TBSE Class 9 Model Question Paper for 2021 Maths
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TBSE Class 9 Model Question Paper for 2021 Maths is available here for free download. Published by Tripura Board for Class 9, this sample paper can be viewed online or downloaded as a PDF (8 pages). Candidates preparing for Class 9 can use TBSE Class 9 Model Question Paper for 2021 Maths to understand the exam pattern, the type of questions asked, and the overall difficulty level.
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TBSE Class 9 Model Question Paper for 2021 Maths – Text
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Page 1
Model Question
Class - IX : Mathemaitcs : 80 Marks : 2020-2021
!Ó˲yàÈüÈÜ /˛ ≤Ã!ï˛!ê˛ ≤Èϟ¿Ó˚ ÙylÈüÈ1 / 1 x 20= 20
!lˆÏã˛Ó˚ ≤ß¿à%!°Ó˚ í˛z_Ó˚ òyG
1ä 3 ~ÓÇ 4 ~Ó˚ ÙôƒÓï˛#≈ ò%!ê˛ Ù)°ò §Çáƒy !°á–
2ä 8 15 ˆÜ˛ 2 3 myÓ˚y ˲yà ܲˆÏÓ˚y–
3ä (2+ 5 ) ~Ó˚ ܲÓ˚î# !lÓ˚§Ü˛ í˛zͲõyòܲ!ê˛ !°á–
4ä x3 – 3x5+x2 Ó•%˛õò Ó˚y!¢!ê˛Ó˚ âyï˛ !°á–
5ä x+2y = 6 §Ù#ܲÓ˚î!ê˛Ó˚ ò%!ê˛ !Ó!˲ߨ §Ùyôyl !°á–
6ä Î!ò (3,4) !Ó®%!ê˛ 3y = ax+7 §Ó˚°ˆÏÓ˚áyÓ˚ í˛z˛õÓ˚ xÓ!fiÌï˛ •Î˚ ï˛ˆÏÓ a ~Ó˚ Ùyl !lî≈Î˚ ܲˆÏÓ˚y–
