\\\\\\\\\\\\

mmmmmmm\m\mmmmmm

ppp\p\\mppp\

\\]\]m\]m\m\\]]m\mmmm]\]\\m]

7\77\m7\mm7\7777\p\7777

]m\::\:

,,,\m\\\\\,,mm],

mmmmmmm\m.

\m,mP\mm7]\m\\]mp\\m

IIIIIIIII

5 :

1. A = {0, 1, 2, 3, 4}, B = {1, -2, 3, 4, 5, 6}

C = {2, 4, 6, 7} A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

.

: B ∩ C = {4, 6}

A ∪ (B ∩ C) = {0, 1, 2, 3, 4, 6} ---- (1)

(A ∪ B) = {-2, 0, 1, 2, 3, 4, 5, 6}

(A ∪ C) = {0, 1, 2, 3, 4, 6, 7}

(A ∪ B) ∩ (A ∪ C) = {0, 1, 2, 3, 4, 6} ---- (2)

(1), (2) LHS = RHS

5. A = {a, b, c, d, e, f, g, x y, z}, B = {1, 2, c, d, e}

C = {d, e, f, g, 2, y}

A \ (B∪C}= (A \ B) ∩ ( A \ C)

(B∪C} = {1, 2, c, d ,e, f, g, y}

A \ (B∪C} = {a, b, x, z}---- (1)

(A \ B) = {a, b, f, g, x, y, z}

( A \ C) = {a, b, c, x, z}

(A \ B) ∩ ( A \ C) = {a, b, x, z}---- (2)

(1), (2) LHS = RHS

2. A = {-3, -1, 0 4, 6, 8, 10}, B = {-1, -2, 3, 4, 5, 6}

C = {-1, 2, 3, 4, 5, 7}

A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) .

B ∩ C = {-1, 3, 4, 5}

A ∪ (B ∩ C) = {-3, -1, 0, 3, 4, 5, 6, 8, 10} ---- (1)

(A ∪ B) = {-3, -2, -1, 0, 3, 4, 5, 6, 8, 10}

(A ∪ C) = {-3, -1, 0, 2, 3, 4, 5, 6, 7, 8, 10}

(A ∪ B) ∩ (A ∪ C) = {-3, -1, 0, 3, 4, 5, 6, 8, 10} ---- (2)

(1), (2) LHS = RHS

6. A = {10, 15, 20, 25, 30, 35, 40, 45, 50}

B = {1, 5, 10, 15, 20, 30}

C = {7, 8, 15, 20, 35, 45, 48}

A \ (B∩C}= (A \ B) ∪ ( A \ C) .

(B∩C} = {15, 20}

A \ (B∩C}= {10, 25, 30, 35, 40, 45, 50} ---- (1)

(A \ B) = {25, 35, 40, 45, 50}

( A \ C) = {10, 25, 30, 40, 50}

(A \ B) ∪ ( A \ C) = {10, 25, 30, 35, 40, 45, 50}---- (2)

(1), (2) LHS = RHS

3. A = {-3, -1, 0 4, 6, 8, 10}, B = {-1, -2, 3, 4, 5, 6}

C = {-1, 2, 3, 4, 5, 7}

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) .

(B ∪ C)= {-2, -1, 2, 3, 4, 5, 6, 7}

A ∩ (B ∪ C) = {-1,4,6} ---- (1)

(A ∩ B) = {-1, 4, 6}

(A ∩ C) = {1, 4}

(A ∩ B) ∪ (A ∩ C) = {-1, 4, 6} ---- (2)

(1), (2) LHS = RHS

7.

.

A = {1, 3, 5, 7, 9, 11, 13, 15}, B = {1, 2, 5, 7}

C = {3, 9, 10, 12, 13}

1: A \ (B∪C}= (A \ B) ∩ ( A \ C)

(B∪C} = {1, 2, 3, 5, 7, 9, 10, 12, 13}

A \ (B∪C} = {11, 15} ---- (1)

(A \ B) = {3, 9, 11, 13, 15 }

( A \ C) = {1, 5, 7, 11, 15}

(A \ B) ∩ ( A \ C) = {11, 15} ---- (2)

(1), (2) LHS = RHS

2:A \ (B∩C}= (A \ B) ∪ ( A \ C)

(B∩C} = { }

A \ (B∩C}= {1, 3, 5, 7, 9, 11, 13, 15} ---- (1)

(A \ B) = {3, 9, 11, 13, 15}

(A \ C) = {1, 5, 7, 11, 15}

(A \ B) ∪ ( A \ C) = {1, 3, 5, 7, 9, 11, 13, 15} ---- (2)

(1), (2) LHS = RHS

4. A = { x / -3 ≤ x < 4, x ∈ R} B = {x / x < 5, x N}

C = {-5, -3, -1, 0, 1, 3}

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) .

