Chapter 1 · ગણ

#1 SUB 0M ✎ Edit ⚠ Log Error

Question

Mk{efhý x2 + x – 2 = 0Lkk Wfu÷økýLku ÞkËeLke heíku ÷¾ku.

Answer

ynª, x2 + x – 2 = 0

∴ (x + 2) (x – 1) = 0

∴ x + 2 = 0 yÚkðk x – 1 = 0

∴ x = –2 yÚkðk x = 1

∴ Wfu÷økýLku ÞkËeLke heíku {–2, 1} ðzu ËþkoðkÞ Au.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Mk{efhý x2 + x – 2 = 0Lkk Wfu÷økýLku ÞkËeLke heíku ÷¾ku.

Answer

ynª, x2 + x – 2 = 0

∴ (x + 2) (x – 1) = 0

∴ x + 2 = 0 yÚkðk x – 1 = 0

∴ x = –2 yÚkðk x = 1

∴ Wfu÷økýLku ÞkËeLke heíku {–2, 1} ðzu ËþkoðkÞ Au.

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#2 SUB 0M ✎ Edit ⚠ Log Error

Question

øký {x : x yu ÄLk ÃkqýkOf MktÏÞk Au yLku x2 < 40} Lku ÞkËeLke heíku ÷¾ku.

Answer

ynª, ykÃkýu yuðe ÄLk ÃkqýkOf MktÏÞk þkuÄðe Au su{Lkku ðøko 40 fhíkk LkkLkku nkuÞ.

su{ fu, 1, 2, 3, 4, 5, 6 Lkku ðøko 40 fhíkkt LkkLkku nkuÞ. íkuÚke ykÃku÷ økýLku {1, 2, 3, 4, 5, 6} ðzu ËþkoðkÞ Au.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

øký {x : x yu ÄLk ÃkqýkOf MktÏÞk Au yLku x2 < 40} Lku ÞkËeLke heíku ÷¾ku.

Answer

ynª, ykÃkýu yuðe ÄLk ÃkqýkOf MktÏÞk þkuÄðe Au su{Lkku ðøko 40 fhíkk LkkLkku nkuÞ.

su{ fu, 1, 2, 3, 4, 5, 6 Lkku ðøko 40 fhíkkt LkkLkku nkuÞ. íkuÚke ykÃku÷ økýLku {1, 2, 3, 4, 5, 6} ðzu ËþkoðkÞ Au.

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#3 FB 1M ✎ Edit ⚠ Log Error

Question

øký A = {1, 4, 9, 16, 25, .....} Lku økwýÄ{oLke heíku ÷¾ku.

Answer

ynª, ykÃkýLku øký A {kt «kf]ríkf MktÏÞkLkk ðøko ykÃku÷k Au. {kxu ykÃku÷k økýLku,

A = {x : x yu «kf]ríkf MktÏÞkLkku ðøko Au.}

yÚkðk

A = {x : x = n2, n ∈ N} ðzu Ãký ÷¾e þfkÞ Au.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

øký A = {1, 4, 9, 16, 25, .....} Lku økwýÄ{oLke heíku ÷¾ku.

Answer

ynª, ykÃkýLku øký A {kt «kf]ríkf MktÏÞkLkk ðøko ykÃku÷k Au. {kxu ykÃku÷k økýLku,

A = {x : x yu «kf]ríkf MktÏÞkLkku ðøko Au.}

yÚkðk

A = {x : x = n2, n ∈ N} ðzu Ãký ÷¾e þfkÞ Au.

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#4 SUB 0M 🖼 3 ✎ Edit ⚠ Log Error

Question

øký Lku økwýÄ{oLke heíku Ëþkoðku.

Answer

ynª, òuE þfkÞ Au fu Ëhuf ½xfLkku ytþ íkuLkk AuËÚke 1 sux÷ku LkkLkku Au íkÚkk ytþ ykuAk{kt ykuAku 1 yLku ðÄw{kt ðÄw 6 Au. {kxu ykÃku÷ økýLku,

{x : x = , n ∈ N, 1 < n < 6} ðzu Ëþkoðe þfkÞ.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

øký Lku økwýÄ{oLke heíku Ëþkoðku.

Answer

ynª, òuE þfkÞ Au fu Ëhuf ½xfLkku ytþ íkuLkk AuËÚke 1 sux÷ku LkkLkku Au íkÚkk ytþ ykuAk{kt ykuAku 1 yLku ðÄw{kt ðÄw 6 Au. {kxu ykÃku÷ økýLku,

{x : x = , n ∈ N, 1 < n < 6} ðzu Ëþkoðe þfkÞ.

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#5 SUB 0M ✎ Edit ⚠ Log Error

Question

Lke[uLkk{ktÚke fÞk Mk{qn øký Ëþkoðu Au ? ík{khku sðkçk [fkMkku.

(i) J Úke þY Úkíkk ytøkúuS fì÷uLzhLkk ð»koLkk ík{k{ {rnLkkykuLkku Mk{qn.

Answer

yk Mk{qn øký Ëþkoðu Au fkhý fu J Úke þY Úkíkk ytøkúuS fì÷uLzhLkk {rnLkkyku January, June yLku July Au. yk{, yk Mk{qn MkwÔÞkÏÞkrÞík Au.

(ii) ¼khíkLkk ËMk yrík «rík¼kþk¤e ÷u¾fkuLkku Mk{qn.

yk Mk{qn øký Ëþkoðíkku LkÚke fkhý fu «rík¼kþk¤e ÷u¾f {kxuLkku yr¼«kÞ ÔÞÂõíkyu ÔÞÂõíkyu çkË÷kíkku nkuðkÚke íku MkwÔÞkÏÞkrÞík LkÚke.

(iii) ËwrLkÞkLkk r¢fuxLkk W¥k{ yrøkÞkh çkìxTMk{uLkkuLke xe{.

yk Mk{qn øký Ëþkoðíkku LkÚke fkhý fu W¥k{ çkìxTMk{uLk {kxuLkku yr¼«kÞ ÔÞÂõíkyu ÔÞÂõíkyu çkË÷kÞ {kxu íku MkwÔÞkÏÞkrÞík LkÚke.

(iv) ík{khk ðøkoLkk çkÄk s AkufhkykuLkku Mk{qn.

yk Mk{qn øký Au fkhý fu AkufhkykuLkku Mk{qn MkwÔÞkÏÞkrÞík Au.

(v) 100 Úke LkkLke çkÄe s «kf]ríkf MktÏÞkykuLkku Mk{qn.

yk Mk{qn øký Ëþkoðu Au fkhý fu 100 Úke LkkLke çkÄe s «kf]ríkf MktÏÞkyku MkwÔÞkÏÞkrÞík Au su{ fu 1, 2, 3, ....., 99.

(vi) ÷u¾f {wLþe «u{[tËu ÷¾u÷e çkÄe s Lkð÷fÚkkykuLkku Mk{qn.

yk Mk{qn øký Au fkhý fu {wLþe «u{[tËu ÷¾u÷e çkÄe s Lkð÷fÚkkykuLkku Mk{qn MkwÔÞkÏÞkrÞík Au.

(vii) çkÄk s Þwø{ ÃkqýkOfkuLkku Mk{qn.

yk Mk{qn øký Au fkhý fu çkÄk s Þwø{ ÃkqýkOfku MkwÔÞkÏÞkrÞík Au.

(viii) yk «fhýLkk çkÄk s «§kuLkku Mk{qn.

yk Mk{qn øký Au fkhý fu yk «fhýLkk çkÄk s «§kuLkku Mk{qn MkwÔÞkÏÞkrÞík Au.

(ix) ËwrLkÞkLkkt ¾qçk s ¼ÞkLkf «kýeykuLkku Mk{qn.

yk Mk{qn øký Ëþkoðíkku LkÚke fkhý fu ËwrLkÞkLkkt ¼ÞkLkf «kýeyku rðþuLkku yr¼«kÞ ÔÞÂõíkyu ÔÞÂõíkyu çkË÷kíkku nkuÞ Au.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Lke[uLkk{ktÚke fÞk Mk{qn øký Ëþkoðu Au ? ík{khku sðkçk [fkMkku.

(i) J Úke þY Úkíkk ytøkúuS fì÷uLzhLkk ð»koLkk ík{k{ {rnLkkykuLkku Mk{qn.

Answer

yk Mk{qn øký Ëþkoðu Au fkhý fu J Úke þY Úkíkk ytøkúuS fì÷uLzhLkk {rnLkkyku January, June yLku July Au. yk{, yk Mk{qn MkwÔÞkÏÞkrÞík Au.

(ii) ¼khíkLkk ËMk yrík «rík¼kþk¤e ÷u¾fkuLkku Mk{qn.

yk Mk{qn øký Ëþkoðíkku LkÚke fkhý fu «rík¼kþk¤e ÷u¾f {kxuLkku yr¼«kÞ ÔÞÂõíkyu ÔÞÂõíkyu çkË÷kíkku nkuðkÚke íku MkwÔÞkÏÞkrÞík LkÚke.

(iii) ËwrLkÞkLkk r¢fuxLkk W¥k{ yrøkÞkh çkìxTMk{uLkkuLke xe{.

yk Mk{qn øký Ëþkoðíkku LkÚke fkhý fu W¥k{ çkìxTMk{uLk {kxuLkku yr¼«kÞ ÔÞÂõíkyu ÔÞÂõíkyu çkË÷kÞ {kxu íku MkwÔÞkÏÞkrÞík LkÚke.

