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Unit Test

F.M.- 10

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314|Mathematics–10

Model Questions Set-A

Group A [3 × (1 + 1) = 6]
ͳǤ ƒǤ ”‹–‡ †‘™ –Š‡ ˆ‘”—Žƒ –‘ ϐ‹† ’‡”…‡–ƒ‰‡ ™Š‡ α ƒ ƒ† ™‹–Š α „ ƒ”‡ ‰‹˜‡Ǥ
„Ǥ ”‹–‡ †‘™ –Š‡ ˆ‘”—Žƒ –‘ ϐ‹† ƒ”‡ƒ ‘ˆ •…ƒŽ‡‡ –”‹ƒ‰Ž‡ having side x cm, y cm and z cm.

ʹǤ ƒǤ ‘” ™Šƒ– ˜ƒŽ—‡ ‘ˆ šǡ ™‹ŽŽ –Š‡”‡ „‡ x + 5 = 9 .
„Ǥ ”‹–‡ †‘™ –Š‡ ˆ‘”—Žƒ –‘ ϐ‹† –Š‡ ƒ…–—ƒŽ ‡†‹ƒ ‘ˆ ‘„•‡”˜ƒ–‹‘• Šƒ˜‹‰ …Žƒ••
‹–‡”˜ƒŽǤ

3. a. If area of ' α Ͷš …2 ƒ† –Š‡ ƒ”‡ƒ ‘ˆ –Š‡ ’ƒ”ƒŽŽ‡Ž‘‰”ƒ α ͶͲ …2 ™Š‹…Š
ƒ”‡ ‹ „‡–™‡‡ –Š‡ •ƒ‡ ’ƒ”ƒŽŽ‡Ž• ƒ† ‘ –Š‡ •ƒ‡ „ƒ•‡ ϐ‹† –Š‡ ˜ƒŽ—‡ ‘ˆ šǤ
„Ǥ ƒŽ…—Žƒ–‡ –Š‡ ˜ƒŽ—‡ ‘ˆ ‘ ™Š‡”‡ –Š‡ ˜ƒŽ—‡ ‘ˆ ‘ α ͻ͸ιǤ


Group – B [17 × 2 = 34]
ͶǤ ƒǤ  ƒ”–‹…Ž‡ ‹• •‘Ž† ƒ– –Š‡ …‘•– ‘ˆ ͷ Ž‡‘• ‹…Ž—†‹‰ ƒ‘—– ™Š‡”‡ –Š‡ …‘•–
™‹–Š‘—– ™ƒ• –Š‡ …‘•– ‘ˆ Ͷ Ž‡‘•Ǥ ‹† –Š‡ ’‡”…‡–ƒ‰‡Ǥ
„Ǥ Š‡ ‘”‹‰‹ƒŽ ’”‹…‡ ‘ˆ ƒ ƒ…Š‹‡ ‹• •Ǥ ʹͲǡͲͲͲǤ – ‹• •‘Ž† ƒ– •Ǥ ͳʹǡͺͲͲ ƒ– –Š‡ ”ƒ–‡ ‘ˆ †‡’”‡…‹ƒ–‹‘ ʹͲΨ
ƒˆ–‡” •‘‡ ›‡ƒ”•Ǥ ‹† –Š‡ –‹‡Ǥ
ͷǤ ƒǤ ˆ ƒ† ‘ˆ ƒ …›Ž‹†‡” ƒ”‡ ʹǡͻͻʹ…2 ƒ† ͳǡ͹͸Ͳ…2 ϐ‹† –Š‡ ”ƒ†‹—• ‘ˆ –Š‡ „ƒ•‡ ‘ˆ –Š‡ …›Ž‹†‡”Ǥ
„Ǥ ‹† –Š‡ ‘ˆ –Š‡ ˜‡••‡Žǡ ‹ˆ –Š‡ …ƒ’ƒ…‹–› ‘ˆ ƒ …‘‹…ƒŽ ˜‡••‡Ž ‘ˆ Š‡‹‰Š– ͵Ͳ … ‹• ͳǤͷͶ Ž‹–‡”•Ǥ
…Ǥ ‹† –Š‡ ˜‘Ž—‡ ‘ˆ –Š‡ ‰‹˜‡ •“—ƒ”‡ „ƒ•‡† ’›”ƒ‹† ‘ˆ •‹†‡ ͳ͸ … ƒ† •Žƒ–‡† Š‡‹‰Š– ‹• ͳͲ …Ǥ
͸Ǥ ƒǤ ‹† –Š‡ ǣ š2 Ȃ ʹš Ȃ ͳͷ ƒ† š2 Ȃ ʹͷǤ

„Ǥ ‹‹‘Ž˜’’‡ŽŽǣ‹‹ ˆˆ3›› ǣǣx 211–46–9341x×× aα2–7 b͵17 4+ F

͹Ǥ ƒǤ 1
„Ǥ 1 – xb–a

…Ǥ ‹† ƒ› –™‘ …‘•‡…—–‹˜‡ ‡˜‡ —„‡”• ™Š‘•‡ ’”‘†—…– ‹• ͳʹͲǤ
ͺǤ ƒǤ ‹† –Š‡ Ž‡‰–Š ‘ˆ †‹ƒ‰‘ƒŽ ‘ˆ ”Š‘„—• ™Š‡”‡ … ‹• –Š‡ ‹† ’‘‹– ‘ˆ
•‹†‡ ǡ †‹ƒ‰‘ƒŽ α ͺ … ƒ† ƒ”‡ƒ ‘ˆ –”‹ƒ‰Ž‡ α ͳͲ …2.