: ( A = {-3, -2, -1, 0, 1, 2, 3},

B = {1, 2, 3, 4}, C = {-5, -3, -1, 0, 1, 3} )

(B ∪ C)= {-5, -3, -1, 0, 1, 2, 3, 4,}

(A ∩ B) = {1, 2, 3}

A ∩ (B ∪ C) = {-3, -1, 0, 1, 2, 3} ---- (1)

(A ∩ C) = {-3, -1, 0, 1, 3}

(A ∩ B) ∪ (A ∩ C) = {-3, -1, 0, 1, 2, 3} ---- (2)

(1), (2) LHS = RHS

.

Page 1 of 15

8. U = {-2, -1, 0, 1, 2, 3, …, 10}, A = {-2, 2, 3, 4, 5}

B = {1, 3, 5, 8, 9} .

.

1: (A ∪ B)’ = A’ ∩ B’

(A ∪ B) = {-2, 1, 2, 3, 4, 5, 8, 9}

(A ∪ B)’ = {-1, 0, 6, 7, 10} ----- (1)

A’ = {-1,0, 1, 6, 7, 8, 9, 10}

B’ = {-2, -1, 0, 2, 4, 6, 7, 10}

A’ ∩ B’ = {-1, 0, 6, 7, 10}---- (2)

(1), (2) LHS = RHS

2: (A ∩ B)’ = A’ ∪ B’

(A ∩ B) = {3, 5}

(A ∩ B)’ = {-2,-1, 0, 1, 2, 4, 6, 7, 8, 9, 10} ----- (3)

A’ = {-1,0, 1, 6, 7, 8, 9, 10}

B’ = {-2, -1, 0, 2, 4, 6, 7, 10}

A’ ∪ B’ ={-2,-1, 0, 1, 2, 4, 6, 7, 8, 9, 10}---- (4)

(3), (4) LHS = RHS

11. A = {5, 10, 15, 20}, B = {6, 10, 12, 18, 24}

C = {7, 10, 12, 14, 21, 28}

A \ (B \ C) = (A \ B) \ C

. .

B \ C = {6, 18, 24}

A \ ( B \ C) = {5, 10, 15, 20} --- (1)

A \ B = {5, 15, 20}

(A \ B) \ C = {5, 15, 20} --- (2)

(1), (2) LHS ≠ RHS

12. A = {-5, -3, -2, -1}, B = {-2, -1, 0}

C = {-6, -4, -2 }

A \ (B \ C) (A \ B) \ C .

.

B \ C = {-1, 0}

A \ ( B \ C) = {-5, -3, -2} --- (1)

A \ B = {-5, -3}

(A \ B) \ C = {-5, -3} --- (2)

(1), (2) LHS ≠ RHS

.

9. U = {a, b, c, d, e, f, g, h}, A = {a, b, f, g}

B = {a, b, c}

.

1: (A ∪ B)’ = A’ ∩ B’

(A ∪ B) = {a, b, c, f ,g}

(A ∪ B)’ = {d, e, h} ----- (1)

A’ = {c, d, e, h}

B’ = {d, e, f, g, h}

A’ ∩ B’ = {d, e, h}---- (2)

(1), (2) LHS = RHS

2: (A ∩ B)’ = A’ ∪ B’

(A ∩ B) = {a, b}

(A ∩ B)’ = { c, d, e, f, g, h } ----- (1)

A’ = {c, d, e, h}

B’ = {d, e, f, g, h}

A’ ∪ B’ ={ c, d, e, f, g, h } ---- (2)

(1), (2) LHS = RHS

13 xUFGéš 65 khzt®fŸ fhšgªJ«, 45 ng®

Ah¡»Í«, 42 ng® »ç¡bf£L« éisahL»wh®fŸ. 20 ng®

fhšgªjh£lK« Ah¡»Í«, 25 ng® fhšgªjh£lK«

»ç¡bf£L«, 15ng® Ah¡»Í« »ç¡bf£L« k‰W« 8ng®

_‹W éiah£LfisÍ« éisahL»wh®fŸ. m¡FGéš

cŸskhzt®fë‹ v©â¡ifia¡ fh©f. (x›bthU

khztD« FiwªjJxUéisah£oidéisahLth®

vd¡ bfhŸf.)

: A = , B= , C =

n(A∪B∪C) = n(A) + n(B) + n(C) – n(A∩ B) – (B∩ C) – n (A∩ C)

+ n(A∩ B ∩ C)

= 65 + 45 + 42 – 20 – 25 – 15 + 8

= 100

14 xUefu¤Âš 85%ng® jäœ bkhê, 40%ng® M§»y

bkhê k‰W« 20%ng® Ϫ bkhêngR»wh®fŸ. 32%

ng® jäG« M§»yK«, 13%ng® jäG« ϪÂÍ«

k‰W«10%ng® M§»yK« ϪÂÍ« ngR»wh®fŸ

våš, _‹W bkhêfisÍ« ngr¤

bjçªjt®fë‹ rjÅj¤Âid¡ fh©f.