(iv) ík{khk ðøkoLkk çkÄk s AkufhkykuLkku Mk{qn.

yk Mk{qn øký Au fkhý fu AkufhkykuLkku Mk{qn MkwÔÞkÏÞkrÞík Au.

(v) 100 Úke LkkLke çkÄe s «kf]ríkf MktÏÞkykuLkku Mk{qn.

yk Mk{qn øký Ëþkoðu Au fkhý fu 100 Úke LkkLke çkÄe s «kf]ríkf MktÏÞkyku MkwÔÞkÏÞkrÞík Au su{ fu 1, 2, 3, ....., 99.

(vi) ÷u¾f {wLþe «u{[tËu ÷¾u÷e çkÄe s Lkð÷fÚkkykuLkku Mk{qn.

yk Mk{qn øký Au fkhý fu {wLþe «u{[tËu ÷¾u÷e çkÄe s Lkð÷fÚkkykuLkku Mk{qn MkwÔÞkÏÞkrÞík Au.

(vii) çkÄk s Þwø{ ÃkqýkOfkuLkku Mk{qn.

yk Mk{qn øký Au fkhý fu çkÄk s Þwø{ ÃkqýkOfku MkwÔÞkÏÞkrÞík Au.

(viii) yk «fhýLkk çkÄk s «§kuLkku Mk{qn.

yk Mk{qn øký Au fkhý fu yk «fhýLkk çkÄk s «§kuLkku Mk{qn MkwÔÞkÏÞkrÞík Au.

(ix) ËwrLkÞkLkkt ¾qçk s ¼ÞkLkf «kýeykuLkku Mk{qn.

yk Mk{qn øký Ëþkoðíkku LkÚke fkhý fu ËwrLkÞkLkkt ¼ÞkLkf «kýeyku rðþuLkku yr¼«kÞ ÔÞÂõíkyu ÔÞÂõíkyu çkË÷kíkku nkuÞ Au.

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#6 SUB 0M ✎ Edit ⚠ Log Error

Question

A = {1, 2, 3, 4, 5, 6} ÷ku íkÚkk ¾k÷e søÞk{kt ÞkuøÞ Mkt¿kk ∈ yÚkðk ∉ {qfku.

Answer

(i) 5 ∈ A

(ii) 8 ∉ A

(iii) 0 ∉ A

(iv) 4 ∈ A

(v) 2 ∈ A

(vi) 10 ∉ A

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

A = {1, 2, 3, 4, 5, 6} ÷ku íkÚkk ¾k÷e søÞk{kt ÞkuøÞ Mkt¿kk ∈ yÚkðk ∉ {qfku.

Answer

(i) 5 ∈ A

(ii) 8 ∉ A

(iii) 0 ∉ A

(iv) 4 ∈ A

(v) 2 ∈ A

(vi) 10 ∉ A

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#7 SUB 0M ✎ Edit ⚠ Log Error

Question

Lke[uLkk økýkuLku ÞkËeLke heíku ÷¾ku :

(i) A = {x : x yu ÃkqýkOf Au yLku –3 < x < 7}

Answer

ynª, ykÃkýu Võík –3 yLku 7 ðå[uLke s ÃkqýkOf MktÏÞkyku ÷¾ðe Au.

∴ A = {–2, –1, 0 , 1, 2, 3, 4, 5, 6}

(ii) B = {x : x yu 6 fhíkkt LkkLke «kf]ríkf MktÏÞk Au.}

∴ B = {1, 2, 3, 4, 5}

(iii) C = {x : x yu suLkk ytfkuLkku Mkhðk¤ku 8 Úkíkku nkuÞ íkuðe çku ytfkuLke MktÏÞk Au.}

∴ C = {17, 26, 35, 44, 53, 62, 71, 80}

fkhý fu, 1 + 7 = 8, 2 + 6 = 8 ðøkuhu.

(iv) D = {x : x yu 60 Lkku ÄLk yðÞð nkuÞ íkuðe yrð¼kßÞ MktÏÞk Au.}

ynª, 60 Lkk fw÷ ÄLk yðÞð 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 Au. íku{ktÚke yrð¼kßÞ 2, 3, 5 Au.

∴ D = {2, 3, 5}

(v) E = TRIGONOMETRY þçËLkk {q¤kûkhkuLkku øký.

E = {T, R, I, G, O, N, M, E, Y}

(vi) F = BETTER þçËLkk {q¤kûkhkuLkku øký.

F = {B, E, T, R}

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Lke[uLkk økýkuLku ÞkËeLke heíku ÷¾ku :

(i) A = {x : x yu ÃkqýkOf Au yLku –3 < x < 7}

Answer

ynª, ykÃkýu Võík –3 yLku 7 ðå[uLke s ÃkqýkOf MktÏÞkyku ÷¾ðe Au.

∴ A = {–2, –1, 0 , 1, 2, 3, 4, 5, 6}

(ii) B = {x : x yu 6 fhíkkt LkkLke «kf]ríkf MktÏÞk Au.}

∴ B = {1, 2, 3, 4, 5}

(iii) C = {x : x yu suLkk ytfkuLkku Mkhðk¤ku 8 Úkíkku nkuÞ íkuðe çku ytfkuLke MktÏÞk Au.}

∴ C = {17, 26, 35, 44, 53, 62, 71, 80}

fkhý fu, 1 + 7 = 8, 2 + 6 = 8 ðøkuhu.

(iv) D = {x : x yu 60 Lkku ÄLk yðÞð nkuÞ íkuðe yrð¼kßÞ MktÏÞk Au.}

ynª, 60 Lkk fw÷ ÄLk yðÞð 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 Au. íku{ktÚke yrð¼kßÞ 2, 3, 5 Au.

∴ D = {2, 3, 5}

(v) E = TRIGONOMETRY þçËLkk {q¤kûkhkuLkku øký.

E = {T, R, I, G, O, N, M, E, Y}

(vi) F = BETTER þçËLkk {q¤kûkhkuLkku øký.

F = {B, E, T, R}

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#8 SUB 0M 🖼 1 ✎ Edit ⚠ Log Error

Question

Lke[uLkk økýkuLku økwýÄ{oLke heíku ÷¾ku :

(i) {3, 6, 9, 12} = A

Answer

ynª, øký{kt ykÃku÷e MktÏÞkyku 3 Lke økwýf Au.

∴ A = {x : x = 3n, 1 < n < 4, n ∈ N}

(ii) B = {2, 4, 8, 16, 32}

ynª, øký{kt ykÃku÷e MktÏÞkyku 2 Lke ½kíkLkk MðYÃk{kt Au.

∴ B = {x : x = 2n, 1 < n < 5, n ∈ N}

(iii) C = {5, 25, 125, 625}

ynª, øký{kt ykÃku÷e MktÏÞkyku 5 Lke ½kíkLkk MðYÃk{kt Au. {kxu, C = {x : x = 5n, 1 < n < 4, n ∈ N}

(iv) {2, 4, 6,.....} = D

ynª, øký{kt ykÃku÷ MktÏÞkyku 2 Lke økwýf (Þwø{ «kf]ríkf MktÏÞkyku) Au íkÚkk yk yLktík MkwÄe Au.

∴ D = { : x = 2n, n ∈ N}

(v) {1, 4, 9,....., 100} = E

ynª, øký{kt ykÃku÷e MktÏÞkyku Ãkqýoðøko «kf]ríkf MktÏÞkyku Au.

su{ fu,

(1)2 = 1, (2)2 = 4, (3)2 = 9, ....., (10)2 = 100

∴ E = {x : x = n2, 1 < n < 10, n ∈ N}

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Lke[uLkk økýkuLku økwýÄ{oLke heíku ÷¾ku :

(i) {3, 6, 9, 12} = A

Answer

ynª, øký{kt ykÃku÷e MktÏÞkyku 3 Lke økwýf Au.

∴ A = {x : x = 3n, 1 < n < 4, n ∈ N}

(ii) B = {2, 4, 8, 16, 32}

ynª, øký{kt ykÃku÷e MktÏÞkyku 2 Lke ½kíkLkk MðYÃk{kt Au.

∴ B = {x : x = 2n, 1 < n < 5, n ∈ N}

(iii) C = {5, 25, 125, 625}

ynª, øký{kt ykÃku÷e MktÏÞkyku 5 Lke ½kíkLkk MðYÃk{kt Au. {kxu, C = {x : x = 5n, 1 < n < 4, n ∈ N}

(iv) {2, 4, 6,.....} = D

ynª, øký{kt ykÃku÷ MktÏÞkyku 2 Lke økwýf (Þwø{ «kf]ríkf MktÏÞkyku) Au íkÚkk yk yLktík MkwÄe Au.

∴ D = { : x = 2n, n ∈ N}

(v) {1, 4, 9,....., 100} = E

ynª, øký{kt ykÃku÷e MktÏÞkyku Ãkqýoðøko «kf]ríkf MktÏÞkyku Au.

su{ fu,

(1)2 = 1, (2)2 = 4, (3)2 = 9, ....., (10)2 = 100

∴ E = {x : x = n2, 1 < n < 10, n ∈ N}

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#9 SUB 0M 🖼 4 ✎ Edit ⚠ Log Error

Question

Lke[uLkk økýLkk çkÄk s ½xfku ÷¾ku.

(i) A = {x : x yu yÞwø{ «kf]ríkf MktÏÞk Au.}

Answer

A = {1, 3, 5, 7, 9, .....}

(ii) B = {x : x yu ÃkqýkOf Au, < x < }

ynª, < x < Lku –0.5 < x < 4.5 ðzu Ëþkoðíkk ynª, –0.5 yLku 4.5 ðå[uLke ÃkqýkOf MktÏÞkyku ËþkoððkLke Au.

