S5

//M1//QN1//MCQ//DL0

çku MkkLík økýLku yLkw¢{u m yLku n ½xf Au. «Úk{ økýLku rîíkeÞ øký fhíkkt 56 sux÷k ðÄw WÃkøký nkuÞ, íkku m = ________, n = ________.

(A) 7, 6 (B) 6, 3 (C) 5, 1 (D) 8, 7

//X

(B) 6, 3

//M1//QN2//MCQ//DL0

A = {64n : n ∈ N}, B = {32n + 2 – 8n – 9, n ∈ N} íkku...

(A) A = B (B) A ⊂ B (C) B ⊂ A (D) yuf Ãký Lknª

//X

(C) B ⊂ A

//M1//QN3//MCQ//DL0

Lke[uLkk Ãkife fÞku øký ¾k÷e øký Au ?

(A) {x | x2 – 1 = 0, x ∈ R} (B) {x | x2 + 1 = 0, x ∈ R} (C) {x | x2 – 9 = 0, x ∈ R} (D) {x | x2 = x + 2, x ∈ R}

//X

(B) {x | x2 + 1 = 0, x ∈ R}

//M1//QN4//MCQ//DL0

X = {4n – 3n – 1, n ∈ N}, Y = {9(n – 1), n ∈ N}, íkku X ∪ Y = ________.

(A) X (B) Y (C) N (D) N – {1}

//X

(B) Y

//M1//QN5//MCQ//DL0//EQ

U = {x | x5 – 6x4 + 11x3 – 6x2 = 0, x ∈ R}, A = {x | x2 – 5x + 6 = 0, x ∈ R}, B = {x | 2 – 3x + 2 = 0, x ∈ R}, íkku (A ∩ B)' = ________.

(A) {1 , 3} (B) {1, 2, 3} (C) {0, 1, 3} (D) {0, 1, 2, 3}

//X

(C) {0, 1, 3}

//M1//QN6//MCQ//DL0

øký A yLku øký BLku yLkw¢{u 3 yLku 6 ½xfku Au, íkku A ∪ B{kt hnu÷ ykuAk{kt ykuAk ½xfkuLke MktÏÞk ?

(A) 3 (B) 9 (C) 6 (D) yuf Ãký Lknª

//X

(C) 6

//M1//QN7//MCQ//DL0

òu Na = {an : n ∈ N}, íkku N6 ∩ N8 = ________.

(A) N6 (B) N8 (C) N24 (D) N44

//X

(C) N24

//M1//QN8//MCQ//DL0

A = {x | x yu 4Lkku økwrýík Au.},B = {x | x yu 6Lkku økwrýík Au.} íkku A ∩ B yu __________ Lkk çkÄk økwrýíkkuLku Mk{kðu Au.

(A) 16 (B) 12 (C) 8 (D) 4

//X

(B) 12

//M1//QN9//MCQ//DL0//EQ

A = {x : x ∈ R, x > 2}, B = {x : x ∈ R, x < 4}, íkku A ∩ B = ________.

(A) {x : x ∈ R, x < 4} (B) {x : x ∈ R, 2 < x < 4} (C) B (D) A

//X

(B) {x : x ∈ R, 2 < x < 4}

//M1//QN10//MCQ//DL0

çku yrhõík øký A yLku B {kxu, n(A ∩ B) = 15 nkuÞ íkÚkk 4n(A) = 3n(B) = 2n(A ∪ B), íkku n(A ∪ B) = ________.

(A) 90 (B) 180 (C) 135 (D) 45

//X

(A) 90

//M1//QN11//MCQ//DL0//EQ

òu A = {(x, y) : x2 + y2 = 25}, B = {(x, y) : x2 + 9y2 = 144} íkku A ∩ B{kt ½xfkuLke MktÏÞk ________ Au.