: A = B= C =

n(A∪B∪C) = n(A) + n(B) + n(C) – n(A∩ B) – (B∩ C) – n (A∩ C)

+ n(A∩ B ∩ C)

100 = 85+40+20-32-13-10+ n(A∩ B ∩ C)

n(A∩ B ∩ C) = 100 – 90

= 10

10. A = {a, b, c, d, e}, B = {a, e, i, o, u}, C = {c, d, e, u}

A \ (B \ C) ≠ (A \ B) \ C .

B \ C = {a, i, o}

A \ ( B \ C) = {b, c, d, e} --- (1)

A \ B = {b, c, d}

(A \ B) \ C = {b} --- (2)

(1), (2) LHS ≠ RHS

Page 2 of 15

15. xU fšÿçæš nrUtj‰F 60 khzt®fŸ

ntÂæaèY«, 40 ng® Ïa‰ÃaèY«,30 ng®

cæçaèY« gÂÎbrŒJŸsd®. 15 ng®

ntÂæaèY« Ïa‰ÃaèY«,10ng® Ïa‰ÃaèY«

cæçaèY« k‰W« 5 ng® cæçaèY«

ntÂæaèY« gÂÎbrŒJŸsd®. _‹W

ghl§fëY« xUtUnk gÂÎ brŒaéšiy våš,

VnjD« xU ghl¤Â‰fhtJ gÂÎ brŒJŸst®fë‹

v©â¡if ahJ?

: A = , B= , C =

n(A∪B∪C) = n(A) + n(B) + n(C) – n(A∩ B) – (B∩ C) – n (A∩ C)

+ n(A∩ B ∩ C)

= 60+40+30-15-10-5+0

= 100

18. வெணடஙகளை னனடுததி

A U (B C) = (A U B) (A U C) எனளதச சரிரரகக.

19. வெணடஙகளை னனடுததி (A U B)’ = A’ B’ எனளதச

சரிரரகக.

20. வெணடஙகளை னனடுததி (A B)’ = A’ U B’ எனளதச

சரிரரகக.

21.வெணடஙகளை னனடுததி A \ (B U C) = (A \ B) (A \ C)

எனனும டி நரரகின கண ெிததினரச ெிதினிளச

சரிரரககவும.

16. 120 FL«g§fŸ cŸs xU »uhk¤Âš 93 FL«g§fŸ

rikaš brŒtj‰F éwif¥ ga‹gL¤J»‹wd®. 63

FL«g§fŸ k©bz©bzæid¥ ga‹

gL¤J»wh®fŸ. 45 FL«g§fŸ rikaš vçthÍit¥

ga‹gL¤J»wh®fŸ. 45 FL«g§fŸ éwF k‰W«

k©bz©bzŒ, 24 FL«g§fŸ k©bz©bzŒ

k‰W« vçthÍ, 27 FL«g§fŸ vçthÍ k‰W« éwF

M»at‰iw¥ ga‹ gL¤J»‹wd®.éwF,

k©bz©bzŒ k‰W« rikaš vçthÍ

Ï«_‹iwÍ« ga‹gL¤J« FL«g§fë‹

v©â¡ifia¡ fh©f.

: A = , B= , C =

n(A∪B∪C) = n(A) + n(B) + n(C) – n(A∩ B) – (B∩ C) – n (A∩ C)

+ n(A∩ B ∩ C)

120 = 93 + 63 + 45 – 45 – 24 – 27 + n(A∩ B ∩ C)

n(A∩ B ∩ C) = 120 – 105

= 15

17. வெணடஙகளை னனடுததி

A (BUC) = (A B)U (A C) எனளதச சரிரரகக.

Page 3 of 15

22 வெணடஙகளை னனடுததி A \ (B C) = (A \ B) U (A \ C)

எனனும டி நரரகின கண ெிததினரச ெிதினிளச

சரிரரககவும.