7ä y x«˛ ˆÌˆÏܲ P(4,3) !Ó®%!ê˛Ó˚ °¡∫ ò)Ó˚c !°á–
8ä 590 ~Ó˚ ˛õ)Ó˚ܲ ˆÜ˛yî!ê˛ !°á–
9ä ∆ ABC ~Ó˚ AB = AC ~ÓÇ ∠ B = 650 •ˆÏ° ∠ C ~ÓÇ ∠ A !lî≈Î˚ ܲˆÏÓ˚y–
A B
10ä ˛õyˆÏ¢Ó˚ !ã˛ˆÏe ABCD ã˛ï%˛Ë)≈˛ˆÏçÓ˚ AP ~ÓÇ DP •°
)
1300
∠ A ~ÓÇ ∠ D ~Ó˚ xhs˝ı§Ù!máu˛Ü˛– x ~Ó˚ Ùyl !lî≈Î˚ ܲÓ˚– x P
600 )
D C
11ä QR = 7cm ~ÓÇ ∠ Q= 600 •ˆÏ°ñ PQ + QR ~Ó˚
ˆÜ˛yl Ùyl §Ù)ˆÏ•Ó˚ çlƒ ∆ PQR xAܲl ܲÓ˚y §Ω˛Ó •ˆÏÓ⁄
12ä 362 3 cm ˛õ!Ó˚§#Ùy !Ó!¢T˛ ~ܲ!ê˛ §ÙÓy•% !eË%˛ˆÏçÓ˚ ˆ«˛eÊ˛° !lî≈Î˚ ܲˆÏÓ˚y–
13ä ~ܲ!ê˛ §Ù!mÓy•% !eË)˛ˆÏçÓ˚ ˛õ!Ó˚§#Ùy 36cm ~ÓÇ §Ùyl Óy•%mˆÏÎ˚Ó˚ ≤Ã!ï˛!ê˛Ó˚ ˜òâ≈ƒ 13 cm ~ÓÇ í˛zFã˛ï˛y 12cm •ˆÏ°ñ
!eË%˛ç!ê˛Ó˚ ˆ«˛eÊ˛° Ü˛ï˛ •ˆÏÓ⁄
14ä ~ܲ!ê˛ xyÎ˚ï˛âlyܲyÓ˚ çˆÏ°Ó˚ ê˛ƒyˆÏAܲÓ˚ ˜òâ≈ƒ 6m ≤ÃfiÌ 5m ~ÓÇ à˲#Ó˚ï˛y 4.5m •ˆÏ°ñ ê˛ƒyAܲ!ê˛ˆÏï˛ Ü˛ï˛ !°ê˛yÓ˚ ç° Ó˚yáy
ÎyˆÏÓ⁄
15ä ~ܲ!ê˛ °¡∫Ó,_yܲyÓ˚ ˆã˛yˆÏ.Ó˚ ÓÜ˛ï˛ˆÏ°Ó˚ ˆ«˛eÊ˛° 88 cm2 ~ÓÇ í˛zFã˛ï˛y 14cm •ˆÏ° ˆã˛yˆÏ.Ó˚ Ë)˛!ÙÓ˚ Óƒy§ Ü˛ï˛ •ˆÏÓ⁄
16ä ~ܲ!ê˛ °¡∫Ó,_yܲyÓ˚ ¢AÜ%˛Ó˚ Ë)˛!ÙÓ˚ ˛õ!Ó˚§#Ùy 44 cm ~ÓÇ !ï˛Î≈ܲ í˛zFã˛ï˛y 10cm •ˆÏ° ¢AÜ%˛Ó˚ ÓÜ˛ï˛ˆÏ°Ó˚ ˆ«˛eÊ˛° !lî≈Î˚
ܲˆÏÓ˚y–
17ä 2 cm ÓƒyˆÏ§Ó˚ ~ܲ!ê˛ xô≈ˆÏày°ˆÏܲÓ˚ §Ù@˝Ãï˛ˆÏ°Ó˚ ˆ«˛eÊ˛°!ê˛ !°á–
18ä ≤ÃÌÙ §yï˛!ê˛ ˆÙÔ!°Ü˛ §ÇáƒyÓ˚ àí˛¸ !lî≈Î˚ ܲˆÏÓ˚y–
19ä ~ܲ!ê˛ ˛õ!Ó˚§Çáƒy !Ó˲yçˆÏlÓ˚ 140 – 150 ˆ◊!î!ê˛Ó˚ ÙôƒÙyl!ê˛ ˆÓÓ˚ ܲˆÏÓ˚y–