(A) 1 (B) 2 (C) 3 (D) 4

//X

(D) 4

//M1//QN12//MCQ//DL0//EQ

A = {x : x2 – 2x + 2 > 0}, B = {x : x2 – 4x + 3 < 0} íkku A ∩ B = ?

(A) [1, ∞) (B) [1, 3] (C) (–∞, 3] (D) (–∞, 1) ∪ (3, ∞)

//X

(B) [1, 3]

//M1//QN13//MCQ//DL0

A = {x : xyu 240Lkk yrð¼kßÞ yðÞð Au.}, B = {x : xyu 240Lkk fkuE Ãký çku yrð¼kßÞ yðÞðLkku Mkhðk¤ku} nkuÞ íkku...

(A) 5∉ A ∩ B (B) 7∈ A ∩ B (C) 8∈ A ∩ B (D) 8∈ A ∪ B

//X

(D) 8∈ A ∪ B

//M1//QN14//MCQ//DL0

òu A, B, C yu yLkw¢{u Student, Progress yLku Congruent þçËLkk {q¤kûkhkuLkku øký nkuÞ íkku n[A ∪ (B ∩ C)] = ________

(A) 8 (B) 9 (C) 10 (D) 11

//X

(B) 9

//M1//QN15//MCQ//DL0

òu n(A) = 25, n(B) = 20, n(C) = 27, n(A ∩ B) = 5, n(A ∩ C) = 7, (B ∩ C) = φ íkku n(A ∪ B ∪ C) = ________.

(A) 65 (B) 60 (C) 68 (D) 72

//X

(B) 60

//M1//QN16//MCQ//DL0

ºký y÷øk øký A, B yLku C {kxu òu n(A) = 10,

n(B) = 6 yLku n(C) = 5, íkku n(A ∪ B ∪ C) = ?

(A) 21 (B) 11 (C) 1 (D) 9

//X

(A) 21

//M1//QN17//MCQ//DL0//EQ

{(a, b) : 2a2 + 3b2 = 35, a, b ∈ Z} íkku øký{kt ykðu÷k MkÇÞkuLke MktÏÞk ________ Au.

(A) 2 (B) 4 (C) 8 (D) 12

//X

(C) 8

//M1//QN18//MCQ//DL0

A = {x : x yu x2 – 1 = 0Lkwt çkes nkuÞ},

B = {x : x yu x2 – 2x + 1 = 0Lkwt çkes nkuÞ} íkku...

(A) A ∩ B = B (B) A ∩ B = A (C) A ∪ B = A (D) A ∩ B = φ

//X

(C) A ∪ B = A

//M1//QN19//MCQ//DL0//EQ

øký A = {x : x ∈ R, x4 – x3 – 2x2 + 2 = 0}, B = {x : x ∈ N, 2x2 – 1 < 7}, íkku...

(A) A = B (B) A ⊂ B (C) B ⊂ A (D) A ∩ B = φ

//X

(C) B ⊂ A

//M1//QN20//MCQ//DL0//EQ

òu U yu Mkkðorºkf øký nkuÞ íkÚkk A ∪ B ∪ C = U, íkku [(A – B) ∪ (B – C) ∪ (C – A)]' = ________.

(A) A ∪ B ∪ C (B) A ∩ B ∩ C (C) A ∪ (B ∩ C) (D) A ∩ (B ∪ C)

//X

(B) A ∩ B ∩ C

//M1//QN21//MCQ//DL0//EQ

çku MkkLík økýkuLku yLkw¢{u m yLku n MkÇÞku Au (m > n) íkÚkk «Úk{ økýLkk WÃkøkýkuLke MktÏÞk yu çkeò økýLkk WÃkøkýkuLke MktÏÞk fhíkkt 112 sux÷e ðÄkhu nkuÞ, íkku mn = ?