1. A = { } நறறும B = { } எனக.

f : A B எனது f(x)=

எ

ெளபனறுககபடடுளைது. சரரபு f - ஐ (i) ெரிளசச

சசரடிகைினகணம(ii)அடடெளண (iii) அமபுககுிப

டமஆகினெறரலகுிகக

: f(x)=

; f(4) = 3; f(6) = 4; f(8) = 5; f(10) = 6

2. A = { }நறறும B = { } என இரு

கணஙகள எனக. f : A B எனனும சரரபு f(x) = 2x + 1

எக வகரடுககபடடுளைது. இசசரரிள

(i) ெரிளசசசசரடிகைினகணம (ii) அடடெளண

(iii) அமபுககுிபடம (iv) ெளபடமஆகினெறரல

குிகக

:f(x) = 2x + 1

f(0) = 1; f(1) = 3; f(2) = 5; f(3) = 7

(i) ெரிளசசசசரடிகைினகணம: f = {(0,1), (1,3), (2,5), (3,7)}

(ii) அடடெளண:

f 0 1 2 3 f(x) 1 3 5 7

3. A = { };B = { } நறறும f:A B

எனது f(x)=

எ ெளபனறுககபடடிருபின

சரரபு f - ஐ (i) ெரிளசசசசரடிகைினகணம

(ii) அடடெளண (iii) அமபுககுிபடம (iv) ெளபடம

ஆகினெறரலகுிகக.

:f(x) =

f(6) = 1; f(9) = 2; f(15) = 4; f(18) = 5; f(21) = 6

4.A = {5,6,7,8},B ={-11, 4, 7, -10, -7, -9, -13} .

f = {(x,y): y = 3 – 2x, xA, yB}

. (i) f- .

(ii) ? (iii) .

(iv) .

: f(5) = –7 ; f(6) = –9; f(7) = –11; f(8) = –13

(i) f = {(5, –7), (6, –9) (7, –11) (8, –13) }

(ii) B ={-11, 4, 7, -10, -7, -9, -13}

(iii) = {–7 , –9, –11, –13}

(iv)

5. f = {(2, 7), (3, 4), (7, 9), (-1, 6), (0, 2), (5, 3)}

A = {-=1, 0 , 2, 3, 5, 7} B = {2, 3, 4, 6, 7, 9}

. f (i)

? (ii) ? (iii)

?

:

i)

(ii)

(ii)

Page 4 of 15

3.

கரபணிபடுததுக. X3 -2x2-5x + 6

கரபணிபடுததுக. X3 -3x2-10x + 24

கரபணிபடுததுக. 2X3 -9x2 + 7x + 6

கரபணிபடுததுக.2X3 - 3x2 - 3x + 2

கரபணிபடுததுக. X3 -10x2- x + 10

Page 5 of 15

கரபணிபடுததுக. 2X3+11x2- 7x - 6 கரபணிபடுததுக. X3 -23x2 + 142x – 120

கரபணிபடுததுக. X3 -5x2- 2x + 24 கரபணிபடுததுக. 4X3 -7x + 3

கரபணிபடுததுக. X3 – 7x + 6 கரபணிபடுததுக. X3+13x2 + 32x + 20

Page 6 of 15

Page 7 of 15

Page 8 of 15

5.

1. . [

] [

] *

+

x2 + 6x = - 9

y2 - 3y = 4

x2 + 6x + 9 = 0

y2 – 3y – 4 = 0

: x = –3, –3

y = 1, – 4

6. A = *

+, B = [ ] C =[ ] (AB)C =

A(BC) .

AB = *

+ [ ]

= * +

(AB)C = * + [ ]

= *

+

BC = [ ] [ ]

= [

]

A(BC) = *

+ [

]

= *

+

2. A = [

] B = *

+ AB

BA .

AB = [

] *

+

= [

]

BA = *

+ [

]

= *

+

7. A = [

] kw;Wk; B = [ ] vd;w mzpfSf;F (AB)T

= BTAT vd;gij rhpghh;f;ft[k;

AT = [ ]

BT = [

]

BTAT = [

] [ ]

= [

]

AB = [

] [ ]

= [

]

(AB)T = [

]

.3. A = *

+ B = *

+ AB BA

. ?

AB = *

+ *

+

= *

+

BA = *

+ *

+

= *

+

AB ≠ BA

4. A=(

)எில A2–4A + 5 = O எிறுவுக

A2–4A + 5

= (

) (

) (

) (

)

= (

) (

) (

) (

)

= (

) (

)

= (

)

= O

8. A = *

+, B = *

+kw;Wk; C = *

+

vdpy; A (B+C) = AB + AC vd;gij rhpghh;f;ft[k; .

(B+C) =*

++*

+=*

+

A (B+C) = *

+ *

+

= *

+

AB = *

+ *

+

=*

+

AC =*

+ *

+

= *

+

AB + AC = *

++*

+

=*

+

5. A = (

), B = (

)kw;Wk; C = (

)vdpy;

(A + B) C kw;Wk; AC + BC vd;w mzpfisf; fhz;f.

nkYk; (A+B)C = AC+BC vd;gJ bka;ahFkh?