∴ B = {0, 1, 2, 3, 4}

(iii) C = {x : x yu ÃkqýkOf Au, x2 < 4}

ynª, yuðe ÃkqýkOf MktÏÞk ÷uðe Au fu su{Lkku ðøko 4 yLku 4 fhíkkt LkkLkku ÚkkÞ.

∴ C = {–2, –1, 0, 1, 2}

(iv) D = {x : x yu “LOYAL” þçËLkku {q¤kûkh Au.}

D = {L, O, Y, A}

(v) E = {x : x yu ð»koLkku 31 rËðMkLkku Lk nkuÞ íkuðku {rnLkku Au.}

E = {Vuçkúwykhe, yur«÷, sqLk, MkÃxuBçkh, LkðuBçkh}

(vi) F = {x : x yu ytøkúuS {q¤kûkhkuLke ¢{kLkwMkkh ÞkËe{kt K Ãknu÷kLkku ÔÞtsLk}

F = {b, c, d, f, g, h, j}

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Lke[uLkk økýLkk çkÄk s ½xfku ÷¾ku.

(i) A = {x : x yu yÞwø{ «kf]ríkf MktÏÞk Au.}

Answer

A = {1, 3, 5, 7, 9, .....}

(ii) B = {x : x yu ÃkqýkOf Au, < x < }

ynª, < x < Lku –0.5 < x < 4.5 ðzu Ëþkoðíkk ynª, –0.5 yLku 4.5 ðå[uLke ÃkqýkOf MktÏÞkyku ËþkoððkLke Au.

∴ B = {0, 1, 2, 3, 4}

(iii) C = {x : x yu ÃkqýkOf Au, x2 < 4}

ynª, yuðe ÃkqýkOf MktÏÞk ÷uðe Au fu su{Lkku ðøko 4 yLku 4 fhíkkt LkkLkku ÚkkÞ.

∴ C = {–2, –1, 0, 1, 2}

(iv) D = {x : x yu “LOYAL” þçËLkku {q¤kûkh Au.}

D = {L, O, Y, A}

(v) E = {x : x yu ð»koLkku 31 rËðMkLkku Lk nkuÞ íkuðku {rnLkku Au.}

E = {Vuçkúwykhe, yur«÷, sqLk, MkÃxuBçkh, LkðuBçkh}

(vi) F = {x : x yu ytøkúuS {q¤kûkhkuLke ¢{kLkwMkkh ÞkËe{kt K Ãknu÷kLkku ÔÞtsLk}

F = {b, c, d, f, g, h, j}

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#10 SUB 0M ▦ 1 ✎ Edit ⚠ Log Error

Question

zkçke çkkswyu ÞkËeLke heíku Ëþkoðu÷k økýkuLku s{ýe çkkswyu íkuLkk s økwýÄ{oLke heíku Ëþkoðu÷k økýku MkkÚku Mkktf¤ku.

(i)	{1, 2, 3, 6}	(a)	{x : x yu yrð¼kßÞ MktÏÞk Au yLku 6 Lkku yðÞð Au.}
(ii)	{2, 3}	(b)	{x : x yu 10 fhíkkt LkkLke yÞwø{ «kf]ríkf MktÏÞk Au.}
(iii)	{M, A, T, H, E, I, C, S}	(c)	{x : x yu «kf]ríkf MktÏÞk Au yLku 6Lkku yðÞð Au.}
(iv)	{1, 3, 5, 7, 9}	(d)	{x : x yu MATHEMATICS þçËLkku {q¤kûkh Au.}

Answer

sðkçkku : (i) → (c) (ii) → (a)

(iii) → (d) (iv) → (b)

su øký yuf Ãký ½xf Ähkðíkku Lk nkuÞ íku{Lku ¾k÷e øký yÚkðk rhõík øký fnu Au.

¾k÷e økýLku Mktfuík{kt φ yÚkðk {} ðzu ËþkoðkÞ Au.

WËknhý : øký A = Éý «kf]ríkf MktÏÞkykuLkku øký.

ynª, fkuE Ãký «kf]ríkf MktÏÞk nt{uþkt ÄLk s nkuÞ {kxu fkuE Éý «kf]ríkf MktÏÞkLkwt yÂMíkíð LkÚke. {kxu yk øký{kt fkuE MkÇÞ Lk nkuðkÚke íku ¾k÷e øký Au.

su øký{kt MkÇÞkuLke MktÏÞk rLkrùíkÃkýu økýe þfkÞ íkuðe nkuÞ yÚkðk su øký ¾k÷e Lk nkuÞ íkuLku yrhõík MkkLík øký fnu Au.

WËknhý : ¼khík{kt ykðu÷k ík{k{ IIT Lkku øký yu MkkLík øký Au.

MkkLík Lk nkuÞ íkuðk økýLku yLktík øký fnu Au. yLktík øký{kt MkÇÞ MktÏÞk Mker{ík LkÚke. íkuÚke yLktík økýLku ÞkËeLke heíku Ëþkoððk {kxu íku øký{kt ykðíkk y{wf MkÇÞku ÷¾eLku ºký xÃkfkt (...) {qfðk{kt ykðu Au.

WËknhý : øký : A = Ãkqýo MktÏÞkykuLkku øký

∴ A = {0, 1, 2, 3,...}

òu çku øký A yLku B çktLkuLkk ½xfku Mk{kLk nkuÞ
(¢{Lkwt {n¥ð LkÚke) íkku íkuðk økýLku Mk{kLk økýku
fnu Au.

íku{Lku Mktfuík{kt A = B ðzu ËþkoðkÞ Au.

WËknhý : A = {a, e, i, o, u},

B = {e, i, a, o, u} ynª, A = B Au.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

zkçke çkkswyu ÞkËeLke heíku Ëþkoðu÷k økýkuLku s{ýe çkkswyu íkuLkk s økwýÄ{oLke heíku Ëþkoðu÷k økýku MkkÚku Mkktf¤ku.

Answer

sðkçkku : (i) → (c) (ii) → (a)

(iii) → (d) (iv) → (b)

su øký yuf Ãký ½xf Ähkðíkku Lk nkuÞ íku{Lku ¾k÷e øký yÚkðk rhõík øký fnu Au.

¾k÷e økýLku Mktfuík{kt φ yÚkðk {} ðzu ËþkoðkÞ Au.

WËknhý : øký A = Éý «kf]ríkf MktÏÞkykuLkku øký.

ynª, fkuE Ãký «kf]ríkf MktÏÞk nt{uþkt ÄLk s nkuÞ {kxu fkuE Éý «kf]ríkf MktÏÞkLkwt yÂMíkíð LkÚke. {kxu yk øký{kt fkuE MkÇÞ Lk nkuðkÚke íku ¾k÷e øký Au.

su øký{kt MkÇÞkuLke MktÏÞk rLkrùíkÃkýu økýe þfkÞ íkuðe nkuÞ yÚkðk su øký ¾k÷e Lk nkuÞ íkuLku yrhõík MkkLík øký fnu Au.

WËknhý : ¼khík{kt ykðu÷k ík{k{ IIT Lkku øký yu MkkLík øký Au.

MkkLík Lk nkuÞ íkuðk økýLku yLktík øký fnu Au. yLktík øký{kt MkÇÞ MktÏÞk Mker{ík LkÚke. íkuÚke yLktík økýLku ÞkËeLke heíku Ëþkoððk {kxu íku øký{kt ykðíkk y{wf MkÇÞku ÷¾eLku ºký xÃkfkt (...) {qfðk{kt ykðu Au.

WËknhý : øký : A = Ãkqýo MktÏÞkykuLkku øký

∴ A = {0, 1, 2, 3,...}

òu çku øký A yLku B çktLkuLkk ½xfku Mk{kLk nkuÞ
(¢{Lkwt {n¥ð LkÚke) íkku íkuðk økýLku Mk{kLk økýku
fnu Au.

íku{Lku Mktfuík{kt A = B ðzu ËþkoðkÞ Au.

WËknhý : A = {a, e, i, o, u},

B = {e, i, a, o, u} ynª, A = B Au.

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#11 SUB 0M 🖼 1 ✎ Edit ⚠ Log Error

Question

Lke[uLkk økýku{ktÚke fÞk MkkLík yLku fÞk yLktík øký Au íku Lk¬e fhku.

(i) {x : x ∈ N yLku (x – 1) (x – 2) = 0}

Answer

ynª, (x – 1) (x – 2) = 0

∴ x – 1 = 0 yÚkðk x – 2 = 0

∴ x = 1 yÚkðk x = 2

∴ ykÃku÷ øký = {1, 2} su MkkLík øký Au.

(ii) {x : x ∈ N yLku x2 = 4}

ynª, x2 = 4

∴ x = ± 2 Ãkhtíkw x ∈ N nkuðkÚke x = 2 ÚkkÞ.

∴ ykÃku÷ øký = {2} su MkkLík øký Au.

(iii) {x : x ∈ N yLku 2x – 1 = 0}

ynª, 2x – 1 = 0 ∴ 2x = 1 ∴ x = ∉ N

Ãkhtíkw x ∈ N nkuðkÚke ykÃku÷ku øký ¾k÷e øký Au. su MkkLík øký Au.

(iv) {x : x ∈ N yLku x yrð¼kßÞ MktÏÞk Au.}

yk øký{kt Ëhuf yrð¼kßÞ MktÏÞkykuLkku Mk{kðuþ Úkíkku nkuðkÚke íku yLktík øký Au.