„Ǥ  –Š‡ ƒ†Œ‘‹‹‰ †‹ƒ‰”ƒǡ ‹• –Š‡ …‡–‡” ‘ˆ ƒ …‹”…Ž‡ ƒ† ‘„–—•‡ ‘ α ͳʹͲιǡ
ϐ‹† –Š‡ ‘ ƒ† ‘ Ǥ


…Ǥ ”‘ –Š‡ ƒ†Œ‘‹‹‰ †‹ƒ‰”ƒ ϐ‹† –Š‡ ˜ƒŽ—‡ ‘ˆ š ™Š‡”‡ ‘ α ͺͲιǡ ‘ α
š ƒ† α Ǥ






ͻǤ ƒǤ Šƒ– ‹• –Š‡ ˜ƒŽ—‡ ‘ˆ Ž‡‰–Š ‘ˆ •‹†‡ ‘ˆ ' ™Š‡”‡ ‘ α ͸Ͳιǡ α ͸… ƒ† ƒ”‡ƒ ‘ˆ ' α ͳʹ

…2?
„Ǥ ˆ ¦ˆš α ͶͲͲ Ϊ ʹͲƒ Ƭ ¦ˆ α ͶͲ Ϊ ʹƒǡ ϐ‹† –Š‡ ˜ƒŽ—‡ ‘ˆ ƒ”‹–Š‡–‹… ‡ƒ ‘ˆ –Š‡ ‘„•‡”˜ƒ–‹‘•Ǥ
ͳͲǤ ƒǤ …ƒ”† ‹• †”ƒ™ ƒ– ”ƒ†‘ ˆ”‘ –Š‡ †‡… ‘ˆ …ƒ”†•Ǥ ‹† –Š‡ ’”‘„ƒ„‹Ž‹–› ‘ˆ –Š‡ …ƒ”† „‡‹‰ ˆƒ…‡ …ƒ”†

‘” …Ž—„ …ƒ”†Ǥ
„Ǥ „ƒ‰ …‘–ƒ‹• ͳ ”‡†ǡ ͳ „Ž—‡ ƒ† ͵ ‰”‡‡ ƒ”„Ž‡•Ǥ ™‘ ƒ”„Ž‡• ƒ”‡ †”ƒ™ ƒ– ”ƒ†‘ ‘‡ ƒˆ–‡”

ƒ‘–Š‡” ™‹–Š‘—– ”‡’Žƒ…‡‡–Ǥ Š‘™ ƒŽŽ –Š‡ ’”‘„ƒ„‹Ž‹–‹‡• ™‹–Š –”‡‡ †‹ƒ‰”ƒǤ

Group – C [10 × 4 = 40]
ͳͳǤ  ƒ …Žƒ•• ‘ˆ •–—†‡–• ͷͲΨ Ž‹‡ –‘ –”ƒ˜‡Ž ‘Šƒ”ƒ ‹ ‡†—…ƒ–‹‘ƒŽ –‘—”ǡ ͸ͲΨ Ž‹‡ –‘ –”ƒ˜‡Ž —„‹‹ǡ ͺΨ

†‘ǯ– Ž‹‡ –‘ –”ƒ˜‡Ž „‘–Š ’Žƒ…‡• ƒ† ʹΨ ™‡”‡ ƒ„•‡–Ǥ ˆ ͵Ͳ •–—†‡–• Ž‹‡ –‘ –”ƒ˜‡Ž ‹ „‘–Š ’Žƒ…‡• „›
†”ƒ™‹‰ ˜‡ †‹ƒ‰”ƒǡ ϐ‹† –‘–ƒŽ —„‡” ‘ˆ •–—†‡–• ƒ† ™Š‘ ™ƒ– –‘ –”ƒ˜‡Ž ‘Ž› ‘‡ ’Žƒ…‡Ǥ
ͳʹǤ Š‡ ’”‹…‡ ‘ˆ ƒ ƒ”–‹…Ž‡ ‹• ƒ”‡† ͶͲΨ ƒ„‘˜‡ –Š‡ …‘•– ’”‹…‡Ǥ Šƒ– ’‡”…‡– ‰ƒ‹ ™‹ŽŽ „‡ –Š‡”‡ ‘ ‰‹˜‹‰
ʹͷΨ †‹•…‘—–ǫ Ž•‘ ϐ‹† –Š‡ ƒ”‡† ’”‹…‡ ‘ˆ –Š‡ ƒ”–‹…Ž‡ ™Š‹…Š ‹• •‘Ž† ƒ– •Ǥ Ͷ͹Ͷ͸ ‹…Ž—†‹‰ ͳ͵Ψ Ǥ
ͳ͵Ǥ  —„”‡ŽŽƒ ‹• ƒ†‡ „› •–‹–…Š‹‰ ͳͲ –”‹ƒ‰—Žƒ” ’‹‡…‡• ‘ˆ …Ž‘–Š ‘ˆ –™‘ †‹ˆˆ‡”‡– …‘Ž‘—”•ǡ ‡ƒ…Š ’‹‡…‡
‡ƒ•—”‹‰ ʹͲ …ǡ ͶͲ … ƒ† ͶͲ … ‘ˆ ‹•‘•…‡Ž‡• –”‹ƒ‰—Žƒ” ’‹‡…‡•Ǥ ‹† –Š‡ …‘•– ‘ˆ …Ž‘–Š‡• —•‡† ‹ ‹– ƒ–
–Š‡ ”ƒ–‡ ‘ˆ •Ǥ ͷͲͲ ’‡” 2.