(A + B) = (

) + (

)

= (

)

(A + B) C = (

) (

) =(

)

AC = (

) (

)= (

)

BC = (

) (

)= (

)

AC+BC = (

) +(

)= (

)

**

**

,

LHS = RHS

,

LHS = RHS ,

LHS = RHS

,

LHS = RHS

,

LHS = RHS

Page 9 of 15

9. A = *

+ kw;Wk; B = *

+ vd;w mzpfSf;F

(AB)T = BTAT vd;gij rhpghh;f;ft[k;

AT = *

+

BT = *

+

BTAT = *

+ *

+

= *

+

AB = *

+ *

+

= *

+

(AB)T = *

+

5.

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

.

=

|

|

=

|

|

=

(

= 28 .

2. (6, 9) (7, 4), (4, 2) (3, 7)

.

=

|

|

=

|

|

=

(

= - 17

= 17 .

10. A = *

+ *

+

A2 - (a+d)A = (bc – ad)

L.H.S: A2 – (a + d) A

=

dc

ba

dc

ba - [a + d]

dc

ba

= 0

0

adbc

adbc

= [bc –ad]

10

01

= [bc – ad] 2

I

= R.H.S

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

.

=

|

|

=

|

|

=

(

= 43 .

4. (-4, 5) (0, 7), (5, -5) (-4, -2)

.

=

|

|

=

|

|

=

(

= – 60.5

= 60.5 .

,

LHS = RHS

Page 10 of 15

Page 11 of 15

10.

1. xU fâj édho édh¥ ngh£oæš 48 khzt®fŸ bg‰w

kÂ¥bg©fŸ ËtU« m£ltizæš ju¥g£LŸsd.

kÂ¥bg©fŸ f 6 7 8 9 10 11 12

ãfœbt©fŸ x 3 6 9 13 8 5 4

= √

(

)

= √

= 1.61

A = 9

x f d = x -A fd fd2

6 3 6 - 9 = -3 -9 27

7 6 7 - 9 = -2 -12 24

8 9 8 - 9 = -1 -9 9

9 13 9 - 9 = 0 0 0

10 8 10 - 9 = 1 8 8

11 5 11 - 9 = 2 10 20

12 4 12 - 9 = 3 12 36

48

0 124

4. Ñœf©l m£ltizæš bfhL¡f¥g£LŸs òŸë étu¤Â‹

£l éy¡f¤ij¡ fz¡»Lf.

x 3 8 13 18 23

f 7 10 15 10 8

= √

(

)

= √

= 6.32

A =13

x f d = x -A fd fd2

3 7 3 - 13 = -10 -70 700

8 10 8 - 13 = -5 -50 250

13 15 13 - 13 = 0 0 0

18 10 18 - 13 = 5 50 250

23 8 23 - 13 = 10 80 800

50

10 2000

5. xU gŸëæYŸs 200 khzt®fŸ xU ò¤jf¡ f©fh£Áæš

th§»a ò¤jf§fë‹ v©â¡ifia¥ g‰¿a étu«

Ñœ¡fhQ« m£ltizæš bfhL¡f¥g£LŸsJ.

ò¤jf§fë‹ v©â¡if 0 1 2 3 4

khzt®fë‹ v©â¡if 35 64 68 18 15

Ï¥òŸë étu¤Â‹ £l éy¡f¤ij¡ fz¡»Lf.

= √

(

)

= √

= 1.107

A =2

x f d = x -A fd fd2

0 35 0 - 2 = -2 -70 140

1 64 1 - 2 = -1 -64 64

2 68 2 - 2 = 0 0 0

3 18 3 - 2 = 1 18 18

4 15 4 - 2 = 2 30 60

200

-86 282

2. ËtU« òŸë étu¤Â‰fhd £l éy¡f« fh©f.

x 70 74 78 82 86 90

f 1 3 5 7 8 12

= √

(

)

= √

= 5.7

A = 82

x f d = x -A fd fd2

70 1 70 - 82 = -12 -12 144

74 3 74 - 82 = -8 -24 192

78 5 78 - 82 = -4 -20 80

82 7 82 - 82 = 0 0 0

86 8 86 - 82 = 4 32 128

90 12 90 - 82 = 8 96 768

36 72 1312

6.ËtU« òŸë étu¤Â‹ éy¡f t®¡f¢ ruhrçia¡

fz¡»Lf.