20ä ~ܲ!ê˛ ˆVÑ˛yܲ¢)lƒ °%ˆÏí˛yÓ˚ SÈE˛yˆÏܲ ~ܲÓyÓ˚ !lˆÏ«˛˛õ ܲÓ˚y •ˆÏ°ñ ˆÎÔ!àܲ §Çáƒy ˛õyGÎ˚yÓ˚ §Ω˛yÓly Ü˛ï˛ •ˆÏÓ⁄
!Ó˲yàÈüÈá / !lˆÏã˛Ó˚ ≤ß¿à%!°Ó˚ í˛z_Ó˚ òyG / 2 x 6 = 12
21ä •ˆÏÓ˚ ܲÓ˚î# !lÓ˚§Ù ܲˆÏÓ˚y
5
5− 6
Class - IX : Mathemaitcs : 80 Marks : 2020-2021
!Ó˲yàÈüÈÜ /˛ ≤Ã!ï˛!ê˛ ≤Èϟ¿Ó˚ ÙylÈüÈ1 / 1 x 20= 20
!lˆÏã˛Ó˚ ≤ß¿à%!°Ó˚ í˛z_Ó˚ òyG
1ä 3 ~ÓÇ 4 ~Ó˚ ÙôƒÓï˛#≈ ò%!ê˛ Ù)°ò §Çáƒy !°á–
2ä 8 15 ˆÜ˛ 2 3 myÓ˚y ˲yà ܲˆÏÓ˚y–
3ä (2+ 5 ) ~Ó˚ ܲÓ˚î# !lÓ˚§Ü˛ í˛zͲõyòܲ!ê˛ !°á–
4ä x3 – 3x5+x2 Ó•%˛õò Ó˚y!¢!ê˛Ó˚ âyï˛ !°á–
5ä x+2y = 6 §Ù#ܲÓ˚î!ê˛Ó˚ ò%!ê˛ !Ó!˲ߨ §Ùyôyl !°á–
6ä Î!ò (3,4) !Ó®%!ê˛ 3y = ax+7 §Ó˚°ˆÏÓ˚áyÓ˚ í˛z˛õÓ˚ xÓ!fiÌï˛ •Î˚ ï˛ˆÏÓ a ~Ó˚ Ùyl !lî≈Î˚ ܲˆÏÓ˚y–
7ä y x«˛ ˆÌˆÏܲ P(4,3) !Ó®%!ê˛Ó˚ °¡∫ ò)Ó˚c !°á–
8ä 590 ~Ó˚ ˛õ)Ó˚ܲ ˆÜ˛yî!ê˛ !°á–
9ä ∆ ABC ~Ó˚ AB = AC ~ÓÇ ∠ B = 650 •ˆÏ° ∠ C ~ÓÇ ∠ A !lî≈Î˚ ܲˆÏÓ˚y–
A B
10ä ˛õyˆÏ¢Ó˚ !ã˛ˆÏe ABCD ã˛ï%˛Ë)≈˛ˆÏçÓ˚ AP ~ÓÇ DP •°
)
1300
∠ A ~ÓÇ ∠ D ~Ó˚ xhs˝ı§Ù!máu˛Ü˛– x ~Ó˚ Ùyl !lî≈Î˚ ܲÓ˚– x P
600 )
D C
11ä QR = 7cm ~ÓÇ ∠ Q= 600 •ˆÏ°ñ PQ + QR ~Ó˚
ˆÜ˛yl Ùyl §Ù)ˆÏ•Ó˚ çlƒ ∆ PQR xAܲl ܲÓ˚y §Ω˛Ó •ˆÏÓ⁄
12ä 362 3 cm ˛õ!Ó˚§#Ùy !Ó!¢T˛ ~ܲ!ê˛ §ÙÓy•% !eË%˛ˆÏçÓ˚ ˆ«˛eÊ˛° !lî≈Î˚ ܲˆÏÓ˚y–