Mathematics–10 | 315

ͳͶǤ ‹’Ž‹ˆ› ǣ x 1 1 + 1 + 1 + x + 2x + 3x
+ x+2 x+3 x3 + x2 x3 + 2x2 x3 + 3x2

ͳͷǤ Š‡ ’”‘†—…– ‘ˆ –Š‡ †‹‰‹–• ‘ˆ –™‘ †‹‰‹–• —„‡” ‹• ʹͳǤ ˆ ͵͸ ‹• •—„–”ƒ…–‡† ˆ”‘ ‹–• ”‡˜‡”•‡† —„‡” –Š‡”‡
™‹ŽŽ „‡ –Š‡ ‘”‹‰‹ƒŽ —„‡”Ǥ ‹† –Š‡ —„‡”Ǥ

ͳ͸Ǥ ”‘˜‡ –Šƒ– ƒ”‡ƒ ‘ˆ ”‡…–ƒ‰Ž‡ ‹• ‡“—ƒŽ –‘ –Š‡ ƒ”‡ƒ ‘ˆ ’ƒ”ƒŽŽ‡Ž‘‰”ƒ Š‹…Š ƒ”‡ •–ƒ†‹‰ ‘
•ƒ‡ „ƒ•‡ ƒ† „‡–™‡‡ •ƒ‡ ’ƒ”ƒŽŽ‡Ž•Ǥ

ͳ͹Ǥ ‡”‹ˆ› ‡š’‡”‹‡–ƒŽŽ› –Šƒ– ‘’’‘•‹–‡ ƒ‰Ž‡• ‘ˆ ƒ …›…Ž‹… “—ƒ†”‹Žƒ–‡”ƒŽ ƒ”‡ •—’’Ž‡‡–ƒ”›Ǥ
ͳͺǤ ‘•–”—…– ƒ “—ƒ†”‹Žƒ–‡”ƒŽ ‘ˆ α α ͸…ǡ α α ͷ… ƒ† †‹ƒ‰‘ƒŽ α ͹…Ǥ Ž•‘ …‘•–”—…– ƒ

‡“—‹˜ƒŽ‡– ' ™‹–Š –Š‡ “—ƒ†”‹Žƒ–‡”ƒŽǤ
ͳͻǤ –”‡‡ ‹• „”‘‡ „› –Š‡ ™‹† ƒ† ‹• ‘– ˆ—ŽŽ› †‡–ƒ…Š‡† ƒ† –Š‡ –‘’ –‘—…Š‡• –Š‡ ‰”‘—† ™‹–Š ƒ ƒ‰Ž‡ ‘ˆ

͵Ͳι ™Š‡”‡ Ž‡‰–Š ‘ˆ –Š‡ „”‘‡ ’ƒ”– ‘ˆ –Š‡ –”‡‡ ‹• ͳʹǤ ‹† –Š‡ ‘”‹‰‹ƒŽ Š‡‹‰Š– ‘ˆ –Š‡ –”‡‡Ǥ
ʹͲǤ ˆ —’’‡” “—ƒ”–‹Ž‡ ‘ˆ –Š‡ ‰‹˜‡ ‘„•‡”˜ƒ–‹‘• ‹• Ͷʹǡ ϐ‹† –Š‡ ˜ƒŽ—‡ ‘ˆ Ǯǯ

Žƒ•• Ͳ Ǧ ͳʹ ͳʹ Ǧ ʹͶ ʹͶ Ǧ ͵͸ ͵͸ Ǧ Ͷͺ Ͷͺ Ǧ ͸Ͳ

f Ͷ m 12 ͳͲ ͷ

Group – D [4 × 5 = 20]
ʹͳǤ Š‡ …‘’‘—† ‹–‡”‡•– ‘ ƒ •— ‘ˆ ‘‡› ƒ– ͳͲΨ …‘’‘—†‡† •‡‹Ǧƒ—ƒŽŽ› ‹ ͳ ›‡ƒ” ͸ ‘–Š• ‹•

‘”‡ –Šƒ –Š‡ •‹’Ž‡ ‹–‡”‡•– „› • ͳͷʹǤͷͲǤ ‹† –Š‡ •—Ǥ
ʹʹǤ Š‡ ”ƒ†‹—• ‘ˆ „ƒ•‡ ƒ† •Žƒ– Š‡‹‰Š– ‘ˆ ƒ …‘‡ ƒ”‡ ‹ –Š‡ ”ƒ–‹‘ Ͷǣͷ ™Š‘•‡ ˜‡”–‹…ƒŽ Š‡‹‰Š– ‹• ͸…Ǥ ˆ ‹– ‹•

…‘‡…–‡† –‘ ƒ …›Ž‹†‡” ƒ† Š‡‹‰Š– ‘ˆ •‘Ž‹† „‡…‘‡• ʹ͹…Ǥ ‹† –Š‡ –‘–ƒŽ •—”ˆƒ…‡ ƒ”‡ƒ ‘ˆ –Š‡ •‘Ž‹†Ǥ

ʹ͵Ǥ ‹’Ž‹ˆ›ǣ


ʹͶǤ  –Š‡ ƒ†Œ‘‹‹‰ †‹ƒ‰”ƒǡ α ǡ ’”‘˜‡ –Šƒ– ȀȀ

****

Model Questions Set-B

Group A [3 × (1 + 1) = 6]
ͳǤ ƒǤ ”‹–‡ †‘™ –Š‡ ˆ‘”—Žƒ –‘ ϐ‹† †‹•…‘—– ’‡”…‡–ƒ‰‡ ™Š‡ ƒ”‡† ’”‹…‡ ƒ† •‡ŽŽ‹‰ ’”‹…‡ ‘ˆ ƒ
ƒ”–‹…Ž‡ ƒ”‡ ‰‹˜‡Ǥ
„Ǥ ”‹–‡ †‘™ –Š‡ ˆ‘”—Žƒ –‘ ϐ‹† ƒ”‡ƒ ‘ˆ ƒ ‹•‘•…‡Ž‡• –”‹ƒ‰Ž‡ ™Š‡ ‡“—ƒŽ •‹†‡•  ƒ† —‡“—ƒŽ •‹†‡ 
ƒ”‡ ‰‹˜‡Ǥ

ʹǤ ƒǤ ‘” ™Šƒ– ˜ƒŽ—‡ ‘ˆ šǡ ™‹ŽŽ –Š‡”‡ „‡ 3 x – 5 α ʹ ǫ
„Ǥ ”‹–‡ †‘™ –Š‡ ˆ‘”—Žƒ –‘ ϐ‹† –Š‡ ƒ”‹–Š‡–‹… ‡ƒ ƒ……‘”†‹‰ –‘ •–‡’ †‡˜‹ƒ–‹‘
method.