=

(

)

= 15.08

x 2 4 6 8 10 12 14 16

f 4 4 5 15 8 5 4 5

A =10

x f d = x -A fd fd2

2 4 2 - 10 = -8 -32 256

4 4 4 - 10 = -6 -24 144

6 5 6 - 10 = -4 -20 80

8 15 8 - 10 = -2 -30 60

10 8 10 - 10 = 0 0 0

12 5 12 - 10 = 2 10 20

14 4 14 - 10 = 4 16 64

16 5 16 - 10 = 6 30 180

50 -50 804

3. xU tF¥Ã‰F el¤j¥g£l bghJ m¿Î¤nj®éš bkh¤j

kÂ¥bg©fŸ 40-¡F, 6 khzt®fŸ bg‰w kÂ¥bg©fŸ 20, 14,

16, 30, 21 k‰W« 25. Ï¥òŸë étu¤Â‹ £l éy¡f« fh©f.

= √

= √

= 5.36

A = 21

x d = x -A d2

14 14 - 21 = -7 49

16 16 - 21 = -5 25

20 20 - 21 = -1 1

21 21 - 21 = 0 0

25 25 - 21 = 4 16

30 30 - 21 = 9 81

0 172

Page 12 of 15

7. xU khj¤Âš 8 khzt®fŸ go¤j ò¤jf§fë‹

v©â¡if ËtUkhW. 2, 5, 8, 11, 14, 6, 12, 10.

Ï¥òŸë étu¤Â‹ £l éy¡f¤ij¡ fz¡»Lf.

= √

(

)

= √

= 3.74

A = 10

x d = x -A d2

2 2 - 10 = -8 64

5 5 - 10 = -5 25

6 6 - 10 = -4 16

8 8 - 10 = -2 4

10 10 - 10 = 0 0

11 11 - 10 = 1 1

12 12 - 10 = 2 4

14 14 - 10 = 4 16

-12 130

10. Ñœ¡fhQ« òŸë étu§fë‹ Â£l éy¡f¤ij¡

fz¡»Lf. 38, 40, 34 ,31, 28, 26, 34.

= √

(

)

= √

= 4.69

A =34

x d = x -A d2

26 26 - 34 =-8 64

28 28 - 34 =-6 36

31 31 - 34 =-3 9

34 34 - 34 =0 0

34 34 - 34 =0 0

38 38 - 34 =4 16

40 40 - 34 =6 36

S -7 161

11. 10 khzt®fŸ fâj¤ nj®éš bg‰w kÂ¥bg©fŸ

ËtUkhW, 80, 70, 40, 50, 90, 60, 100, 60, 30, 80. ϫ

kÂ¥òfS¡F £l éy¡f« fh©f

= √

(

)

= √

= 21.07

A = 70

x d = x -A d2

30 30 - 70 = -40 1600

40 40 - 70 = -30 900

50 50 - 70 = -20 400

60 60 - 70 = -10 100

60 60 - 70 = -10 100

70 70 - 70 = 0 0

80 80 - 70 = 10 100

80 80 - 70 = 10 100

90 90 - 70 = 20 400

100 100 - 70 = 30 900

S -40 4600

8. 62, 58, 53, 50, 63, 52, 55 M»a v©fS¡F £l

éy¡f« fh©f.

= √

(

)

= √

= 4.64

A = 55

x d = x -A d2

50 50 - 55 = -5 25

52 52 - 55 = -3 9

53 53 - 55 = -2 4

55 55 - 55 = 0 0

58 58 - 55 = 3 9

62 62 - 55 = 7 49

63 63 - 55 = 8 64

S 8 160

12. 18, 20, 15, 12, 25 v‹w étu§fS¡F khWgh£L¡

bfGit¡ fh©f.

= √

= √

= 4.427

C.V =

= 24.6

A =18

x d = x -A d2

12 12 - 18 =-6 36

15 15 - 18 =-3 9

18 18 - 18 =0 0

20 20 - 18 =2 4

25 25 - 18 =7 49

S 0 98 9. Ñœ¡fhQ« òŸë étu§fë‹ Â£l éy¡f¤ij¡

fz¡»Lf. 10, 20, 15, 8, 3, 4

= √

= √

= 5.97

A =10

x d = x -A d2

3 3 - 10 =-7 49

4 4 - 10 =-6 36

8 8 - 10 =-2 4

10 10 - 10 =0 0

15 15 - 10 =5 25

20 20 - 10 =10 100

S 0 214

13. ËtU« kÂ¥òfë‹ khWgh£L¡ bfGit¡

fz¡»Lf 20, 18, 32, 24, 26.

= √

= √

= 4.9

C.V=

= 20.42

A =24

x d = x -A d2

18 18 - 24 = -6 36

20 20 - 24 = -4 16

24 24 - 24 =0 0

26 26 - 24 =2 4

32 32 - 24 =8 64

S 0 120

Page 13 of 15

12.

1. xU Óuhd gfil xU Kiw cU£l¥gL»wJ.