(v) {x : x ∈ N yLku x yÞwø{ ÃkqýkOf Au.}

yk øký{kt Ëhuf yÞwø{ ÃkqýkOf MktÏÞkykuLkku Mk{kðuþ Úkíkku nkuðkÚke íku yLktík øký Au.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Lke[uLkk økýku{ktÚke fÞk MkkLík yLku fÞk yLktík øký Au íku Lk¬e fhku.

(i) {x : x ∈ N yLku (x – 1) (x – 2) = 0}

Answer

ynª, (x – 1) (x – 2) = 0

∴ x – 1 = 0 yÚkðk x – 2 = 0

∴ x = 1 yÚkðk x = 2

∴ ykÃku÷ øký = {1, 2} su MkkLík øký Au.

(ii) {x : x ∈ N yLku x2 = 4}

ynª, x2 = 4

∴ x = ± 2 Ãkhtíkw x ∈ N nkuðkÚke x = 2 ÚkkÞ.

∴ ykÃku÷ øký = {2} su MkkLík øký Au.

(iii) {x : x ∈ N yLku 2x – 1 = 0}

ynª, 2x – 1 = 0 ∴ 2x = 1 ∴ x = ∉ N

Ãkhtíkw x ∈ N nkuðkÚke ykÃku÷ku øký ¾k÷e øký Au. su MkkLík øký Au.

(iv) {x : x ∈ N yLku x yrð¼kßÞ MktÏÞk Au.}

yk øký{kt Ëhuf yrð¼kßÞ MktÏÞkykuLkku Mk{kðuþ Úkíkku nkuðkÚke íku yLktík øký Au.

(v) {x : x ∈ N yLku x yÞwø{ ÃkqýkOf Au.}

yk øký{kt Ëhuf yÞwø{ ÃkqýkOf MktÏÞkykuLkku Mk{kðuþ Úkíkku nkuðkÚke íku yLktík øký Au.

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#12 SUB 0M ✎ Edit ⚠ Log Error

Question

Mk{kLk økýkuLke òuze þkuÄku (òu nkuÞ íkku). ík{khk W¥kh {kxu fkhý ykÃkku.

A = {0}, B = {x : x > 15 yLku x < 5},

C = {x : x – 5 = 0}, D = {x : x2 = 25},

E = {x : x yu Mk{efhý x2 – 2x – 15 = 0 Lkwt ÄLk ÃkqýkOf çkes Au.}

Answer

ynª, A = {0}, B = φ, C = {5}, D = {–5, 5}, E = {5}

ynª, Võík C = E Au.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Mk{kLk økýkuLke òuze þkuÄku (òu nkuÞ íkku). ík{khk W¥kh {kxu fkhý ykÃkku.

A = {0}, B = {x : x > 15 yLku x < 5},

C = {x : x – 5 = 0}, D = {x : x2 = 25},

E = {x : x yu Mk{efhý x2 – 2x – 15 = 0 Lkwt ÄLk ÃkqýkOf çkes Au.}

Answer

ynª, A = {0}, B = φ, C = {5}, D = {–5, 5}, E = {5}

ynª, Võík C = E Au.

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#13 SUB 0M 🖼 2 ✎ Edit ⚠ Log Error

Question

Lke[uLkk{ktÚke fE òuzeLkk øký Mk{kLk Au ? ík{khk sðkçkLke ÞÚkkÚkoíkk [fkMkku.

(i) “ALLOY” Lkk {q¤kûkhkuLkku øký X yLku “LOYAL” Lkk {q¤kûkhkuLkku øký B Au.

Answer

ynª, X = {A, L, O, Y} Úkþu íkÚkk B = {L, O, Y, A} su Mk{kLk Au. {kxu X = B Úkþu.

(ii) A = {n : ∈ Z yLku n2 < 4}, B = {x : x ∈ R yLku x2 – 3x + 2 = 0}

ynª, A = {–2, –1, 0, 1, 2} íkÚkk B = {2, 1} ynª, A ≠ B nkuðkÚke Mk{kLk øký LkÚke.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Lke[uLkk{ktÚke fE òuzeLkk øký Mk{kLk Au ? ík{khk sðkçkLke ÞÚkkÚkoíkk [fkMkku.

(i) “ALLOY” Lkk {q¤kûkhkuLkku øký X yLku “LOYAL” Lkk {q¤kûkhkuLkku øký B Au.

Answer

ynª, X = {A, L, O, Y} Úkþu íkÚkk B = {L, O, Y, A} su Mk{kLk Au. {kxu X = B Úkþu.

(ii) A = {n : ∈ Z yLku n2 < 4}, B = {x : x ∈ R yLku x2 – 3x + 2 = 0}

ynª, A = {–2, –1, 0, 1, 2} íkÚkk B = {2, 1} ynª, A ≠ B nkuðkÚke Mk{kLk øký LkÚke.

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#14 SUB 0M ✎ Edit ⚠ Log Error

Question

Lke[uLkk{ktÚke fÞk øký ¾k÷e økýLkkt WËknhý Au ?

(i) 2 ðzu rð¼kßÞ yÞwø{ «kf]ríkf MktÏÞkykuLkku øký.

Answer

2 ðzu rð¼kßÞ nkuÞ íkuðe Ëhuf «kf]ríkf MktÏÞkyku nt{uþkt Þwø{ s nkuÞ.

∴ ykÃku÷ku øký ¾k÷e øký Au.

(ii) Þwø{ yrð¼kßÞ «kf]ríkf MktÏÞkykuLkku øký.

2 yu Þwø{ yrð¼kßÞ «kf]ríkf MktÏÞk nkuðkÚke ykÃku÷ku øký ¾k÷e øký LkÚke.

(iii) {x : x yu «kf]ríkf MktÏÞk Au, x < 5 yLku x > 7}

fkuE «kf]ríkf MktÏÞk 5 fhíkkt LkkLke nkuÞ yLku 7 fhíkkt {kuxe nkuÞ íku yufMkkÚku þõÞ LkÚke. {kxu ykÃku÷ øký ¾k÷e øký Au.

(iv) {y : y yu çku r¼LLk Mk{ktíkh hu¾kykuLkwt Mkk{kLÞ ®çkËw Au.}

fkuE çku r¼LLk Mk{ktíkh hu¾kyku õÞkhuÞ yufçkeòLku AuËu Lknª. {kxu íku{Lkwt Mkk{kLÞ ®çkËw {¤u Lknª. {kxu ykÃku÷ øký ¾k÷e øký Au.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Lke[uLkk{ktÚke fÞk øký ¾k÷e økýLkkt WËknhý Au ?

(i) 2 ðzu rð¼kßÞ yÞwø{ «kf]ríkf MktÏÞkykuLkku øký.

Answer

2 ðzu rð¼kßÞ nkuÞ íkuðe Ëhuf «kf]ríkf MktÏÞkyku nt{uþkt Þwø{ s nkuÞ.

∴ ykÃku÷ku øký ¾k÷e øký Au.

(ii) Þwø{ yrð¼kßÞ «kf]ríkf MktÏÞkykuLkku øký.

2 yu Þwø{ yrð¼kßÞ «kf]ríkf MktÏÞk nkuðkÚke ykÃku÷ku øký ¾k÷e øký LkÚke.

(iii) {x : x yu «kf]ríkf MktÏÞk Au, x < 5 yLku x > 7}

fkuE «kf]ríkf MktÏÞk 5 fhíkkt LkkLke nkuÞ yLku 7 fhíkkt {kuxe nkuÞ íku yufMkkÚku þõÞ LkÚke. {kxu ykÃku÷ øký ¾k÷e øký Au.

(iv) {y : y yu çku r¼LLk Mk{ktíkh hu¾kykuLkwt Mkk{kLÞ ®çkËw Au.}

fkuE çku r¼LLk Mk{ktíkh hu¾kyku õÞkhuÞ yufçkeòLku AuËu Lknª. {kxu íku{Lkwt Mkk{kLÞ ®çkËw {¤u Lknª. {kxu ykÃku÷ øký ¾k÷e øký Au.

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#15 SUB 0M ✎ Edit ⚠ Log Error

Question

Lke[uLkk{ktÚke fÞk øký MkkLík øký yLku fÞk øký yLktík øký Au ?

(i) ð»koLkk {rnLkkykuLkku øký

Answer

ynª, ð»koLkk {rnLkkyku 12 rLkrùík nkuðkÚke íku MkkLík øký Au.

(ii) {1, 2, 3,.....}

ykÃku÷ku øký «kf]ríkf MktÏÞk øký nkuðkÚke íku yLktík øký Au.

(iii) {1, 2, 3,....., 99, 100}

ykÃku÷ku øký yu 1 Úke 100 MkwÄeLke «kf]ríkf MktÏÞkykuLkku Mk{kðuþ fhu Au su rLkrùík nkuðkÚke MkkLík øký Au.

(iv) 100 fhíkkt {kuxk ÄLk ÃkqýkOfkuLkku øký.

ykÃku÷k øký{kt 100 fhíkkt {kuxk nkuÞ íkuðk ík{k{ ÄLk ÃkqýkOfkuLkku Mk{kðuþ Úkíkku nkuðkÚke MkÇÞkuLke MktÏÞk yrLkrùík Au. {kxu ykÃku÷ku øký yLktík øký Au.

(v) 99 fhíkkt LkkLke yrð¼kßÞ MktÏÞkykuLkku øký.

ykÃku÷k øký{kt 99 fhíkkt LkkLke ík{k{ yrð¼kßÞ MktÏÞkykuLkku Mk{kðuþ Úkíkku nkuðkÚke íku{kt MkÇÞkuLke MktÏÞk rLkrùík Au. {kxu ykÃku÷ku øký MkkLík øký Au.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Lke[uLkk{ktÚke fÞk øký MkkLík øký yLku fÞk øký yLktík øký Au ?