3. a. If area of ' α ʹͲ…2ǡ ™Šƒ– ™‹ŽŽ „‡ –Š‡ ƒ”‡ƒ ‘ˆ ’ƒ”ƒŽŽ‡Ž‘‰”ƒ ™Š‹…Š ƒ”‡ ‹
„‡–™‡‡ –Š‡ •ƒ‡ ’ƒ”ƒŽŽ‡Ž•Ǥ
„Ǥ ƒŽ…—Žƒ–‡ –Š‡ ˜ƒŽ—‡ ‘ˆ ‘ ™Š‡”‡ –Š‡ ˜ƒŽ—‡ ‘ˆ ‘ α ͶͲιǤ

Group – B [17×2 = 34]
ͶǤ ƒǤ  ƒ”–‹…Ž‡ ‹• •‘Ž† ƒ– •Ǥ ͷ͸ͷ ‹…Ž—†‹‰ ƒ‘—– •Ǥ ͸ͷǡ ϐ‹† –Š‡ ’‡”…‡–ƒ‰‡Ǥ
„Ǥ Š‡ ’”‡•‡– ’‘’—Žƒ–‹‘ ‘ˆ ƒ ’Žƒ…‡ ‹• ʹͲǡͲͲͲǤ ˆ–‡” ʹ ›‡ƒ”• ‹– …Šƒ‰‡• –‘ ʹʹǡ͵ͲͲ ™‹–Š ‹‰”ƒ–‹‘ ‘ˆ
ʹͷͲ ’‡‘’Ž‡ –‘ Š‡”‡ ˆ”‘ ‘–Š‡” ’Žƒ…‡•Ǥ ‹† –Š‡ ‰”‘™–Š ”ƒ–‡ ‘ˆ ’‘’—Žƒ–‹‘Ǥ
ͷǤ ƒǤ ˆ ͵ •’Š‡”‡• ‘ˆ ”ƒ†‹‹ ͳ…ǡ ͸… ƒ† ͺ… ƒ”‡ ‡Ž–‡† ƒ† ƒ ‡™ •’Š‡”‡ ‹• ƒ†‡ǡ

ϐ‹† –Š‡ ”ƒ†‹—• ‘ˆ ‡™ •’Š‡”‡Ǥ
„Ǥ  –Š‡ ‰‹˜‡ …‘‡ α ͳͶ…ǡ ‘ α ͸ͲιǤ ‹† ‹–• Ǥ
…Ǥ ˆ ˜‘Ž—‡ ‘ˆ –Š‡ ‰‹˜‡ ’”‹• ‹• ͳͺͲ 3…3ǡ ϐ‹† –Š‡ Ž‡‰–Š ‘ˆ Ǥ




͸…

ʹͲ…

316|Mathematics–10

͸Ǥ ƒǤ ‹† –Š‡ ‘ˆ ǣ š3 – 1 ƒ† š2 + 1 + 1
„Ǥ ‹’Ž‹ˆ›ǣ 3 375 + 3 2x43 – 3 648 x2

͹Ǥ ƒǤ ‹’Ž‹ˆ›ǣ 7x+1 – 49 × 7x–2
„Ǥ ‘Ž˜‡ǣ x 7+x x–1
– 7 – x7
α ͹
…Ǥ ‹† ƒ› –™‘ —„‡”• ™Š‘•‡ •— ‹• ͹ ƒ† –Š‡‹” ’”‘†—…– ‹• ͳͲǤ

ͺǤ ƒǤ ‹† –Š‡ Ž‡‰–Š ‘ˆ ™Š‡”‡ ‹• ƒ ”Š‘„—•ǡ α ǡ α ͸… Ƭ ƒ”‡ƒ ‘ˆ ' αʹͶ…2.






„Ǥ  –Š‡ ƒ†Œ‘‹‹‰ †‹ƒ‰”ƒǡ ȀȀ ǡ ‘ α ͳͲͷιǡ ‘ α ͺͷιǡ ϐ‹† –Š‡ ˜ƒŽ—‡ ‘ˆ ‘ Ǥ


F


…Ǥ ”‘ –Š‡ ƒ†Œ‘‹‹‰ †‹ƒ‰”ƒ ϐ‹† –Š‡ ˜ƒŽ—‡ ‘ˆ ”ƒ†‹—• ‘ˆ …‹”…Ž‡ ™Š‡”‡ α ͺ…ǡ α ͳʹ…Ǥ






ͻǤ ƒǤ Šƒ– ‹• –Š‡ ˜ƒŽ—‡ ‘ˆ ‘ ‘ˆ ƒ ' ™Š‡”‡ α ͸…ǡ α ͺ … ƒ† ƒ”‡ƒ ‘ˆ ' α ͳʹ …2?
„Ǥ ˆ •— ‘ˆ –Š‡ ’”‘†—…–• ‘ˆ ˆ”‡“—‡…› ƒ† ‘„•‡”˜ƒ–‹‘• ‹• ͶͲ Ϊ ʹͲƒǡ •— ‘ˆ –Š‡ ˆ”‡“—‡…› ‹• ͳͺ Ϊ ʹƒ

ƒ† ‡ƒ ‹• ʹͲǤ ‹† –Š‡ ˜ƒŽ—‡ ‘ˆ ǮƒǯǤ
ͳͲǤ ƒǤ …ƒ”† ‹• †”ƒ™ ƒ– ”ƒ†‘ ˆ”‘ –Š‡ —„‡” …ƒ”†• ‘ˆ ͵ –‘ ͵ͲǤ ‹† –Š‡ ’”‘„ƒ„‹Ž‹–› ‘ˆ –Š‡ …ƒ”† „‡‹‰

’”‹‡ ‘” —Ž–‹’Ž‡ ‘ˆ –Š”‡‡Ǥ
„Ǥ †‹…‡ ‹• –Š”‘™ –™‹…‡Ǥ ‹† –Š‡ ’”‘„ƒ„‹Ž‹–› ‘ˆ ‰‡––‹‰ ‘†† ‹ „‘–Š –Š”‘™ „› —•‹‰ –”‡‡ †‹ƒ‰”ƒǤ