13ä ~ܲ!ê˛ §Ù!mÓy•% !eË)˛ˆÏçÓ˚ ˛õ!Ó˚§#Ùy 36cm ~ÓÇ §Ùyl Óy•%mˆÏÎ˚Ó˚ ≤Ã!ï˛!ê˛Ó˚ ˜òâ≈ƒ 13 cm ~ÓÇ í˛zFã˛ï˛y 12cm •ˆÏ°ñ
!eË%˛ç!ê˛Ó˚ ˆ«˛eÊ˛° Ü˛ï˛ •ˆÏÓ⁄
14ä ~ܲ!ê˛ xyÎ˚ï˛âlyܲyÓ˚ çˆÏ°Ó˚ ê˛ƒyˆÏAܲÓ˚ ˜òâ≈ƒ 6m ≤ÃfiÌ 5m ~ÓÇ à˲#Ó˚ï˛y 4.5m •ˆÏ°ñ ê˛ƒyAܲ!ê˛ˆÏï˛ Ü˛ï˛ !°ê˛yÓ˚ ç° Ó˚yáy
ÎyˆÏÓ⁄
15ä ~ܲ!ê˛ °¡∫Ó,_yܲyÓ˚ ˆã˛yˆÏ.Ó˚ ÓÜ˛ï˛ˆÏ°Ó˚ ˆ«˛eÊ˛° 88 cm2 ~ÓÇ í˛zFã˛ï˛y 14cm •ˆÏ° ˆã˛yˆÏ.Ó˚ Ë)˛!ÙÓ˚ Óƒy§ Ü˛ï˛ •ˆÏÓ⁄
16ä ~ܲ!ê˛ °¡∫Ó,_yܲyÓ˚ ¢AÜ%˛Ó˚ Ë)˛!ÙÓ˚ ˛õ!Ó˚§#Ùy 44 cm ~ÓÇ !ï˛Î≈ܲ í˛zFã˛ï˛y 10cm •ˆÏ° ¢AÜ%˛Ó˚ ÓÜ˛ï˛ˆÏ°Ó˚ ˆ«˛eÊ˛° !lî≈Î˚
ܲˆÏÓ˚y–
17ä 2 cm ÓƒyˆÏ§Ó˚ ~ܲ!ê˛ xô≈ˆÏày°ˆÏܲÓ˚ §Ù@˝Ãï˛ˆÏ°Ó˚ ˆ«˛eÊ˛°!ê˛ !°á–
18ä ≤ÃÌÙ §yï˛!ê˛ ˆÙÔ!°Ü˛ §ÇáƒyÓ˚ àí˛¸ !lî≈Î˚ ܲˆÏÓ˚y–
19ä ~ܲ!ê˛ ˛õ!Ó˚§Çáƒy !Ó˲yçˆÏlÓ˚ 140 – 150 ˆ◊!î!ê˛Ó˚ ÙôƒÙyl!ê˛ ˆÓÓ˚ ܲˆÏÓ˚y–
20ä ~ܲ!ê˛ ˆVÑ˛yܲ¢)lƒ °%ˆÏí˛yÓ˚ SÈE˛yˆÏܲ ~ܲÓyÓ˚ !lˆÏ«˛˛õ ܲÓ˚y •ˆÏ°ñ ˆÎÔ!àܲ §Çáƒy ˛õyGÎ˚yÓ˚ §Ω˛yÓly Ü˛ï˛ •ˆÏÓ⁄
!Ó˲yàÈüÈá / !lˆÏã˛Ó˚ ≤ß¿à%!°Ó˚ í˛z_Ó˚ òyG / 2 x 6 = 12
21ä •ˆÏÓ˚ ܲÓ˚î# !lÓ˚§Ù ܲˆÏÓ˚y
5
5− 6
Page 2
22ä P(x) = x3–x2+x–1 •ˆÏ° P(–2) !lî≈Î˚ ܲˆÏÓ˚y–
23ä (2,10) !Ó®%àyÙ# ò%!ê˛ §Ó˚°ˆÏÓ˚áyÓ˚ §Ù#ܲÓ˚î !°á–
24ä ˛õyˆÏ¢Ó˚ !ã˛ˆÏe ABCD ê˛∆y!˛õ!çÎ˚yˆÏÙÓ˚ AD ~ÓÇ BC ~Ó˚
A 12cm B
Ùôƒ!Ó®% X ~ÓÇ Y– AB=12 cm, XY=14cm →
•ˆÏ° DC ~Ó˚ Ùyl Ü˛ï˛ ⁄ X Y
14cm
→
D C