(A) 46 (B) 36 (C) 28 (D) 18

//X

(C) 28

//M1//QN22//MCQ//DL0

yMk{íkk x4 – 29x2 + 100 < 0Lkwt Mk{kÄkLk fhíke xLke _______ ®f{íkku {¤u. (ßÞkt, x ∈ Z)

(A) 8 (B) 6 (C) 4 (D) 2

//X

(C) 4

//M1//QN23//MCQ//DL0

òu n(A) = 10, n(B) = 15, n(A ∪ B) = x, íkku...

(A) 15 < x < 25 (B) 5 < x < 15 (C) 15 < x < 25 (D) 5 < x < 25

//X

(A) 15 < x < 25

//M1//QN24//MCQ//DL0

òu U = {x : x ∈ N, 2 < x < 12}, A = {x | x yu çkufe yrð¼kßÞ MktÏÞk Au.} B = {x : x yu 12Lkk yðÞð nkuÞ}, íkku Lke[uLkk{ktÚke fÞwt MkíÞ LkÚke ?

(A) A – B = φ (B) A – B = B ∩ A' (C) A' – B' = B – A (D) (A ∩ B)' = A' ∪ B'

//X

(B) A – B = B ∩ A'

//M1//QN25//SUB//DL0

(i) A – f = _______ . (ii) f – A = ________.(a) U (b) A'(c) f(d) A

//X

ÔÞkÏÞk ÃkhÚke,

A – f = {x | x ∈ A yLku x ∉ f}

ÃkhÚke f Lku fkuE MkÇÞ LkÚke.

∴ A – f = {x | x ∈ A} = A

f – A = {x | x ∈ f yLku x ∉ A}

ÃkhÚke f Lku fkuE MkÇÞ LkÚke.

∴ f – A = f

//M1//QN26//MCQ//DL0

A ∪ f = _______ .

(A) A (B) A' (C) U (D) f

//X

(A) A

//M1//QN27//MCQ//DL0

A ⊂ B ⇔ A – B = ________ .

(A) U (B) f (C) A (D) B

//X

(B) f

//M1//QN28//MCQ//DL0

A – B = B – A = f ⇔ ________ .

(A) A ≠ B ≠ f (B) A ≠ B (C) A ⊂ B (D) A = B

//X

(D) A = B

//M1//QN29//MCQ//DL0

Míkt¼ A{kt øký ÞkËeLke heíku yLku Míkt¼ B{kt økwýÄ{oLke heíku Ëþkoðu÷ Au : Lke[u ÃkifeLke fE òuz ÞkuøÞ Au ?

(A)		(B)
(1)	{L, A, T}	(A)	{x \| x yu 4Úke LkkLke «kf]ríkf MktÏÞk Au.}
(2)	{–2, –1, 0, 1, 2}	(B)	{x \| x yu LATA þçËLkku {q¤kûkh Au.}
(3)	{1, 2, 3}	(C)	{x \| x ∈ Z, x2 < 5}

//X

(answer not detected)

//M1//QN30//MCQ//DL0

A = 100Úke LkkLke Þwø{ MktÏÞkykuLkku Mk{qn B = 20{e MkËeLkk h{íkðehkuLkku Mk{qn C = W{kþtfh òu»keyu ÷¾u÷ frðíkkykuLkku Mk{qn Lke[uLkkt Ãkife fÞwt rðÄkLk MkíÞ Au ?

(A) A yLku B øký Au. (B) B yu øký LkÚke. (C) A yLku C øký LkÚke. (D) A, B yLku C øký Au.

//X

(B) B yu øký LkÚke.

//M1//QN31//MCQ//DL0

A = {x | x ∈ Z, x4 – 16 = 0} nkuÞ, íkku

(A) A = {– 2, 2} (B) A = {2} (C) A = {– 4} (D) A = {– 4, 4, – 2, 2}

//X

(A) A = {– 2, 2}

//M1//QN32//MCQ//DL0

òu A = {y | y ∈ N, y3 – 27 = 0} nkuÞ, íkku fÞwt rðÄkLk MkíÞ Au ?