Group – C [10 × 4 = 40]
ͳͳǤ  ƒ •—”˜‡› ‘ˆ ͳͷͲ ’‡‘’Ž‡ǡ –Š‡ —„‡” ‘ˆ ’‡‘’Ž‡ ™Š‘ Ž‹‡ –‘ ”‡ƒ†
‘”Šƒ’ƒ–”ƒ ‘Ž› ‹• †‘—„Ž‡ –Š‡ ’‡‘’Ž‡
™Š‘ Ž‹‡ –‘ ”‡ƒ† ƒ–‹’—” Ž›Ǥ ˆ ͵Ͳ Ž‹‡ –‘ ”‡ƒ† „‘–Šǡ ʹͷ ‡‹–Š‡” ‘ˆ –Š‡ ƒ† ʹͲ ™‡”‡ ƒ„•‡–ǡ ϐ‹† –Š‡
ˆ‘ŽŽ‘™‹‰ „› †”ƒ™‹‰ ˜‡ †‹ƒ‰”ƒǤ
‹Ǥ Š‘ Ž‹‡ –‘ ”‡ƒ† ƒ–‹’—”Ǥ
‹‹Ǥ Š‘ †‘ǯ– Ž‹‡ –‘ ”‡ƒ†
‘”‰Šƒ’ƒ–”ƒǤ
ͳʹǤ  ƒ”–‹…Ž‡ ‹• „‘—‰Š– „› ƒ …‘•—‡” ƒ– •Ǥ ͵ͺͶʹ ™‹–Š –Š‡ †‹•…‘—– ‘ˆ •Ǥ ͸ͲͲ …Ž—†‹‰ ͳ͵Ψ Ǥ ‹† –Š‡
ƒ”‡† ’”‹…‡ ƒ† ’‡”…‡–ƒ‰‡ ‘ˆ †‹•…‘—–Ǥ
ͳ͵Ǥ ‹† –Š‡ …‘•– ‘ˆ ’ƒ˜‹‰ –Š‡ ›ƒ”† ‘ˆ ƒ Š‘—•‡ ‰‹˜‡ ‹ †‹ƒ‰”ƒ ƒ– –Š‡ ”ƒ–‡ ‘ˆ •Ǥ ʹͲ ’‡” ’‹‡…‡ ‘ˆ •–‘‡ ‘ˆ
•‹œ‡ ͶͲ… έ ͷͲ…Ǥ
ͳͲ

13m

x+1 22m
x2 + x + x –1 2
ͳͶǤ ‹’Ž‹ˆ›ǣ 1 – x2– x + 1 + x4 –x2 + 1

ͳͷǤ Š‡ •— ‘ˆ –Š‡ ƒ‰‡• ‘ˆ ˆƒ–Š‡” ƒ† Š‹• •‘ ‹• ͹Ͷ ›‡ƒ”•Ǥ ‘–Š ‘ˆ –Š‡ Ž‹˜‡ ‘ –‹ŽŽ –Š‡ •‘ ™‹ŽŽ „‡ ƒ• —…Š ƒ•
ˆƒ–Š‡” ‘™ ƒ† •— ‘ˆ –Š‡‹” ƒ‰‡• ™‹ŽŽ „‡ ͳ͹Ͷ ›‡ƒ”•Ǥ ‹† –Š‡‹” ’”‡•‡– ƒ‰‡•Ǥ

ͳ͸Ǥ ”‘˜‡ –Šƒ– ƒ”‡ƒ ‘ˆ ' ‹• ‡“—ƒŽ –‘ ŠƒŽˆ ‘ˆ –Š‡ ƒ”‡ƒ ‘ˆ Ǥ Š‹…Š ƒ”‡ •–ƒ†‹‰ ‘ •ƒ‡ „ƒ•‡ ƒ†
„‡–™‡‡ ȀȀ Ǥ

Mathematics–10 | 317

ͳ͹Ǥ ‡”‹ˆ› ‡š’‡”‹‡–ƒŽŽ› –Šƒ– ‡š–‡”‹‘” ƒ‰Ž‡ ‘ˆ ƒ …›…Ž‹… “—ƒ†”‹Žƒ–‡”ƒŽ ‹• ‡“—ƒŽ –‘ ‹–• ‘’’‘•‹–‡ ‹–‡”‹‘”
ƒ‰Ž‡Ǥ

ͳͺǤ ‘•–”—…– ƒ ' Šƒ˜‹‰ α ͸…ǡ ‘ α ͸Ͳιǡ ‘ α ͶͷιǤ Ž•‘ …‘•–”—…– ƒ ‡“—‹˜ƒŽ‡– ”‡…–ƒ‰Ž‡ ‘ ‹–Ǥ
ͳͻǤ „‘› ‘ˆ Š‡‹‰Š– ͳǤ͸ ‹• ϐŽ›‹‰ ƒ ‹–‡ ™Š‡”‡ –Š‡ –Š”‡ƒ† ‘ˆ Ž‡‰–Š ʹͲͲ ƒ‡• ƒ ƒ‰Ž‡ ǮɅǯ ™‹–Š Š‘”‹œ‘–ƒŽ

Ž‹‡ ƒ† –Š‡ ‹–‡ ‹• ƒ– ƒ Š‡‹‰Š– ‘ˆ ͳͲͳǤ͸ ˆ”‘ –Š‡ ‰”‘—†Ǥ ‹† –Š‡ ˜ƒŽ—‡ ‘ˆ ǮɅǯǤ
ʹͲǤ ‹† –Š‡ ‡†‹ƒǤ

‹† ˜ƒŽ—‡ ‘ˆ ƒ”• ͳͷ ʹͷ ͵ͷ Ͷͷ ͷͷ

‘Ǥ ‘ˆ •–—†‡–• ͷ͸ͺ ͳͲ 3

Group – D [4 × 5 = 20]
ʹͳǤ Š‡ …‘’‘—† ‹–‡”‡•– ‘ ƒ •— ‘ˆ ‘‡› ‹ ʹ ›‡ƒ”• ƒ† Ͷ ›‡ƒ”• ƒ”‡ ”‡•’‡…–‹˜‡Ž› •Ǥ ͶʹͲͲǡ •Ǥ ͻʹͺʹǤ
‹† –Š‡ ”ƒ–‡ ƒ† •—Ǥ