25ä ˛õyˆÏ¢Ó˚ !ã˛ˆÏe PQ || ST, ∠ PQR=1100, S → T
)
∠ RST=130 , ∠ QRS ˆÓÓ˚ ܲˆÏÓ˚y–
0
0
Q 130
P →
)
1100
R
26ä ˛õyˆÏ¢Ó˚ !ã˛ˆÏe ∠ DAB= ∠ ABC, AD=BC •ˆÏ°
ˆòáyG BD=AC
A
)
B ) D
C
!Ó˲yàÈüÈà /˛ !lˆÏã˛Ó˚ ≤ß¿à%!°Ó˚ í˛z_Ó˚ òyG /˛ 3 x 8=24
p
27ä 2.12 34 ˆÜ˛ q xyܲyˆÏÓ˚ ≤Ãܲy¢ ܲˆÏÓ˚y–
28ä í˛zͲõyòܲ í˛z˛õ˛õyòƒ ÓƒÓ•yÓ˚ ܲˆÏÓ˚ y2–2y+6 ˆÜ˛ í˛zͲõyòˆÏܲ !ӈϟ’£Ïî ܲˆÏÓ˚y–
D xÌÓy
í˛z˛õÎ%=˛ xˆÏ˲ò ÓƒÓ•yÓ˚ ܲˆÏÓ˚ (101)3 ~Ó˚ Ùyl !lî≈Î˚ ܲÓ˚–
29ä 3x–4y =12 §Ù#ܲÓ˚ˆÏîÓ˚ ˆ°á!ã˛e xAܲl ܲˆÏÓ˚y– ˆ°á!ã˛e!ê˛ x x«˛ ~ÓÇ y x«˛ˆÏܲ ˆÎ !Ó®%ˆÏï˛ ˆSÈò ܲˆÏÓ˚ ï˛yÓ˚ fiÌylyAܲ
!lî≈Î˚ ܲˆÏÓ˚y–
30ä ~ܲ!ê˛ §%!Óôyçlܲ ~ܲܲ !lˆÏÎ˚ l#ˆÏã˛Ó˚ ˆÏê˛!ӈϰ ≤Ãò_ !Ó®%à%ˆÏ°yˆÏܲ ~ܲ!ê˛ SÈܲ ܲyàˆÏç ≤Ã!ï˛fiÌy˛õl ܲÓ˚ û
x –2 –1 0
y 8 7 –1.5
31ä ≤ÃÙyî ܲˆÏÓ˚y ~ܲ!ê˛ !eË%˛ˆÏçÓ˚ !ï˛l!ê˛ xhs˝fïÏܲyˆÏîÓ˚ §Ù!T˛ 1800–
32ä ∆ ABC xAܲl ܲˆÏÓ˚y ˆÎáyˆÏl BC= 7cm, ∠ B=750, AB + AC = 13cm.
33ä ~ܲ!ê˛ ê˛∆y!˛õ!çÎ˚yÙyܲyÓ˚ ÙyˆÏë˛Ó˚ §Ùyhs˝Ó˚y° Óy•%ò%!ê˛Ó˚ ˜òâ≈ƒ 25m ~ÓÇ 10m ~ÓÇ x˛õÓ˚ ò%!ê˛ Óy•%Ó˚ ˜òâ≈ƒ14m ~ÓÇ 13m
•ˆÏ° ÙyˆÏë˛Ó˚ ˆ«˛eÊ˛° !lî≈Î˚ ܲˆÏÓ˚y–
23ä (2,10) !Ó®%àyÙ# ò%!ê˛ §Ó˚°ˆÏÓ˚áyÓ˚ §Ù#ܲÓ˚î !°á–
24ä ˛õyˆÏ¢Ó˚ !ã˛ˆÏe ABCD ê˛∆y!˛õ!çÎ˚yˆÏÙÓ˚ AD ~ÓÇ BC ~Ó˚
A 12cm B
Ùôƒ!Ó®% X ~ÓÇ Y– AB=12 cm, XY=14cm →
•ˆÏ° DC ~Ó˚ Ùyl Ü˛ï˛ ⁄ X Y