(i) ð»koLkk {rnLkkykuLkku øký

Answer

ynª, ð»koLkk {rnLkkyku 12 rLkrùík nkuðkÚke íku MkkLík øký Au.

(ii) {1, 2, 3,.....}

ykÃku÷ku øký «kf]ríkf MktÏÞk øký nkuðkÚke íku yLktík øký Au.

(iii) {1, 2, 3,....., 99, 100}

ykÃku÷ku øký yu 1 Úke 100 MkwÄeLke «kf]ríkf MktÏÞkykuLkku Mk{kðuþ fhu Au su rLkrùík nkuðkÚke MkkLík øký Au.

(iv) 100 fhíkkt {kuxk ÄLk ÃkqýkOfkuLkku øký.

ykÃku÷k øký{kt 100 fhíkkt {kuxk nkuÞ íkuðk ík{k{ ÄLk ÃkqýkOfkuLkku Mk{kðuþ Úkíkku nkuðkÚke MkÇÞkuLke MktÏÞk yrLkrùík Au. {kxu ykÃku÷ku øký yLktík øký Au.

(v) 99 fhíkkt LkkLke yrð¼kßÞ MktÏÞkykuLkku øký.

ykÃku÷k øký{kt 99 fhíkkt LkkLke ík{k{ yrð¼kßÞ MktÏÞkykuLkku Mk{kðuþ Úkíkku nkuðkÚke íku{kt MkÇÞkuLke MktÏÞk rLkrùík Au. {kxu ykÃku÷ku øký MkkLík øký Au.

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#16 SUB 0M ✎ Edit ⚠ Log Error

Question

Lke[uLkk økýku{ktÚke fÞk øký MkkLík yLku fÞk øký yLktík Au íku þkuÄku.

(i) X - yûkLku Mk{ktíkh hu¾kykuLkku øký.

Answer

X - yûkLku Mk{ktíkh nkuÞ íkuðe yLktík hu¾kyku Ëkuhe þfkíke nkuðkÚke ykÃku÷ku øký yLktík øký Au.

(ii) ytøkúuS {q¤kûkhkuLkku øký.

ytøkúuSLkk fw÷ 26 {q¤kûkhku nkuðkÚke ykÃku÷ku øký MkkLík Au.

(iii) 5 Lke økwrýík MktÏÞkykuLkku øký.

ynª, {5, 10, 15, 20,.....} su yLktík øký Ëþkoðu Au.

(iv) Ãk]Úðe Ãkh ðMkíkk «kýeykuLkku øký.

Ãk]Úðe Ãkh økýe þfkÞ íkux÷e MktÏÞk{kt «kýeyku ðMku Au. {kxu ykÃku÷ku øký MkkLík øký Au.

(v) Wøk{®çkËw (0, 0) {ktÚke ÃkMkkh Úkíkkt ðíkwo¤kuLkku øký.

Wøk{®çkËw{ktÚke ÃkMkkh Úkíkk nkuÞ íkuðk yLktík ðíkwo¤ku Ëkuhe þfkÞ. {kxu ykÃku÷ku øký yLktík øký Au.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Lke[uLkk økýku{ktÚke fÞk øký MkkLík yLku fÞk øký yLktík Au íku þkuÄku.

(i) X - yûkLku Mk{ktíkh hu¾kykuLkku øký.

Answer

X - yûkLku Mk{ktíkh nkuÞ íkuðe yLktík hu¾kyku Ëkuhe þfkíke nkuðkÚke ykÃku÷ku øký yLktík øký Au.

(ii) ytøkúuS {q¤kûkhkuLkku øký.

ytøkúuSLkk fw÷ 26 {q¤kûkhku nkuðkÚke ykÃku÷ku øký MkkLík Au.

(iii) 5 Lke økwrýík MktÏÞkykuLkku øký.

ynª, {5, 10, 15, 20,.....} su yLktík øký Ëþkoðu Au.

(iv) Ãk]Úðe Ãkh ðMkíkk «kýeykuLkku øký.

Ãk]Úðe Ãkh økýe þfkÞ íkux÷e MktÏÞk{kt «kýeyku ðMku Au. {kxu ykÃku÷ku øký MkkLík øký Au.

(v) Wøk{®çkËw (0, 0) {ktÚke ÃkMkkh Úkíkkt ðíkwo¤kuLkku øký.

Wøk{®çkËw{ktÚke ÃkMkkh Úkíkk nkuÞ íkuðk yLktík ðíkwo¤ku Ëkuhe þfkÞ. {kxu ykÃku÷ku øký yLktík øký Au.

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#17 SUB 0M ✎ Edit ⚠ Log Error

Question

Lke[uLkk{ktÚke Lk¬e fhku fu A = B Au fu Lknª.

(i) A = {a, b, c, d}, B = {d, c, b, a}

Answer

ynª, çktLku øký{kt Mk{kLk MkÇÞku nkuðkÚke çktLku øký Mk{kLk Au. {kxu A = B ÚkkÞ.

(ii) A = {4, 8, 12, 16}, B = {8, 4, 16, 18}

ynª, çktLku øký{kt y÷øk MkÇÞku nkuðkÚke A ≠ B.

(iii) A = {2, 4, 6, 8, 10}, B = {x : x yu Þwø{ ÄLk ÃkqýkOf Au yLku x < 10}

ynª, øký B = {2, 4, 6, 8, 10} su øký A Lku Mk{kLk Au. {kxu A = B Au.

(iv) A = {x : x yu 10 Lkku økwrýík Au.}

B = {10, 15, 20, 25, 30,.....}

A = {10, 20, 30, 40,.....} ynª A yLku B çktLku økýLkk MkÇÞku y÷øk nkuðkÚke A ≠ B.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Lke[uLkk{ktÚke Lk¬e fhku fu A = B Au fu Lknª.

(i) A = {a, b, c, d}, B = {d, c, b, a}

Answer

ynª, çktLku øký{kt Mk{kLk MkÇÞku nkuðkÚke çktLku øký Mk{kLk Au. {kxu A = B ÚkkÞ.

(ii) A = {4, 8, 12, 16}, B = {8, 4, 16, 18}

ynª, çktLku øký{kt y÷øk MkÇÞku nkuðkÚke A ≠ B.

(iii) A = {2, 4, 6, 8, 10}, B = {x : x yu Þwø{ ÄLk ÃkqýkOf Au yLku x < 10}

ynª, øký B = {2, 4, 6, 8, 10} su øký A Lku Mk{kLk Au. {kxu A = B Au.

(iv) A = {x : x yu 10 Lkku økwrýík Au.}

B = {10, 15, 20, 25, 30,.....}

A = {10, 20, 30, 40,.....} ynª A yLku B çktLku økýLkk MkÇÞku y÷øk nkuðkÚke A ≠ B.

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#18 SUB 0M ✎ Edit ⚠ Log Error

Question

Lke[u ykÃku÷e òuzeykuLkk øký Mk{kLk Au ? fkhý ykÃkku.

(i) A = {2, 3}, B = {x : x yu x2 + 5x + 6 = 0 Lkku Wfu÷ Au.}

Answer

ynª, Mk{efhý x2 + 5x + 6 = 0

∴ x2 + 3x + 2x + 6 = 0

∴ x (x + 3) + 2 (x + 3) = 0

∴ (x + 3) (x + 2) = 0

∴ x + 3 = 0 yÚkðk x + 2 = 0

∴ x = –3 yÚkðk x = –2

{kxu, B = {–3, –2} íkÚkk A = {2, 3} ykÃku÷ Au.

∴ A ≠ B.

(ii) A = {x : x yu FOLLOW þçËLkku {q¤kûkh Au.}

B = {y : y yu WOLF þçËLkku {q¤kûkh Au.}

A = {F, O, L, W} íkÚkk

B = {W, O, L, F}.

ynª, çktLku øký{kt Mk{kLk MkÇÞku nkuðkÚke A = B Úkþu.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Lke[u ykÃku÷e òuzeykuLkk øký Mk{kLk Au ? fkhý ykÃkku.

(i) A = {2, 3}, B = {x : x yu x2 + 5x + 6 = 0 Lkku Wfu÷ Au.}

Answer

ynª, Mk{efhý x2 + 5x + 6 = 0

∴ x2 + 3x + 2x + 6 = 0

∴ x (x + 3) + 2 (x + 3) = 0

∴ (x + 3) (x + 2) = 0

∴ x + 3 = 0 yÚkðk x + 2 = 0

∴ x = –3 yÚkðk x = –2

{kxu, B = {–3, –2} íkÚkk A = {2, 3} ykÃku÷ Au.

∴ A ≠ B.

(ii) A = {x : x yu FOLLOW þçËLkku {q¤kûkh Au.}

B = {y : y yu WOLF þçËLkku {q¤kûkh Au.}

A = {F, O, L, W} íkÚkk

B = {W, O, L, F}.

ynª, çktLku øký{kt Mk{kLk MkÇÞku nkuðkÚke A = B Úkþu.

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#19 SUB 0M ✎ Edit ⚠ Log Error

Question

Lke[u ykÃku÷k øký{ktÚke Mk{kLk øký ÃkMktË fhku.