ʹʹǤ ˆ ’ Ϊ “ Ϊ ” α ǡ ’”‘˜‡ –Šƒ–ǣ x2p + x2p + xm–r + x2q + x2r α ͳ
xm–q x2q + xm–r + xm–p x2r + xm–p + xm–q

ʹ͵Ǥ ˆ ˜‘Ž—‡ ‘ˆ –Š‡ ‰‹˜‡ –‡– ‹• ͵ͷͺͶ 3ǡ ϐ‹† –Š‡ …‘•– ‘ˆ …ƒ˜ƒ• —•‡† ‹ ‹– ƒ– –Š‡ ”ƒ–‡ ‘ˆ ͷ ’ƒ‹•ƒ ’‡” …2.

ͻš ͸š

ͺš
ʹͶǤ  –Š‡ ƒ†Œ‘‹‹‰ †‹ƒ‰”ƒǡ ǡ ƒ† ƒ”‡ –Š‡ ‹†Ǧ’‘‹–• ‘ˆ •‹†‡•

‘ˆ ο ǡ ‹• ’‡”’‡†‹…—Žƒ” –‘ Ǥ ”‘˜‡ –Šƒ– ‹• ƒ …›…Ž‹…
“—ƒ†”‹Žƒ–‡”ƒŽǤ


****

Model Questions Set-C

Group A [3 × (1 + 1) = 6]
ͳǤ ƒǤ ˆ α š ƒ† ™‹–Š α ›ǡ ϐ‹† –Š‡ ’‡”…‡–ƒ‰‡Ǥ
„Ǥ ‹† –Š‡ ƒ”‡ƒ ‘ˆ ƒ ‡“—‹Žƒ–‡”ƒŽ –”‹ƒ‰Ž‡ Šƒ˜‹‰ •‹†‡•  …Ǥ
‹”‹–’‡Ž ‹†ˆ›‘ǣ™ šm ––nŠ÷‡ ˆ‘x1”n–m —Žƒ ‘ˆ ƒ”‹–Š‡–‹… ‡ƒ „› —•‹‰ •–‡’ †‡˜‹ƒ–‹‘ ‡–Š‘†Ǥ
ʹǤ ƒǤ
„Ǥ
͵Ǥ ƒǤ ˆ ƒ”‡ƒ ‘ˆ ο α ͸ …2 ǡ ϐ‹† –Š‡ ƒ”‡ƒ ‘ˆ ƒ”ƒŽŽ‡Ž‘‰”ƒ ‹ˆ –Š‡› ƒ”‡ •–ƒ†‹‰ ‘ –Š‡ •ƒ‡ „ƒ•‡
ƒ† „‡–™‡‡ –Š‡ •ƒ‡ ’ƒ”ƒŽŽ‡Ž Ž‹‡Ǥ
„Ǥ ”‘ –Š‡ ƒ†Œ‘‹‹‰ †‹ƒ‰”ƒǡ ϐ‹† –Š‡ ˜ƒŽ—‡ ‘ˆ ǮšǯǤ


š

ͳͷͲι


Group ’B’ [ 17 x 2 = 34 ]
ͶǤ ƒǤ Š‡ …‘•– ‘ˆ ƒ ™ƒ–…Š ‹…Ž—†‹‰ ‹• •Ǥ ͶͷʹͲ ™Š‡”‡ ƒ‘—– ‹• •Ǥ ͷʹͲǡ ϐ‹† –Š‡ ’‡”…‡–ƒ‰‡ ‘ˆ

Ǥ
„Ǥ Š‡ ’‘’—Žƒ–‹‘ ‘ˆ ƒ ’Žƒ…‡ „‡…‘‡• ʹʹǡʹͲͲ ™‹–Š ‰”‘™–Š ”ƒ–‡ ‘ˆ ͷΨ ‹ –™‘ ›‡ƒ”• ™Š‡”‡ ͳͷͲ ’‡‘’Ž‡

‹‰”ƒ–‡† –‘ Š‡”‡ ˆ”‘ ‘–Š‡” ’Žƒ…‡•Ǥ ‹† –Š‡ ’‘’—Žƒ–‹‘ „‡ˆ‘”‡ ʹ ›‡ƒ”•Ǥ
ͷǤ ƒǤ •’Š‡”‹…ƒŽ ‡–ƒŽŽ‹… „ƒŽŽ ‘ˆ ”ƒ†‹—• ʹǤͳ … ‹• ‡Ž–‡† ƒ† ƒ ™‹”‡ Šƒ˜‹‰ –Š‹…‡•• ʹǤͳ  ‹• ƒ†‡ǡ ϐ‹†

–Š‡ Ž‡‰–Š ‘ˆ –Š‡ ™‹”‡Ǥ
„Ǥ ƒ–‡”ƒŽ •—”ˆƒ…‡ ƒ”‡ƒ ‘ˆ ƒ •“—ƒ”‡ „ƒ•‡† ’›”ƒ‹† ‘ˆ •Žƒ–‡† Š‡‹‰Š– ͳͲ … ‹• ͵ʹͲ …2ǡ ϐ‹† –Š‡ ƒ”‡ƒ ‘ˆ

‹–• „ƒ•‡Ǥ
…Ǥ ‹† –Š‡ …—”˜‡ •—”ˆƒ…‡ ƒ”‡ƒ ‘ˆ –Š‡ …‘‡ ™Š‘•‡ „ƒ•‡ ƒ† ˜‡”–‹…ƒŽ Š‹‰Š– ƒ”‡ ͳͷͶ …2 ƒ ͺ…