14cm
→
D C
25ä ˛õyˆÏ¢Ó˚ !ã˛ˆÏe PQ || ST, ∠ PQR=1100, S → T
)
∠ RST=130 , ∠ QRS ˆÓÓ˚ ܲˆÏÓ˚y–
0
0
Q 130
P →
)
1100
R
26ä ˛õyˆÏ¢Ó˚ !ã˛ˆÏe ∠ DAB= ∠ ABC, AD=BC •ˆÏ°
ˆòáyG BD=AC
A
)
B ) D
C
!Ó˲yàÈüÈà /˛ !lˆÏã˛Ó˚ ≤ß¿à%!°Ó˚ í˛z_Ó˚ òyG /˛ 3 x 8=24
p
27ä 2.12 34 ˆÜ˛ q xyܲyˆÏÓ˚ ≤Ãܲy¢ ܲˆÏÓ˚y–
28ä í˛zͲõyòܲ í˛z˛õ˛õyòƒ ÓƒÓ•yÓ˚ ܲˆÏÓ˚ y2–2y+6 ˆÜ˛ í˛zͲõyòˆÏܲ !ӈϟ’£Ïî ܲˆÏÓ˚y–
D xÌÓy
í˛z˛õÎ%=˛ xˆÏ˲ò ÓƒÓ•yÓ˚ ܲˆÏÓ˚ (101)3 ~Ó˚ Ùyl !lî≈Î˚ ܲÓ˚–
29ä 3x–4y =12 §Ù#ܲÓ˚ˆÏîÓ˚ ˆ°á!ã˛e xAܲl ܲˆÏÓ˚y– ˆ°á!ã˛e!ê˛ x x«˛ ~ÓÇ y x«˛ˆÏܲ ˆÎ !Ó®%ˆÏï˛ ˆSÈò ܲˆÏÓ˚ ï˛yÓ˚ fiÌylyAܲ
!lî≈Î˚ ܲˆÏÓ˚y–
30ä ~ܲ!ê˛ §%!Óôyçlܲ ~ܲܲ !lˆÏÎ˚ l#ˆÏã˛Ó˚ ˆÏê˛!ӈϰ ≤Ãò_ !Ó®%à%ˆÏ°yˆÏܲ ~ܲ!ê˛ SÈܲ ܲyàˆÏç ≤Ã!ï˛fiÌy˛õl ܲÓ˚ û
x –2 –1 0
y 8 7 –1.5
31ä ≤ÃÙyî ܲˆÏÓ˚y ~ܲ!ê˛ !eË%˛ˆÏçÓ˚ !ï˛l!ê˛ xhs˝fïÏܲyˆÏîÓ˚ §Ù!T˛ 1800–
32ä ∆ ABC xAܲl ܲˆÏÓ˚y ˆÎáyˆÏl BC= 7cm, ∠ B=750, AB + AC = 13cm.
33ä ~ܲ!ê˛ ê˛∆y!˛õ!çÎ˚yÙyܲyÓ˚ ÙyˆÏë˛Ó˚ §Ùyhs˝Ó˚y° Óy•%ò%!ê˛Ó˚ ˜òâ≈ƒ 25m ~ÓÇ 10m ~ÓÇ x˛õÓ˚ ò%!ê˛ Óy•%Ó˚ ˜òâ≈ƒ14m ~ÓÇ 13m
•ˆÏ° ÙyˆÏë˛Ó˚ ˆ«˛eÊ˛° !lî≈Î˚ ܲˆÏÓ˚y–
Page 3
34ä 5!ê˛ ÓƒyˆÏàÓ˚ ≤Ã!ï˛!ê˛ ˆÌˆÏܲ Îò,FSÈ˲yˆÏÓ 50!ê˛ Ü˛ˆÏÓ˚ Ó#ç §Ç@˝Ã• ܲˆÏÓ˚ xAÜ%˛ˆÏÓ˚yòàˆÏÙÓ˚ çlƒ xl%Ü)˛° ˛õ!Ó˚ˆÏӈϢ Ó˚yáy •ˆÏÎ˚ˆÏSÈ