ËtU« ãfœ¢ÁfS¡fhd ãfœjfÎfis¡ fh©f. (i)

v© 4 »il¤jš

(ii) xU Ïu£il¥gil v© »il¤jš

(iii) 6-‹ gfh fhuâfŸ »il¤jš

(iv) 4-I él¥ bgça v© »il¤jš

: n(S) = 6

(i) (

(ii) (

(iii) (

(iv) (

7. _‹W ehza§fŸ xnu neu¤Âš R©l¥gL»‹wd.

ãfœjfé‹ T£lš nj‰w¤ij ga‹gL¤Â, rçahf ÏU

ó¡fŸ mšyJ Fiwªjg£r« xU jiyahtJ »il¡F«

ãfœ¢Áæ‹ ãfœjféid¡ fh©f.

n(S) = 8

(

(

(

(

=

8. xU gfil ÏUKiw cU£l¥gL»wJ. FiwªjJ

xU cU£lèyhtJ v© 5 »il¥gj‰fhd

ãfœjféid¡ fh©f.

n(S) = 36

(

(

(

(

=

2. xU Óuhd ehza« Ïu©L Kiw

R©l¥gL»wJ. Ñœ¡fhQ« ãfœ¢ÁfS¡fhd

ãfœjféid¡ fh©f. (i) ÏU jiyfŸ »il¤jš (ii)

FiwªjJ xU jiy »il¤jš

(iii) xU ó k£L« »il¤jš.

: n(S) = 4

(i) (

(ii) (

(iii) (

9. xU khzé¡F kU¤Jt¡ fšÿçæš nr®¡if

»il¥gj‰fhd ãfœjfÎ 0.16 v‹f. bgh¿æaš

fšÿçæš nr®¡if »il¥gj‰fhd ãfœjfÎ

0.24 k‰W« ÏU fšÿçfëY« nr®¡if »il¥gj‰fhd

ãfœjfÎ 0.11 våš, (i) kU¤Jt« k‰W« bgh¿æaš

fšÿçfëš VnjD« xU fšÿçæš nr®¡if

»il¥gj‰fhd ãfœjfÎ fh©f. (ii) kU¤Jt¡

fšÿçæš k£Lnkh mšyJ bgh¿æaš fšÿçæš k£Lnkh nr®¡if »il¥gj‰fhd ãfœjfÎ fh©f.

( ( (

(i) ( =

(ii) ( ( = 0.18

3. ÏU Óuhd gfilfŸ xU Kiw

cU£l¥gL»‹wd. Ñœ¡fhQ« ãfœ¢ÁfS¡fhd

ãfœjféid¡ fh©f. (i) Kf v©fë‹ TLjš 8 Mf

ÏU¤jš (ii) Kf v©fŸ xnu v©fshf (doublet)

ÏU¤jš (iii) Kf v©fë‹ TLjš 8-I él mÂfkhf

ÏU¤jš

: n(S) = 36

(i) (

(ii) (

(iii) (

4. e‹F fiy¤J it¡f¥g£l 52 Ó£Lfis¡ bfh©l

Ó£L¡ f£oèUªJ rkthŒ¥ò¢ nrhjid Kiwæš xU

Ó£L vL¡f¥gL»wJ. mªj¢ Ó£L ËtUtdthf ÏU¡f

ãfœjfÎfis¡ fh©f.

(i) Ïuhrh (ii) fU¥ò Ïuhrh (iii) °ngL (iv) lak©£ 10

: n(S) = 52

(i) (

(ii) (

(iii) (

(iv) (

10. xU igæš 10 btŸis, 5 fU¥ò, 3 g¢ir k‰W« 2

Át¥ò ãw¥ gªJfŸ cŸsd. rkthŒ¥ò Kiwæš

nj®ªbjL¡f¥gL« xU gªJ, btŸis mšyJ fU¥ò

mšyJ g¢ir ãwkhf ÏU¥gj‰fhd ãfœjféid¡

fh©f.

n(S) = 20

(

(

(

(

=

5. _‹W ehza§fŸ xnu neu¤Âš R©l¥gL»‹wd.

ËtU« ãfœ¢ÁfS¡F ãfœjféid¡ fh©f.

(i) FiwªjJ xU jiy »il¥gJ (ii) ÏU ó¡fŸ k£L«

»il¥gJ (iii) FiwªjJ ÏU jiyfŸ »il¥gJ.