(A) 9 ∈ A (B) – 3 ∈ A (C) 3 ∈ A (D) – 9 ∈ A

//X

(C) 3 ∈ A

//M1//QN33//MCQ//DL0

òu B = {x | x ∈ Z, x2 – 16 = 0} nkuÞ, íkku ¾hwt rðÄkLk ÃkMktË fhku.

(A) 4 ∈ B (B) – 4 ∉ A (C) 2 ∉ B (D) 2 ∈ B

//X

(A) 4 ∈ B

//M1//QN34//MCQ//DL0

òu B = {f} nkuÞ, íkku

(A) B ¾k÷e øký Au. (B) B MkkLík øký Au. (C) B yLktík øký Au. (D) B yu øký LkÚke.

//X

(B) B MkkLík øký Au.

//M1//QN35//MCQ//DL0

A = {x | x ∈ N, x2 + 4 = 0} nkuÞ, íkku

(A) A = {– 2, 2} (B) A = {2} (C) A = f (D) A = {f}

//X

(C) A = f

//M1//QN36//MCQ//DL0

a = {x | x yu ALPHA þçËLkku {q¤kûkh Au.} b = {x | x yu ALPA þçËLkku {q¤kûkh Au.} g = {L, P, A, H} íkku yMkíÞ rðÄkLk ÃkMktË fhku.

(A) a = g (B) b = {A, L, P} (C) a = b (D) b ∩ g ≠ f

//X

(C) a = b

//M1//QN37//MCQ//DL0

Míkt¼ A{kt y{wf øký ykÃku÷k Au yLku Míkt¼ B{kt WÃkøkýku ykÃku÷k Au. òu Míkt¼ A{ktLkk ºký økýLku Míkt¼ B{kt íkuLkk WÃkøký MkkÚku òuzeyu íkku Lke[uLkkt{ktÚke fE òuze ÞkuøÞ Au ?

	Míkt¼ A		Míkt¼ B
(1)	{1, 3, 5, 7....}	(A)	{1, 19, 21}
(2)	{2, 4, 6, 8....}	(B)	{2, 5, 6, 8, 19}
(3)	{1, 2, 3, 4....}	(C)	{8, 28, 38}

//X

(answer not detected)

//M1//QN38//MCQ//DL0

ðkMíkrðf MktÏÞk øký R {kxu Lke[uLkk Ãkife fÞwt rðÄkLk Mkk[wt LkÚke ?

(A) N ⊂ R (B) (a, b) ⊂ R; a < b (C) π ∉ R (D) f ⊂ R

//X

(C) π ∉ R

//M1//QN39//MCQ//DL0

A = {1, 5, 7}, B = {1, 10}, C = {11, 12, ..., 20}

fÞk økýLkk WÃkøký Au ?

(A) {1, 2, 3, ..., 20} (B) {1, 3, 5, ..., 21} (C) f (D) {1, 11, 111, 1111}

//X

(A) {1, 2, 3, ..., 20}

//M1//QN40//MCQ//DL0

A = {1, 2, 3, 4}, B = {– 1, 1, 0, – 2, 2},

C = {1, 3, 4} fÞk økýLkk WÃkøký Au ?

(A) [1, 4] (B) [– 1, 4] (C) [– 2, 2] (D) [– 2, 4]

//X

(D) [– 2, 4]

//M1//QN41//MCQ//DL0//EQ

ytíkhk÷ (– 1, 1] {kxu Lke[uLkk Ãkife fÞwt rðÄkLk Mkk[wt Au ?42. fE ðuLk ykf]ríkLkku htøkeLk «Ëuþ ¼køk A ∩ B Ëþkoðu Au ?43. Lke[uLke ðuLk ykf]rík {kxu ¾hwt rðÄkLk ÃkMktË fhku.