”‡•’‡…–‹˜‡Ž›Ǥ

318|Mathematics–10

͸Ǥ ƒǤ ‹† –Š‡ ‘ˆǣ Ͷš2 Ȃ ͳͲͲ ƒ† ͸ ȋš2 Ȃ ͵š Ȃ ͳͲȌ
„ƒǤǤ ‹˜ƒŽ’—Žƒ‹ˆ–›‡ǣǣ 351x+852xx–+215y+2x–51 έ×x– 193 912x4 y–5

͹Ǥ
„Ǥ ‘Ž˜‡ ǣ ʹx + 1 + 2x Ȃ ͵ α Ͳ

…ƒǤǤ ˆ ‹ ƒ†” ‡ƒƒ  ‘—ˆ ’„ƒ‡”ƒ” Ž™Ž‡ŠŽ‘‘‰•”‡ƒ •—  ™ ‹ –Š α‹– •Ͷ ͺ”‡……‹’2 ”‹‘… ƒ–ŠŽ ‡‹• ‰‹1˜14‡25 .
ͺǤ †‹ƒ‰”ƒ ™Š‡”‡
‘ α ͳͷͲι ƒ† α ͳʹ…Ǥ ‹† –Š‡ Ž‡‰–Š ‘ˆ –Š‡ •‹†‡ Ǥ

„Ǥ ‹† –Š‡ ˜ƒŽ—‡ ‘ˆ ‘ ™Š‡”‡ ‹• –Š‡ …‡–”‡ ‘ˆ ƒ …‹”…Ž‡ ‘ ǡ ‘
α ͵ͷι ‹ –Š‡ ƒ†Œ‘‹‹‰ †‹ƒ‰”ƒǤ


͵ͷι


…Ǥ  –Š‡ ƒ†Œ‘‹‹‰ †‹ƒ‰”ƒ ‘ α ͶͲι ƒ† ‘ α ͸ͲιǤ ‹† –Š‡ ˜ƒŽ—‡ ‘ˆ ‘ ™Š‡”‡ ‹• ƒ –ƒ‰‡–
ƒ– ƒ† ‹• –Š‡ …‡–‡” ‘ˆ –Š‡ …‹”…Ž‡ǤǤ




ͻǤ ƒǤ ‹† –Š‡ ƒ”‡ƒ ‘ˆ –”‹ƒ‰Ž‡ ‰‹˜‡ ‹ †‹ƒ‰”ƒ ™Š‡”‡ α α ͺ … ƒ† ‘ α ͹ͷιǤ



„Ǥ ¦ˆ† α ͸ͲͲǡ ¦ˆ α ͵Ͳ ƒ† ƒ••—‡ ‡ƒ α ʹͷǤ ‹† –Š‡ ˜ƒŽ—‡ ‘ˆ ƒ”‹–Š‡–‹… ‡ƒǤ

ͳͲǤ ƒǤ „ƒ‰ …‘–ƒ‹• ͵ ”‡†ǡ Ͷ ‰”‡‡ ƒ† ͷ ›‡ŽŽ‘™ „ƒŽŽ•Ǥ ‡ „ƒŽŽ ‹• †”ƒ™ ƒ– ”ƒ†‘ǡ ϐ‹† –Š‡ ’”‘„ƒ„‹Ž‹–›
‘ˆ –Š‡ „ƒŽŽ „‡‹‰ ”‡† ‘” ›‡ŽŽ‘™Ǥ

„Ǥ ™‘ …ƒ”†• ƒ”‡ †”ƒ™ ƒ– ”ƒ†‘ ‘‡ ƒˆ–‡” ƒ‘–Š‡” ˆ”‘ ƒ †‡… ‘ˆ …ƒ”†• ™‹–Š ”‡’Žƒ…‡‡–Ǥ ‹† –Š‡
’”‘„ƒ„‹Ž‹–‹‡• ‘ˆ –Š‡ …ƒ”†• „‡‹‰ „‘–Š ˆƒ…‡ …ƒ”†• „› †”ƒ™‹‰ –”‡‡ †‹ƒ‰”ƒǤ

Group - C (10 x 4 = 40)
ͳͳǤ  ƒ •—”˜‡› ‘ˆ ʹͲͲ ’‡‘’Ž‡ ™Š‘ Ž‹‡ ˆ‘‘–„ƒŽŽ –‡ƒ ƒ† …”‹…‡– –‡ƒ ‘ˆ ‘—” …‘—–”› ‹ –Š‡ ”ƒ–‹‘ ͵ǣͶ ™Š‡”‡
ͳͲ †‘ǯ– Ž‹‡ „‘–Š –Š‡ –‡ƒ• ƒ† ͻͲ Ž‹‡ „‘–Š –Š‡ –‡ƒ•Ǥ ‹† –Š‡ —„‡” ‘ˆ ’‡‘’Ž‡ „› †”ƒ™‹‰ ˜‡
†‹ƒ‰”ƒ ™Š‘ Ž‹‡Ǥ
‹Ǥ ‘‘–„ƒŽŽ –‡ƒ ‘Ž›Ǥ
‹‹Ǥ ‘ǯ– Ž‹‡ …”‹…‡– –‡ƒǤ
ͳʹǤ –‘—”‹•– „”‘—‰Š– ƒ ƒ”–‹…Ž‡ ™‹–Š ͳʹΨ †‹•…‘—– ‹…Ž—†‹‰ ͳ͵Ψ Ǥ ˆ Š‡ ”‡…‡‹˜‡† •Ǥ ʹͺ͸Ͳ „ƒ… ƒ– –Š‡
ƒ‹”’‘”– †—”‹‰ Ž‡ƒ˜‹‰ ‡’ƒŽǤ ‘™ —…Š ’ƒ‹† „› Š‹ –‘ –Š‡ ƒ”–‹…Ž‡ ‹…Ž—†‹‰ ǫ
ͳ͵Ǥ Š‡ •‹†‡ ‘ˆ ƒ •“—ƒ”‡ ‹• ͺš …ǡ Š‡‹‰Š– ‹• ͵š … ƒ† ˜‘Ž—‡ ‹• ͷͳʹ …3 ‘ˆ ƒ •“—ƒ”‡ „ƒ•‡ ’›”ƒ‹† ‰‹˜‡ ‹
†‹ƒ‰”ƒǤ ‹† ‹–ǯ• –‘–ƒŽ •—”ˆƒ…‡ ƒ”‡ƒǤ