A = {2, 4, 8, 12}, B = {1, 2, 3, 4}, C = {4, 8, 12, 14},

D = {3, 1, 4, 2}, E = {–1, 1}, F = {0, a},

G = {1, –1}, H = {0, 1}

Answer

ynª, B = {1, 2, 3, 4} yLku D = {3, 1, 4, 2} yu Mk{kLk økýLke òuz Au.

ynª, E = {–1, 1} yLku G = {1, –1} yu Mk{kLk økýLke òuz Au.

òu øký A Lkku «íÞuf ½xf yu øký B Lkku Ãký ½xf nkuÞ íkku øký A Lku øký B Lkku WÃkøký fnuðkÞ Au.

WÃkøkýLku Mktfuík{kt ‘⊂’ ðzu ËþkoðkÞ Au.

ßÞkhu a ∈ A nkuÞ íÞkhu a ∈ B nkuÞ íkku A ⊂ B ÚkkÞ.

òu A yu B Lkku WÃkøký Lk nkuÞ íkku íkuLku A ⊄ B ðzu ËþkoðkÞ Au.

WÃkøkýLke ÔÞkÏÞk ÃkhÚke fne þfkÞ fu, “Ëhuf øký yu ÃkkuíkkLkku WÃkøký Au.”

¾k÷e øký (φ) yu Ëhuf økýLkku WÃkøký Au.

yk{ fne þfkÞ fu, ¾k÷e øký rMkðkÞLkk Ëhuf økýLku ykuAk{kt ykuAk çku WÃkøký íkku nkuÞ s. (a) ¾k÷e øký yLku (b) íku øký Ãkkuíku s.

ynª, MÃkü heíku fne þfkÞ fu,

N ⊂ Z ⊂ Q ⊂ R.

ynª, yMkt{uÞ MktÏÞkøkýLku T ðzu ËþkoðkÞ Au.

T = {x : x ∈ R, x ∉ Q}

∴ T ⊂ R Ãký N ⊄ T.

çku øký A yLku B {kxu òu A ⊂ B yLku A ≠ B íkku A Lku B Lkku Wr[ík WÃkøký fnu Au yLku B Lku A Lkku yrÄøký fnu Au.

òu øký A {kt yuf s MkÇÞ nkuÞ íkku A Lku yufkfe øký (Singleton) fnu Au.

òu øký A {kt MkÇÞkuLke MktÏÞk m nkuÞ íkku íkuLkk fw÷ WÃkøkýkuLke MktÏÞk 2m ÚkkÞ, m > 1, m ∈ N.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Lke[u ykÃku÷k øký{ktÚke Mk{kLk øký ÃkMktË fhku.

A = {2, 4, 8, 12}, B = {1, 2, 3, 4}, C = {4, 8, 12, 14},

D = {3, 1, 4, 2}, E = {–1, 1}, F = {0, a},

G = {1, –1}, H = {0, 1}

Answer

ynª, B = {1, 2, 3, 4} yLku D = {3, 1, 4, 2} yu Mk{kLk økýLke òuz Au.

ynª, E = {–1, 1} yLku G = {1, –1} yu Mk{kLk økýLke òuz Au.

òu øký A Lkku «íÞuf ½xf yu øký B Lkku Ãký ½xf nkuÞ íkku øký A Lku øký B Lkku WÃkøký fnuðkÞ Au.

WÃkøkýLku Mktfuík{kt ‘⊂’ ðzu ËþkoðkÞ Au.

ßÞkhu a ∈ A nkuÞ íÞkhu a ∈ B nkuÞ íkku A ⊂ B ÚkkÞ.

òu A yu B Lkku WÃkøký Lk nkuÞ íkku íkuLku A ⊄ B ðzu ËþkoðkÞ Au.

WÃkøkýLke ÔÞkÏÞk ÃkhÚke fne þfkÞ fu, “Ëhuf øký yu ÃkkuíkkLkku WÃkøký Au.”

¾k÷e øký (φ) yu Ëhuf økýLkku WÃkøký Au.

yk{ fne þfkÞ fu, ¾k÷e øký rMkðkÞLkk Ëhuf økýLku ykuAk{kt ykuAk çku WÃkøký íkku nkuÞ s. (a) ¾k÷e øký yLku (b) íku øký Ãkkuíku s.

ynª, MÃkü heíku fne þfkÞ fu,

N ⊂ Z ⊂ Q ⊂ R.

ynª, yMkt{uÞ MktÏÞkøkýLku T ðzu ËþkoðkÞ Au.

T = {x : x ∈ R, x ∉ Q}

∴ T ⊂ R Ãký N ⊄ T.

çku øký A yLku B {kxu òu A ⊂ B yLku A ≠ B íkku A Lku B Lkku Wr[ík WÃkøký fnu Au yLku B Lku A Lkku yrÄøký fnu Au.

òu øký A {kt yuf s MkÇÞ nkuÞ íkku A Lku yufkfe øký (Singleton) fnu Au.

òu øký A {kt MkÇÞkuLke MktÏÞk m nkuÞ íkku íkuLkk fw÷ WÃkøkýkuLke MktÏÞk 2m ÚkkÞ, m > 1, m ∈ N.

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#20 FB 1M ✎ Edit ⚠ Log Error

Question

øký φ, A = {1, 3}, B = {1, 5, 9}, C = {1, 3, 5, 7, 9} ykÃku÷kt Au. Lke[u Ëþkoðu÷e Ëhuf økýLke òuzeyku ðå[u Mkt¿kk ⊂ yÚkðk ⊄ Mk{krðü fhku.

(i) φ.....B (ii) A.....B (iii) A.....C (iv) B.....C

Answer

sðkçk : (i) φ yu Ëhuf økýLkku WÃkøký nkuðkÚke,

φ ⊂ B Úkþu.

(ii) A Lkku ½xf 3 yu B {kt Lk nkuðkÚke,

A ⊄ B Úkþu.

(iii) A Lkk çktLku ½xfku C {kt nkuðkÚke,

A ⊂ C Úkþu.

(iv) B Lkk Ëhuf ½xf C {kt nkuðkÚke,

B ⊂ C Úkþu.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

øký φ, A = {1, 3}, B = {1, 5, 9}, C = {1, 3, 5, 7, 9} ykÃku÷kt Au. Lke[u Ëþkoðu÷e Ëhuf økýLke òuzeyku ðå[u Mkt¿kk ⊂ yÚkðk ⊄ Mk{krðü fhku.

(i) φ.....B (ii) A.....B (iii) A.....C (iv) B.....C

Answer

sðkçk : (i) φ yu Ëhuf økýLkku WÃkøký nkuðkÚke,

φ ⊂ B Úkþu.

(ii) A Lkku ½xf 3 yu B {kt Lk nkuðkÚke,

A ⊄ B Úkþu.

(iii) A Lkk çktLku ½xfku C {kt nkuðkÚke,

A ⊂ C Úkþu.

(iv) B Lkk Ëhuf ½xf C {kt nkuðkÚke,

B ⊂ C Úkþu.

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#21 SUB 0M ✎ Edit ⚠ Log Error

Question

A = {a, e, i, o, u}, B = {a, b, c, d} ÷ku. A yu B Lkku WÃkøký Au ? Lkk. (þk {kxu ?) B yu A Lkku WÃkøký Au ? Lkk. (þk {kxu ?)

Answer

ynª, A Lkku ½xf e yu B {kt LkÚke {kxu A yu B Lkku WÃkøký LkÚke. íkuðe s heíku øký B Lkku ½xf b yu A {kt LkÚke {kxu B yu A Lkku WÃkøký LkÚke.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

A = {a, e, i, o, u}, B = {a, b, c, d} ÷ku. A yu B Lkku WÃkøký Au ? Lkk. (þk {kxu ?) B yu A Lkku WÃkøký Au ? Lkk. (þk {kxu ?)

Answer

ynª, A Lkku ½xf e yu B {kt LkÚke {kxu A yu B Lkku WÃkøký LkÚke. íkuðe s heíku øký B Lkku ½xf b yu A {kt LkÚke {kxu B yu A Lkku WÃkøký LkÚke.

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#22 SUB 0M 🖼 1 ✎ Edit ⚠ Log Error

Question

A, B yLku C ºký øký Au. òu A ∈ B yLku B ⊂ C íkku A ⊂ C Mkk[wt Au ? òu ík{khku W¥kh Lkk nkuÞ íkku WËknhý ykÃkku.

Answer

‘Lkk.’

Äkhku fu, A = {a},

B = {{a}, b},

C = {{a}, b, c} {kxu

ynª, A Lkku ½xf ‘a’ yu øký C Lkku ½xf LkÚke.

{kxu A ⊄ C ÚkkÞ.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

A, B yLku C ºký øký Au. òu A ∈ B yLku B ⊂ C íkku A ⊂ C Mkk[wt Au ? òu ík{khku W¥kh Lkk nkuÞ íkku WËknhý ykÃkku.

Answer

‘Lkk.’

Äkhku fu, A = {a},

B = {{a}, b},

C = {{a}, b, c} {kxu

ynª, A Lkku ½xf ‘a’ yu øký C Lkku ½xf LkÚke.

{kxu A ⊄ C ÚkkÞ.