20 !òl ˛õˆÏÓ˚ ≤Ã!ï˛!ê˛ §Ç@˝Ã• ˆÌˆÏܲ xAÜ%˛!Ó˚ï˛ Ó#çà%ˆÏ°y àîly ܲˆÏÓ˚ !lˆÏ¡¨ ≤Ãò_ §yÓ˚!îˆÏï˛ !°!˛õÓÂô ܲÓ˚y •°
Óƒyà 1 2 3 4 5
xAÜ%˛!Ó˚ï˛ Ó#ˆÏçÓ˚ §Çáƒy 40 48 42 39 41
xAÜ%˛ˆÏÓ˚yòàˆÏÙÓ˚ §Ω˛yÓly !lî≈Î˚ ܲˆÏÓ˚y Îál û åܲä ~ܲ!ê˛ ÓƒyˆÏà 40!ê˛Ó˚ ˆÓ!¢ Ó#ç ÌyˆÏܲ–
áä ~ܲ!ê˛ ÓƒyˆÏà 49!ê˛ Ó#ç ÌyˆÏܲ–
àä ~ܲ!ê˛ ÓƒyˆÏà 35!ê˛Ó˚ ˆÓ!¢ Ó#ç ÌyˆÏܲ–
!Ó˲yàÈüÈâ / !lˆÏã˛Ó˚ ≤ß¿à%!°Ó˚ í˛z_Ó˚ òyG / 4 x 6 = 24
35ä ˲yà ly ܲˆÏÓ˚ ˆòáyG ˆÎ x3–3x2–13x+15 Ó•%˛õò Ó˚y!¢!ê˛ x2+2x–3myÓ˚y !Ó˲y烖
D xÌÓy
˲yà ˛õÂô!ï˛ˆÏï˛ 3x4–4x3–3x–1 Ó•%˛õò Ó˚y!¢!ê˛ˆÏܲ (x–1) !òˆÏÎ˚ ˲yà ܲˆÏÓ˚ñ ˲yàˆÏ¢£Ï!ê˛ !lî≈Î˚ܲˆÏÓ˚y–
36ä ~ܲ•z Ë)˛!Ù BC ~Ó˚ í˛z˛õÓ˚ ò%!ê˛ §Ù!mÓy•% !eË%˛ç ABC ~ÓÇ DBC xÓ!fiÌï˛ •ˆÏ° ≤ÃÙyî ܲˆÏÓ˚y ∠ ABD = ∠ ACD
1
37ä ˛õyˆÏ¢Ó˚ !ã˛ˆÏe ∆ PQR ~Ó˚ PS ~ÓÇ RT ò%!ê˛ ÙôƒÙy ~ÓÇ SM || RT ≤ÃÙyÙ Ü˛ˆÏÓ˚y QM= PQ
4
P
T
→
R
M →
S
Q
D xÌÓy
˛õyˆÏ¢Ó˚ !ã˛ˆÏe ABCD ê˛∆y!˛õ!çÎ˚ˆÏÙÓ˚ AB||CD ~ÓÇ AD=BC. ≤ÃÙyî ܲˆÏÓ˚y
(i) ∠ A= ∠ B (ii) ∆ ABC ≅ ∆ BAD
A B (iii) AC=BD
D C
20 !òl ˛õˆÏÓ˚ ≤Ã!ï˛!ê˛ §Ç@˝Ã• ˆÌˆÏܲ xAÜ%˛!Ó˚ï˛ Ó#çà%ˆÏ°y àîly ܲˆÏÓ˚ !lˆÏ¡¨ ≤Ãò_ §yÓ˚!îˆÏï˛ !°!˛õÓÂô ܲÓ˚y •°
Óƒyà 1 2 3 4 5
xAÜ%˛!Ó˚ï˛ Ó#ˆÏçÓ˚ §Çáƒy 40 48 42 39 41
xAÜ%˛ˆÏÓ˚yòàˆÏÙÓ˚ §Ω˛yÓly !lî≈Î˚ ܲˆÏÓ˚y Îál û åܲä ~ܲ!ê˛ ÓƒyˆÏà 40!ê˛Ó˚ ˆÓ!¢ Ó#ç ÌyˆÏܲ–