A

4

7

1

3

2

6

5

B

U

44. Lke[uLke ðuLk ykf]rík {kxu fÞwt rðÄkLk ¾hwt LkÚke.

a

b

c

d

A

f

g

B

e

U

(A) A = {c, d, f, g} (B) B = f (C) U = {a, b, c, d, e, f, g} (D) A ∪ B = {c, d, f, g}

//X

(B) B = f

//M1//QN42//MCQ//DL0

A = {x | x yu 8 fhíkkt LkkLke «kf]ríkf MktÏÞk Au.} B = {x | x yu 5 fhíkkt {kuxe yLku 18 fhíkkt LkkLke «kf]ríkf MktÏÞk Au.}, íkku46. Lke[u Ãkife fÞwt rðÄkLk ¾hwt Au ? (A ≠ φ)47. Lke[uLkkt Ãkife fÞwt rðÄkLk ¾hwt Au ? (A ≠ B)

(A) (A ∩ B) ⊂ A (B) (A ∪ B) ⊂ A (C) (A ∪ B) ∩ B = A (D) (A ∪ B) ⊂ B

//X

(A) (A ∩ B) ⊂ A

//M1//QN43//MCQ//DL0

òu A ⊂ B nkuÞ, íkku

(A) A ∩ B = f (B) A ∩ B = A (C) A ∩ B = B (D) A ∪ B = A

//X

(B) A ∩ B = A

//M1//QN44//MCQ//DL0

U = {x | x ∈ N, x ≤ 10}, A = {1, 3, 5, 7, 9}, B = {2, 4, 6, 8, 10}, íkku (A ∪ B)' = _______

(A) U (B) {2} (C) f (D) {1, 4, 7, 8}

//X

(C) f

//M1//QN45//MCQ//DL0

ðkMíkrðf MktÏÞkykuLkk øký R Lku Mkkðorºkf øký ÷Eyu íkku Q' =______

(A) N (B) Z (C) T (D) R

//X

(C) T

//M1//QN46//MCQ//DL0//EQ

«kf]ríkf MktÏÞkykuLkk økýLku Mkkðorºkf øký ÷Eyu yLku A = {x | x – 8 = 3}, A' = ______52. U = {x | x ∈ R, 1 < x < 5}, A = {x | x ∈ N, x2 – 6x + 5 = 0} nkuÞ, íkku A' = ______53. U = [1, 2], A = {x | x ∈ N, x2 + x – 2 = 0} nkuÞ, íkku A' = ______54. Lke[u Ãkife fE ðuLk ykf]rík{kt htøkeLk ¼køk (A ∩ B)' Ëþkoðu Au.55. A = {a, b, d, e}, B = {c, d, f, l, m} yLku C = {a, l, m, o} nkuÞ, íkku C ∩ (A ∪ B) = ______56. òu A yLku B çku økýku nkuÞ, íkku A ∩ (A ∪ B) = ______57. òu A = {1, 2, 3}, B = {3, 4}, C = {4, 5, 6} íkku A ∪ (B ∩ C) = ______58. òu øký A yLku øký B{kt yLkw¢{u 8 íkÚkk 6 MkÇÞku nkuÞ, íkku A ∪ B {kt ykuAk{kt ykuAk ____ MkÇÞku nkuÞ.59. Lke[uLkkt Ãkife fÞku øký ¾k÷e øký Au ?60. çku MkkLík øký{kt yLkw¢{u m yLku n MkÇÞku Au. «Úk{ økýLkkt WÃkøkýkuLke MktÏÞk çkeò økýLkk WÃkøkýkuLke MktÏÞk fhíkkt 56 ðÄkhu Au, íkku m íkÚkk nLke ®f{ík yLkw¢{u ______ Au.61. òu X yLku Y çku økýku nkuÞ, íkku X ∩ (Y ∪ X)' = ______

(A) X (B) Y (C) f (D) U

//X

(D) U

//M1//QN47//MCQ//DL0

òu A = {1, 3, 5, 7, 9, 11, 13, 15, 17}, B = {2, 4, 6, 8, .... 18}, N = U, íkku A' ∪ ((A ∪ B) ∩ B') = ______63. òu A = {x | x yu 3 Lkku økwýktf Au}, B = {x | x yu 5 Lkku økwýktf Au}, íkku A ∩ B = _____64. Lke[uLkkt Ãkife fÞku øký MkkLíkøký Au ?