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#23 FB 1M ✎ Edit ⚠ Log Error

Question

Lke[uLkkt rðÄkLkku MkíÞ çkLku íku heíku ¾k÷e søÞk{kt Mkt¿kk ⊂ yÚkðk ⊄ Ãkqhku :

(i) {2, 3, 4}.....{1, 2, 3, 4, 5}

Answer

⊂

(ii) {a, b, c}.....{b, c, d}

⊄

(iii) {x : x yu ík{khe þk¤kLkku Äkuhý XI Lkku rðãkÚkeo Au.} ..... {x : x yu ík{khe þk¤kLkku rðãkÚkeo Au.}

⊂

(iv) {x : x yu Mk{ík÷{kt ðíkwo¤ Au.} ..... {x : x yu yk s Mk{ík÷Lkwt 1 yuf{ rºkßÞkðk¤wt ðíkwo¤ Au.}

⊄

(v) {x : x yu Mk{ík÷{kt rºkfkuý Au} ..... {x : x yu yk Mk{ík÷{kt ÷tçk[kuhMk Au.}

⊄

(vi) {x : x yu Mk{ík÷{kt Mk{çkksw rºkfkuý Au.} ..... {x : x yu yk s Mk{ík÷Lkku rºkfkuý Au.}

⊂

(vii) {x : x yu Þwø{ «kf]ríkf MktÏÞk Au.} ..... {x : x yu ÃkqýkOf MktÏÞk Au.}

⊂

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Lke[uLkkt rðÄkLkku MkíÞ çkLku íku heíku ¾k÷e søÞk{kt Mkt¿kk ⊂ yÚkðk ⊄ Ãkqhku :

(i) {2, 3, 4}.....{1, 2, 3, 4, 5}

Answer

⊂

(ii) {a, b, c}.....{b, c, d}

⊄

(iii) {x : x yu ík{khe þk¤kLkku Äkuhý XI Lkku rðãkÚkeo Au.} ..... {x : x yu ík{khe þk¤kLkku rðãkÚkeo Au.}

⊂

(iv) {x : x yu Mk{ík÷{kt ðíkwo¤ Au.} ..... {x : x yu yk s Mk{ík÷Lkwt 1 yuf{ rºkßÞkðk¤wt ðíkwo¤ Au.}

⊄

(v) {x : x yu Mk{ík÷{kt rºkfkuý Au} ..... {x : x yu yk Mk{ík÷{kt ÷tçk[kuhMk Au.}

⊄

(vi) {x : x yu Mk{ík÷{kt Mk{çkksw rºkfkuý Au.} ..... {x : x yu yk s Mk{ík÷Lkku rºkfkuý Au.}

⊂

(vii) {x : x yu Þwø{ «kf]ríkf MktÏÞk Au.} ..... {x : x yu ÃkqýkOf MktÏÞk Au.}

⊂

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#24 SUB 0M ✎ Edit ⚠ Log Error

Question

Lke[uLkkt rðÄkLkku MkíÞ Au fu yMkíÞ íkuLke [fkMkýe fhku.

(i) {a, b} ⊄ {b, c, a}

Answer

{a, b} ⊂ {b, c, a} nkuðkÚke yMkíÞ Au.

(ii) {a, e} ⊂ {x : x yu ytøkúuS {q¤kûkh ÃkifeLkku yuf Mðh Au.}

MkíÞ Au.

(iii) {1, 2, 3} ⊂ {1, 3, 5}

ynª, 2 ∉ {1, 3, 5} {kxu yMkíÞ Au.

(iv) {a} ⊂ {a, b, c}

MkíÞ Au.

(v) {a} ∈ {a, b, c}

yMkíÞ Au.

(vi) {x : x yu 6 fhíkkt LkkLke Þwø{ «kf]ríkf MktÏÞk Au.} ⊂ {x : x yu 36 Lkku yðÞð nkuÞ íkuðe «kf]ríkf MktÏÞk Au.}

ynª, «Úk{ øký {2, 4} íkÚkk rîíkeÞ øký {1, 2, 3, 4, 6, 9, 12, 18, 36} Au. {2, 4} ⊂ {1, 2, 3, 4, 6, 9, 12, 18, 36} nkuðkÚke ykÃku÷wt rðÄkLk MkíÞ Au.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Lke[uLkkt rðÄkLkku MkíÞ Au fu yMkíÞ íkuLke [fkMkýe fhku.

(i) {a, b} ⊄ {b, c, a}

Answer

{a, b} ⊂ {b, c, a} nkuðkÚke yMkíÞ Au.

(ii) {a, e} ⊂ {x : x yu ytøkúuS {q¤kûkh ÃkifeLkku yuf Mðh Au.}

MkíÞ Au.

(iii) {1, 2, 3} ⊂ {1, 3, 5}

ynª, 2 ∉ {1, 3, 5} {kxu yMkíÞ Au.

(iv) {a} ⊂ {a, b, c}

MkíÞ Au.

(v) {a} ∈ {a, b, c}

yMkíÞ Au.

(vi) {x : x yu 6 fhíkkt LkkLke Þwø{ «kf]ríkf MktÏÞk Au.} ⊂ {x : x yu 36 Lkku yðÞð nkuÞ íkuðe «kf]ríkf MktÏÞk Au.}

ynª, «Úk{ øký {2, 4} íkÚkk rîíkeÞ øký {1, 2, 3, 4, 6, 9, 12, 18, 36} Au. {2, 4} ⊂ {1, 2, 3, 4, 6, 9, 12, 18, 36} nkuðkÚke ykÃku÷wt rðÄkLk MkíÞ Au.

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#25 SUB 0M ✎ Edit ⚠ Log Error

Question

A = {1, 2, {3, 4}, 5} íkku Lke[uLkkt rðÄkLkku Ãkife fÞkt rðÄkLkku yMkíÞ Au yLku þk {kxu ?

(i) {3, 4} ⊂ A

Answer

ynª {3, 4} yu øký A Lkku MkÇÞ Au. ykÚke {3, 4} ∈ A ÚkkÞ {kxu ykÃku÷wt rðÄkLk yMkíÞ Au.

(ii) {3, 4} ∈ A

{3, 4} yu øký A Lkku ½xf nkuðkÚke ykÃku÷wt rðÄkLk MkíÞ Au.

(iii) {{3, 4}} ⊂ A

ynª, {3, 4} yu øký A Lkku ½xf nkuðkÚke øký {{3, 4}} yu øký A Lkku WÃkøký fnuðkÞ. {kxu rðÄkLk MkíÞ Au.

(iv) 1 ∈ A

1 yu øký A Lkku MkÇÞ nkuðkÚke ykÃku÷wt rðÄkLk MkíÞ Au.

(v) 1 ⊂ A

1 yu øký A Lkku MkÇÞ nkuðkÚke {1} ⊂ A ÚkkÞ {kxu ykÃku÷wt rðÄkLk yMkíÞ Au.

(vi) {1, 2, 5} ⊂ A

ynª, 1, 2, 5 yu øký A Lkk ½xfku nkuðkÚke ykÃku÷wt rðÄkLk MkíÞ Au.

(vii) {1, 2, 5} ∈ A

ykÃku÷wt rðÄkLk yMkíÞ Au fkhý fu {1, 2, 5} ⊂ A Au.

(viii) {1, 2, 3} ⊂ A

ynª, 3 yu øký A Lkku ½xf Lk nkuðkÚke ykÃku÷wt rðÄkLk yMkíÞ Au.

(ix) φ ∈ A

ynª, φ yu øký A Lkku MkÇÞ Lk nkuðkÚke ykÃku÷wt rðÄkLk yMkíÞ Au.

(x) φ ⊂ A

¾k÷e øký yu Ëhuf økýLkku WÃkøký nkuðkÚke ykÃku÷wt rðÄkLk MkíÞ Au.

(xi) {φ} ⊂ A

ykÃku÷wt rðÄkLk yMkíÞ Au fkhý fu φ ⊂ A Au.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

A = {1, 2, {3, 4}, 5} íkku Lke[uLkkt rðÄkLkku Ãkife fÞkt rðÄkLkku yMkíÞ Au yLku þk {kxu ?

(i) {3, 4} ⊂ A

Answer

ynª {3, 4} yu øký A Lkku MkÇÞ Au. ykÚke {3, 4} ∈ A ÚkkÞ {kxu ykÃku÷wt rðÄkLk yMkíÞ Au.

(ii) {3, 4} ∈ A

{3, 4} yu øký A Lkku ½xf nkuðkÚke ykÃku÷wt rðÄkLk MkíÞ Au.

(iii) {{3, 4}} ⊂ A

ynª, {3, 4} yu øký A Lkku ½xf nkuðkÚke øký {{3, 4}} yu øký A Lkku WÃkøký fnuðkÞ. {kxu rðÄkLk MkíÞ Au.

(iv) 1 ∈ A

1 yu øký A Lkku MkÇÞ nkuðkÚke ykÃku÷wt rðÄkLk MkíÞ Au.

(v) 1 ⊂ A

1 yu øký A Lkku MkÇÞ nkuðkÚke {1} ⊂ A ÚkkÞ {kxu ykÃku÷wt rðÄkLk yMkíÞ Au.

(vi) {1, 2, 5} ⊂ A

ynª, 1, 2, 5 yu øký A Lkk ½xfku nkuðkÚke ykÃku÷wt rðÄkLk MkíÞ Au.

(vii) {1, 2, 5} ∈ A

ykÃku÷wt rðÄkLk yMkíÞ Au fkhý fu {1, 2, 5} ⊂ A Au.

(viii) {1, 2, 3} ⊂ A

ynª, 3 yu øký A Lkku ½xf Lk nkuðkÚke ykÃku÷wt rðÄkLk yMkíÞ Au.

(ix) φ ∈ A

ynª, φ yu øký A Lkku MkÇÞ Lk nkuðkÚke ykÃku÷wt rðÄkLk yMkíÞ Au.

(x) φ ⊂ A

¾k÷e øký yu Ëhuf økýLkku WÃkøký nkuðkÚke ykÃku÷wt rðÄkLk MkíÞ Au.

