHrO fv56=9" q^{HrO fv56=9

4~XYO*9 LO> +,x LÒ+7`.1. 1/3 2. 2/3 3.3/2 4.3/4

75. S,S1are the foci of an ellipse, B is the an end of the minor axes and SBS1is an equilateral

triangle then eccentricity of the ellipse is

y~z=NÒ H GK S,S1" q^{HrO H -H JQO B=) SBS1-H =q| IKO J~` +,xLÒ+7`

1. 1/4 2. 1/3 3. 1/2 4. 2/375. The distance between the foci is equal to the minor axes of an ellipse then its eccentricity is

y~z=NÒ GK =+7@+7#~O" q^{HrOfv56=9ab =#$O J~` +,x LÒ+7`

1. 1/3 2. 1/2 3. 1/5 4. 4/576. The angle between the asymptotes of the hyperbola x23y2=3 is

x23y2=3JI *~G=O H J$O` ~m~2=+7@H

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76. The asymptotes of a rectangular hyperbola intersect at an angle is

Ou JI *~G=O H J$O` ~m~2=+7@H

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II.

/ 2

7

0

cos x dx

b) 128/315

III.

/ 2

10

0

cos x dx

c) 63/5121. a,b,c 2. b,c,a 3. b,a,c 4. a,c,b

79. Match the following HYOp !GXYx `*~=.

I.6

0

sin x dx

a) 1

II.5

0

cos x dx

b) 5/6

III.

/ 2

0

sinx dx

c) 01. b,a,c 2. b,c,a 3. a,b,c 4. c,a,b

79. Match the following HYOp !GXYx `*~=

I.7

sin x dx

a) 16/35

II.

/ 2

7

0

cos x dx

b) 0

III.

/ 2

10

0

cos x dx

c) 63/512

1. b,a,c 2. a,b,c 3. c,a,b 4. b,c,a79. Match the following HYOp !GXYx `*~=

I.

/8

6

0

cos 4x dx

a) 35/128

II.

/ 4

7

0

sin 2x dx

b) 8/35

III.8

0

sin2

xdx

c) 5/1281. a,b,c 2. c,a,b 3. c,b,a 4. b,c,a

79. Match the following HYOp !GXYx `*~=

I.

/ 2

8 2

0

sin cosx x dx

a) 0

II.

/ 2

6 5

0

cos sinx x dx

b) 7/512

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III.

/ 2

5 3

/ 2

cos sinx x dx

c) 8/693

1. b,c,a 2. c,a,b 3. c,b,a 4. a,b,c

80. I. If A =

0 1 2

2 3 4 ,

4 5 6

B=

1 2 3

0 1 0

0 0 1

then 4A 5B =

5 6 7

8 7 16

16 20 19

II. If A=1 2 3

,3 2 1

B=3 2 1

1 2 3

then 3B 2A=7 2 3

3 2 7

1. only I is true I=#`! `@O 2. only II is true II=#`! `@O

3. both I,II are true I,II 4~O56# `@O 4. both I,II are false I,II4~O56# J`@O

80. I. If A=2 1 0

3 4 5

, B=

1 2

4 3

1 5

then A+BT=1 5 1

5 7 0

II. If A=2 1 2

1 3 1

, B=3 2 1

2 0 1

then (ABT)T=10 2

4 3



80. I. If A=2 3 1

,6 1 5

B=1 2 1

0 1 3

and A + B X = 0 then X =3 5 0

6 2 8

Xoooo ph

II. If A=9 1

,4 3

B=1 5

,6 11

3A+5B+2x=0 then X=16 14

21 32


3. both I,II are true I,II 4~O56# `@O 4. both I,II are false I,II

4~O56# J`@O

80. I. If A+B=1 0

1 1

, A 2B=1 1

0 1

then A =1/ 3 1/ 3

2 / 3 1/ 3

II. If A+B=2 3

6 1

, A- B =2 1

0 1

then B=0 1

3 0


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80. I. If A=

1 3 0

1 2 1 ,

0 0 2

B=

2 3 4

1 2 3

1 1 2

then AB =

5 9 13

1 2 4

2 2 4

II. If A=

2 1 3

4 1 2 ,

0 5 1

B=

4 3

2 1

3 2

then AB=

19 1

20 9

7 3



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1. / 2. M 3. & 4. & 5. Z 6. Z 7. / 8. M 9. & 10. &//. / 12. / 13. / 14. M 15. / 16. & 17. & 18. M 19. Z 20. &&/. M 22. M 23. M 24. / 25. M 26. & 27. / 28. & 29. Z 30. &Z/. / 32. & 33. / 34. & 35. M 36. & 37. M 38. M 39. / 40. MM/. / 42. / 43. & 44. & 45. & 46. / 47. Z 48. Z 49. M 50. &D/. M 52. / 53. M 54. & 55. & 56. & 57. M 58. Z 59. & 60. Z/. / 62. / 63. Z 64. & 65. Z 66. & 67. Z 68. Z 69. & 70. /'/. / 72. Z 73. & 74. & 75. M 76. Z 77. Z 78. & 79. & 80. M/. & 82. M 83. / 84. & 85. Z 86. Z 87. & 88. Z 89. M 90. Z/. M 92. M 93. / 94. / 95. Z 96. / 97. / 98. & 99. Z 100. //(/. Z 102. & 103. M 104. / 105. M 106. Z 107. M 108. M 109. / 110. &///. / 112. Z 113. Z 114. Z 115. / 116. & 117. & 118. Z 119. / 120. &/&/. Z 122. / 123. Z 124. & 125. Z 126. & 127. M 128. / 129. / 130. &/Z/. & 132. & 133. Z 134. & 135. Z 136. / 137. & 138. M 139. & 140. /

/M/. & 142. Z 143. / 144. M 145. / 146. / 147. & 148. & 149. / 150. &/D/. & 152. & 153. M 154. & 155. / 156. Z 157. / 158. Z 159. M 160. M//. / 162. / 163. & 164. & 165. / 166. & 167. / 168. M 169. Z 170. M/'/. / 172. M 173. Z 174. Z 175. & 176. / 177. M 178. M 179. M 180. M//. & 182. Z 183. M 184. / 185. & 186. / 187. Z 188. M 189. Z 190. Z//. Z 192. & 193. / 194. Z 195. / 196. Z 197. / 198. / 199. Z 200. Z

eswar rao 47 to 80

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