(A) A = {x | x ∈ Z yLku x2 Þwø{ Au.} (B) B = {x | x ∈ N x > 5} (C) C = {x | x ∈ R, 0 < x < 1}} (D) D = {x | x ∈ Z, x2 – 5x + 6 = 0}

//X

(B) B = {x | x ∈ N x > 5}

//M1//QN48//MCQ//DL0

Äkhku fu U = N. A = Þwø{ «kf]ríkf MktÏÞkykuLkku øký íkku A' =______.

(A) yÞwø{ «kf]ríkf MktÏÞkykuLkku øký (B) yrð¼kßÞ MktÏÞkykuLkku øký (C) Þwø{ MktÏÞkykuLkku øký (D) N

//X

(A) yÞwø{ «kf]ríkf MktÏÞkykuLkku øký

//M1//QN49//MCQ//DL0

øký A = {x | x ∈ R, x2 = 16 yLku 2x = 6} yu ________ Au.

(A) φ (B) (4, –4) (C) {4, –4, 3} (D) {3}

//X

(A) φ

//M1//QN50//MCQ//DL0//EQ

òu A, B, C ºký yrhõíkøkýku nkuÞ íkku, (A ∩ B) ∩ (B ∩ C) ∩ (C ∩ A) ______

(A) A ∪ B ∪ C (B) A ∩ B ∩ C (C) φ (D) U

//X

(B) A ∩ B ∩ C

//M1//QN51//MCQ//DL0

Éý ðkMíkrðf MktÏÞkykuLkku øký

(A) (–∞, 0] (B) (–∞, 0) (C) {..., –3, –2, –1) (D) {x | x ∈ Q, x < 0}

//X

(B) (–∞, 0)

//M1//QN52//MCQ//DL0

yLk]ý ðkMíkrðf MktÏÞkykuLkku øký

(A) [0, ∞) (B) (0, ∞) (C) (–∞, 0) (D) N

//X

(A) [0, ∞)

//M1//QN53//MCQ//DL0

ytíkhk÷ [5, ∞) Lke ÷tçkkE ______.

(A) 5 (B) 4 (C) Lk {¤u (D) 0

//X

(C) Lk {¤u

//M1//QN54//MCQ//DL0

B = {2, 3, 4}, C = {2, 3, 5}, X ⊂ B, X ≠ B, X ⊄ C þhíkkuLkwt Ãkk÷Lk fhíkkt ík{k{ X = ______.

(A) {4}, {2, 4}, {3, 4} (B) {4}, {2, 5}, {3, 4} (C) {2}, {3}, {2, 3} (D) {4}

//X

(A) {4}, {2, 4}, {3, 4}

//M1//QN55//MCQ//DL0//EQ

òu U = N, A = {x | x ∈ N, x yu 3Lkku yðÞðe}, íkku (A')' =______.

(A) N (B) A (C) {x | x ∈ N, x yu 3Lkku yðÞðe Lk nkuÞ} (D) φ

//X

(B) A

//M1//QN56//MCQ//DL0

òu n(A) = p, n(B) = q yLku A Lkk fw÷ WÃkøkýkuLke MktÏÞk BLkk fw÷ WÃkøkýkuLke MktÏÞk fhíkkt 16 økýe Au, íkku p – q______.

(A) 4 (B) 2 (C) 16 (D) 8

//X

(A) 4

//M1//QN57//MCQ//DL0//EQ

òu A = {x | 3x2 – 7x – 6 = 0, x ∈ R} yLku B = {x | 6x2 – 5x – 6 = 0, x ∈ R} íkku A ∩ B = ______.

(A) (B) (C) {3} (D) φ

//X

(B)