: n(S) = 8

(i) (

(ii) (

(iii) (

11. xU gfil ÏUKiw cU£l¥gL»wJ. Kjyhtjhf

cU£l¥gL«nghJ xU Ïu£il¥gil v© »il¤jš

mšyJ m›éU cU£lèš Kf v©fë‹ TLjš

8 Mf ÏU¤jš vD« ãfœ¢Áæ‹ ãfœjféid¡

fh©f.

n(S) = 36

(

(

(

(

=

=

6. ÏU gfilfŸ xnuneu¤Âš cU£l¥gL«nghJ

»il¡F« Kf v©fë‹ bgU¡f‰gy‹xU gfh

v©zhf ÏU¥gj‰fhd ãfœjféid¡ fh©f

n(S) = 36

(i) (

Page 14 of 15

12. 1 Kjš 50 tiuæyhd KG¡fëèUªJ rkthŒ¥ò

Kiwæš X® v© nj®ªbjL¡f¥

gL«nghJ m›bt© 4 mšyJ 6 Mš tFgLtj‰fhd

ãfœjfÎ fh©f.

n(S) = 50

(

(

(

(

=

=

17. e‹F fiy¤J mL¡» it¡f¥g£l 52 Ó£Lfis¡

bfh©l Ó£L¡ f£oèUªJ rkthŒ¥ò Kiwæš xU Ó£L

vL¡f¥gL»wJ. mªj¢ Ó£L °nglhfnth (Spade) mšyJ

Ïuhrhthfnth (King) ÏU¥gj‰fhd ãfœjféid¡

fh©f.

n(S) = 52

(

(

(

(

=

=

13. xU igæš 50 kiu MâfS« (bolts), 150 ÂUF

kiufS« (nuts) cŸsd. mt‰WŸ gh kiu MâfS«,

gh ÂUF kiufS« JU¥Ão¤jit. rkthŒ¥ò

Kiwæš VnjD« x‹iw¤ nj®ªbjL¡F« nghJ mJ

JU¥Ão¤jjhf mšyJ xU kiu Mâahf ÏU¥gj‰fhd

ãfœjféid¡ fh©f.

n(S) = 200

(

(

(

(

=

=

18. xUòÂak»œÎªJ (car)mjDila totik¥Ã‰fhf

éUJ bgW« ãfœjfÎ 0.25 v‹f. Áwªj Kiwæš

vçbghUŸ ga‹gh£o‰fhd éUJ bgW« ãfœjfÎ 0.35

k‰W« ÏU éUJfS« bgWtj‰fhd ãfœjfÎ 0.15

våš, m«k»œÎªJ (i) FiwªjJ VjhtJ xU éUJ

bgWjš (ii) xnu xU éUJ k£L« bgWjš M»a

ãfœ¢ÁfS¡fhd ãfœjfÎfis¡ fh©f

( ( (

(i) ( =

(ii) ( ( = 0.3

14. ÏU gfilfŸ xnu neu¤Âš nru cU£l¥gL«nghJ

»il¡F« Kf v©fë‹ TLjš 3 Mš k‰W« 4 Mš

tFglhkèU¡f ãfœjfÎ fh©f.

n(S) = 36

(

(

(

(

=

=

19. A, B, C M»nah® xU édhé‰F¤ Ô®Î

fh©gj‰fhd ãfœjfÎfŸ Kiwna

v‹f. A

k‰W« B ÏUtU« nr®ªJ ԮΠfh©gj‰fhd

ãfœjfÎ

. B k‰W« C ÏUtU« nr®ªJ Ô®Î

fh©gj‰fhd ãfœjfÎ

. A k‰W« C ÏUtU«

nr®ªJ ԮΠfhz ãfœjfÎ

, _tU« nr®ªJ Ô®Î

fhz ãfœjfÎ

ahnuD« xUt® m›édhé‹

ԮΠfh©gj‰fhd ãfœjféid¡ fh©f.

(

; (

; (

(

; (

; (

(

(

15. xU Tilæš 20 M¥ÃŸfS« 10 MuŠR¥

gH§fS« cŸsd. mt‰WŸ 5 M¥ÃŸfŸ k‰W« 3

MuŠRfŸ mG»ait. rkthŒ¥ò Kiwæš xUt® xU

gH¤ij vL¤jhš, mJ M¥Ãshfnth mšyJ ešy

gHkhfnth ÏU¥gj‰fhd ãfœjféid¡

fh©f.

n(S) = 30

(

(

(

(

=

=

16. xU tF¥Ãš cŸs khzt®fëš 40% ng® fâj

édho édh ãfœ¢ÁæY«, 30% ng® m¿éaš édho

édh ãfœ¢ÁæY«, 10% ng® m›éu©L édho édh

ãfœ¢ÁfëY« fyªJ bfh©ld®. m›tF¥ÃèUªJ

rkthŒ¥ò Kiwæš xU khzt‹ nj®ªbjL¡f¥g£lhš,

mt® fâj édho édh ãfœ¢Áænyh mšyJ m¿éaš

édho édh ãfœ¢Áænyh mšyJ ÏU ãfœ¢ÁfëYnkh

fyªJ bfh©lj‰fhd ãfœjfÎ fh©f.

(

(

(

(

=

=

Page 15 of 15