(xi) {φ} ⊂ A

ykÃku÷wt rðÄkLk yMkíÞ Au fkhý fu φ ⊂ A Au.

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#26 SUB 0M ✎ Edit ⚠ Log Error

Question

Lke[u ykÃku÷k økýkuLkk ík{k{ WÃkøkýku ÷¾ku.

(i) {a}

Answer

φ, {a}

(ii) {a, b}

φ, {a, b}, {a}, {b}

(iii) {1, 2, 3}

φ, {1, 2, 3}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}

(iv) φ

φ

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Lke[u ykÃku÷k økýkuLkk ík{k{ WÃkøkýku ÷¾ku.

(i) {a}

Answer

φ, {a}

(ii) {a, b}

φ, {a, b}, {a}, {b}

(iii) {1, 2, 3}

φ, {1, 2, 3}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}

(iv) φ

φ

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#27 SUB 0M ✎ Edit ⚠ Log Error

Question

Lke[uLkkLku ytíkhk÷ MðYÃku Ëþkoðku :

(i) {x : x ∈ R, –4 < x < 6}

Answer

(–4, 6]

(ii) {x : x ∈ R, –12 < x < –10}

(–12, –10)

(iii) {x : x ∈ R, 0 < x < 7}

[0, 7)

(iv) {x : x ∈ R, 3 < x < 4}

[3, 4]

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Lke[uLkkLku ytíkhk÷ MðYÃku Ëþkoðku :

(i) {x : x ∈ R, –4 < x < 6}

Answer

(–4, 6]

(ii) {x : x ∈ R, –12 < x < –10}

(–12, –10)

(iii) {x : x ∈ R, 0 < x < 7}

[0, 7)

(iv) {x : x ∈ R, 3 < x < 4}

[3, 4]

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#28 SUB 0M ✎ Edit ⚠ Log Error

Question

Lke[u ykÃku÷k ytíkhk÷kuLku økwýÄ{oLke heíku ÷¾ku :

(i) (–3, 0)

Answer

{x : x ∈ R, –3 < x < 0}

(ii) [6, 12]

{x : x ∈ R, 6 < x < 12}

(iii) (6, 12]

{x : x ∈ R, 6 < x < 12}

(iv) [–23, 5)

{x : x ∈ R, –23 < x < 5}

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Lke[u ykÃku÷k ytíkhk÷kuLku økwýÄ{oLke heíku ÷¾ku :

(i) (–3, 0)

Answer

{x : x ∈ R, –3 < x < 0}

(ii) [6, 12]

{x : x ∈ R, 6 < x < 12}

(iii) (6, 12]

{x : x ∈ R, 6 < x < 12}

(iv) [–23, 5)

{x : x ∈ R, –23 < x < 5}

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#29 SUB 0M ✎ Edit ⚠ Log Error

Question

Lke[uLkkt rðÄkLkku {kxu ík{u fÞk økýLku Mkkðorºkf øký íkhefu ÃkMktË fhþku ?

(i) fkxfkuý rºkfkuýkuLkku øký

Answer

ynª, ‘Mk{ík÷{kt ykðu÷k ík{k{ rºkfkuýkuLkk Mk{qn’Lku Mkkðorºkf øký íkhefu ÃkMktË fhe þfkÞ.

(ii) Mk{rî¼ws rºkfkuýkuLkku øký

ynª, ‘Mk{ík÷{kt ykðu÷k ík{k{ rºkfkuýkuLkk Mk{qn’Lku Mkkðorºkf øký íkhefu ÃkMktË fhe þfkÞ.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

Lke[uLkkt rðÄkLkku {kxu ík{u fÞk økýLku Mkkðorºkf øký íkhefu ÃkMktË fhþku ?

(i) fkxfkuý rºkfkuýkuLkku øký

Answer

ynª, ‘Mk{ík÷{kt ykðu÷k ík{k{ rºkfkuýkuLkk Mk{qn’Lku Mkkðorºkf øký íkhefu ÃkMktË fhe þfkÞ.

(ii) Mk{rî¼ws rºkfkuýkuLkku øký

ynª, ‘Mk{ík÷{kt ykðu÷k ík{k{ rºkfkuýkuLkk Mk{qn’Lku Mkkðorºkf øký íkhefu ÃkMktË fhe þfkÞ.

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#30 SUB 0M 🖼 1 ✎ Edit ⚠ Log Error

Question

A = {1, 3, 5}, B = {2, 4, 6}, C = {0, 2, 4, 6, 8} ykÃku÷ku øký Au. yk ºký øký A, B yLku C {kxu Lke[uLkk{ktÚke fÞk økýLku Mkkðorºkf øký íkhefu ÷E þfkÞ ?

(i) {0, 1, 2, 3, 4, 5, 6}

(ii) φ

(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(iv) {1, 2, 3, 4, 5, 6, 7, 8}

Answer

ynª, ykÃku÷k ºkýuÞ øký A, B, C Lkku Mk{kðuþ (iii) {kt ÚkkÞ Au. {kxu (iii) Lku Mkkðorºkf øký íkhefu ÷E þfkÞ Au.

økýku ðå[uLkk ½ýk¾hk MktçktÄkuLku ykf]ríkyku îkhk hsq fhðk{kt ykðu Au. íku{Lku ðuLk ykf]rík fnuðkÞ Au.

ytøkúuS íkfoþkMºke John Venn Lkk Lkk{ ÃkhÚke ðuLk ykf]rík Lkk{ ykÃkðk{kt ykÔÞwt.

Mkk{kLÞ heíku ynª, Mkkðorºkf økýLku (U) ÷tçk[kuhMk ðzu yLku íku{ktÚke çkLkíkk çkeò økýLku ÷tçk[kuhMkLke ytËh ðíkwo¤ku îkhk Ëþkoððk{kt ykðu Au.

(A) Þkuøkøký : fkuE çku øký A yLku B {kxu, A yLku B Lkku Þkuøkøký (Union Set) yux÷u A Lkk ík{k{ ½xfku yLku B Lkk ík{k{ ½xfku y™u íku{Lkk Mkk{kLÞ ½xfkuLku Võík yuf ð¾ík ÷uðkÚke çkLkíkku øký. ÞkuøkøkýLku Mktfuík{kt ‘∪’ ðzu ËþkoðkÞ Au.

∴ A ∪ B = {x : x ∈ A yÚkðk x ∈ B}

Þkuøkøký (∪) {kxu ‘yÚkðk’Lkku Ëk¾÷k{kt WÃkÞkuøk fhðku.

Type SUB — Subjective MCQ — Multiple Choice TF — True / False YN — Yes / No IA — Interactive Activity FB — Fill in the Blanks OW — One Word MT — Match the Following GLO — Glossary RCEMT — Reading Comp. – Extracts – MT SN — Short Notes CBTFQ — Content-Based T/F RCMTP — Reading Comp. – MT – Poem RCSR — Reading Comp. – Supp. Reader RCNV — Reading Comp. – Nonverbal RCUDI — Reading Comp. – Unseen D/I IFMC — Identify Function – Match Cols CTD — Complete the Dialogue CTS — Complete the Sentences VCPB — Vocab: Complete Para – Blanks VFNM — Vocab: Nearest Meaning – SR INDS — Indirect Speech CONJ — Conjunction EDTNG — Editing DASD — Do as Directed STCQ — Select the Correct PARAW — Paragraph Writing EFRW — Email / Report Writing PICD — Picture Description PARA — Paragraph CS — Case Study Marks

Question

A = {1, 3, 5}, B = {2, 4, 6}, C = {0, 2, 4, 6, 8} ykÃku÷ku øký Au. yk ºký øký A, B yLku C {kxu Lke[uLkk{ktÚke fÞk økýLku Mkkðorºkf øký íkhefu ÷E þfkÞ ?

(i) {0, 1, 2, 3, 4, 5, 6}

(ii) φ

(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(iv) {1, 2, 3, 4, 5, 6, 7, 8}

Answer

ynª, ykÃku÷k ºkýuÞ øký A, B, C Lkku Mk{kðuþ (iii) {kt ÚkkÞ Au. {kxu (iii) Lku Mkkðorºkf øký íkhefu ÷E þfkÞ Au.

økýku ðå[uLkk ½ýk¾hk MktçktÄkuLku ykf]ríkyku îkhk hsq fhðk{kt ykðu Au. íku{Lku ðuLk ykf]rík fnuðkÞ Au.

ytøkúuS íkfoþkMºke John Venn Lkk Lkk{ ÃkhÚke ðuLk ykf]rík Lkk{ ykÃkðk{kt ykÔÞwt.

Mkk{kLÞ heíku ynª, Mkkðorºkf økýLku (U) ÷tçk[kuhMk ðzu yLku íku{ktÚke çkLkíkk çkeò økýLku ÷tçk[kuhMkLke ytËh ðíkwo¤ku îkhk Ëþkoððk{kt ykðu Au.

(A) Þkuøkøký : fkuE çku øký A yLku B {kxu, A yLku B Lkku Þkuøkøký (Union Set) yux÷u A Lkk ík{k{ ½xfku yLku B Lkk ík{k{ ½xfku y™u íku{Lkk Mkk{kLÞ ½xfkuLku Võík yuf ð¾ík ÷uðkÚke çkLkíkku øký. ÞkuøkøkýLku Mktfuík{kt ‘∪’ ðzu ËþkoðkÞ Au.

∴ A ∪ B = {x : x ∈ A yÚkðk x ∈ B}

Þkuøkøký (∪) {kxu ‘yÚkðk’Lkku Ëk¾÷k{kt WÃkÞkuøk fhðku.

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