͵š

ͺš

Mathematics–10 | 319

ͳͶǤ Š‡ ƒ‰‡ ‘ˆ ˆƒ–Š‡” ʹ ›‡ƒ”• ƒ‰‘ ™ƒ• ‘”‡ –Šƒ ͸ –‹‡• –Š‡ ƒ‰‡ ‘ˆ Š‹• •‘ „› ͶǤ ‹š ›‡ƒ”• Š‡…‡ Š‡ ™‹ŽŽ „‡
Ž‡•• –Šƒ ͳͲ –‹‡• –Š‡ ƒ‰‡ ‘ˆ Š‹• •‘ ™ƒ• ͵ ›‡ƒ”• ƒ‰‘ „› ʹ ›‡ƒ”•Ǥ
1 2 4 8
ͳͷǤ ‹’Ž‹ˆ› ǣ x+1 + x2 + 1 + x4 + 1 – 1 – x8

ͳ͸Ǥ ”‘˜‡ –Šƒ– ƒ”‡ƒ ‘ˆ ' ƒ† ' •–ƒ†‹‰ ‘ •ƒ‡ „ƒ•‡ ƒ† „‡–™‡‡ •ƒ‡ ’ƒ”ƒŽŽ‡Ž• ƒ”‡ ‡“—ƒŽ ‹ ƒ”‡ƒǤ
ͳ͹Ǥ ‡”‹ˆ› ‡š’‡”‹‡–ƒŽŽ› –Šƒ– –Š‡ ‹•…”‹„‡† ƒ‰Ž‡ ‹• ŠƒŽˆ ‘ˆ –Š‡ …‡–”ƒŽ ƒ‰Ž‡ •–ƒ†‹‰ ‘ •ƒ‡ ƒ”… ‘ˆ ƒ

…‹”…Ž‡Ǥ ȋ ƒ†‹—• ‘ˆ „‘–Š …‹”…Ž‡• •Š‘—Ž† ‘– „‡ Ž‡•• –Šƒ ͵ …Ȍ
ͳͺǤ ‘•–”—…– ƒ “—ƒ†”‹Žƒ–‡”ƒŽ Šƒ˜‹‰ α ͸Ǥͷ …ǡ α ͷǤͷ …ǡ α ͷ …ǡ α ͷǤͷ … ƒ† ‘ α ͸ͲιǤ Ž•‘

…‘•–”—…– ƒ ‡“—‹˜ƒŽ‡– ' ™‹–Š –Š‡ “—ƒ†”‹Žƒ–‡”ƒŽǤ
ͳͻǤ „‘› ‹• ϐŽ›‹‰ ƒ ‹–‡ ™Š‡”‡ –Š‡ ‹–‡ ‹• ƒ– –Š‡ Š‡‹‰Š– ‘ˆ ͳͲʹ  ˆ”‘ –Š‡ ‰”‘—† ƒ† ʹͲͲ  Ž‘‰ •–”‹‰

ƒ‡• ƒ ƒ‰Ž‡ ‘ˆ ͵Ͳι ™‹–Š –Š‡ Š‘”‹œ‘–ƒŽ Ž‹‡Ǥ ‹† –Š‡ Š‡‹‰Š– ‘ˆ –Š‡ „‘›Ǥ
ʹͲǤ ‹† –Š‡ —’’‡” “—ƒ”–‹Ž‡ ‘ˆ –Š‡ ‰‹˜‡ ‘„•‡”˜ƒ–‹‘• ˆ”‘ –Š‡ ˆ‘ŽŽ‘™‹‰•ǣ

ƒ”• Ͳ Ǧ ͺ Ͳ Ǧ ͳ͸ Ͳ Ǧ ʹͶ Ͳ Ǧ ͵ʹ Ͳ Ǧ ͶͲ

‘Ǥ ‘ˆ •–—†‡–• ͷ ͳͷ ʹͺ ͵Ͷ ͶͲ

Group - D ( 4 x 5 = 20 )
ʹͳǤ Š‡ …‘’‘—† ƒ‘—– ‘ ƒ •— ‘ˆ ‘‡› ‹ ͳ ›‡ƒ” ƒ† ͳ ›‡ƒ” ͸ ‘–Š• ‹• •Ǥ ʹʹǡͲͷͲ ƒ† •Ǥ ʹ͵ǡͳͷʹǤͷͲ

”‡•’‡…–‹˜‡Ž› …‘’‘—†‡† •‡‹Ǧƒ—ƒŽŽ›Ǥ ‹† –Š‡ ”ƒ–‡ ƒ† •—Ǥ
ʹʹǤ ‹† –Š‡ ‘–ƒŽ •—”ˆƒ…‡ ƒ”‡ƒ ‘ˆ –Š‡ …‹”…—Žƒ” „ƒ•‡† –‡– ‰‹˜‡ ‹ –Š‡ †‹ƒ‰”ƒǤ

ͳͷ
͹

͵Ͳ

ʹ͵Ǥ ˆ ƒ„… Ϊ ͳ α Ͳǡ ’”‘˜‡ –Šƒ– ǣ 1 – 1 b–1 + 1 + 1 a–1 α ͳ
a– 1 – b – c–1 1–c–

ʹͶǤ  –Š‡ ƒ†Œ‘‹‹‰ †‹ƒ‰”ƒǡ ‹• ƒ †‹ƒ‡–‡” ‘ˆ ƒ …‹”…Ž‡ǡ ‘ α ‘ ǡ ’”‘˜‡ –Šƒ– ‹• ƒ ’‡”’‡†‹…—Žƒ”
–‘ –Š‡ †‹ƒ‡–‡” ‘ˆ Ǥ








The End

320|Mathematics–10