áä ~ܲ!ê˛ ÓƒyˆÏà 49!ê˛ Ó#ç ÌyˆÏܲ–
àä ~ܲ!ê˛ ÓƒyˆÏà 35!ê˛Ó˚ ˆÓ!¢ Ó#ç ÌyˆÏܲ–
!Ó˲yàÈüÈâ / !lˆÏã˛Ó˚ ≤ß¿à%!°Ó˚ í˛z_Ó˚ òyG / 4 x 6 = 24
35ä ˲yà ly ܲˆÏÓ˚ ˆòáyG ˆÎ x3–3x2–13x+15 Ó•%˛õò Ó˚y!¢!ê˛ x2+2x–3myÓ˚y !Ó˲y烖
D xÌÓy
˲yà ˛õÂô!ï˛ˆÏï˛ 3x4–4x3–3x–1 Ó•%˛õò Ó˚y!¢!ê˛ˆÏܲ (x–1) !òˆÏÎ˚ ˲yà ܲˆÏÓ˚ñ ˲yàˆÏ¢£Ï!ê˛ !lî≈Î˚ܲˆÏÓ˚y–
36ä ~ܲ•z Ë)˛!Ù BC ~Ó˚ í˛z˛õÓ˚ ò%!ê˛ §Ù!mÓy•% !eË%˛ç ABC ~ÓÇ DBC xÓ!fiÌï˛ •ˆÏ° ≤ÃÙyî ܲˆÏÓ˚y ∠ ABD = ∠ ACD
1
37ä ˛õyˆÏ¢Ó˚ !ã˛ˆÏe ∆ PQR ~Ó˚ PS ~ÓÇ RT ò%!ê˛ ÙôƒÙy ~ÓÇ SM || RT ≤ÃÙyÙ Ü˛ˆÏÓ˚y QM= PQ
4
P
T
→
R
M →
S
Q
D xÌÓy
˛õyˆÏ¢Ó˚ !ã˛ˆÏe ABCD ê˛∆y!˛õ!çÎ˚ˆÏÙÓ˚ AB||CD ~ÓÇ AD=BC. ≤ÃÙyî ܲˆÏÓ˚y
(i) ∠ A= ∠ B (ii) ∆ ABC ≅ ∆ BAD
A B (iii) AC=BD
D C
Page 4
38ä 1.1 !Ùê˛yÓ˚ ã˛Gí˛¸y ~ܲ!ê˛ Ü˛y˛õí˛¸ !òˆÏÎ˚ 12 !Ùê˛yÓ˚ í˛zFã˛ï˛y G 16 !Ùê˛yÓ˚ Ë)˛!ÙÓ˚ Óƒy§ !Ó!¢T˛ ~ܲ!ê˛ ï˛yÓ% ˜ï˛!Ó˚ ܲÓ˚y •ˆÏ°ñ
ܲy˛õí˛¸!ê˛Ó˚ ˜òâ≈ƒ !lî≈ΠܲˆÏÓ˚y– Î!ò ≤Ã!ï˛ !Ùê˛yÓ˚ ܲy˛õˆÏí˛¸Ó˚ òyÙ 14 ê˛yܲy •Î˚ ï˛ˆÏÓ ï˛yÓ%!ê˛ ˜ï˛!Ó˚ ܲÓ˚ˆÏï˛ ˆÙyê˛ Ü˛ï˛ ê˛yܲy áÓ˚ã˛ ˛õí˛¸ˆÏÓ⁄
D xÌÓy
~ܲ!ê˛ ôyï˛Ó ӈϰÓ˚ Óƒy§ 4.2cm Î!ò ôyï%˛Ó˚ âlc 8.9g/cm3 •Î˚ ï˛ˆÏÓ Ó°!ê˛Ó˚ ˲Ó˚ !lî≈Î˚ ܲˆÏÓ˚y–
39ä ˆÜ˛ylG ~ܲ!ê˛ ¢•ˆÏÓ˚ ç#ÓlÎyeyÓ˚ áÓ˚ˆÏã˛Ó˚ §)ã˛Ü˛ !Ó£ÏÎ˚ܲ ~ܲ!ê˛ xôƒÎ˚ˆÏl ˛õyGÎ˚y §yÆy!•Ü˛ ˛õÎ≈ˆÏÓ«˛î !lˆÏã˛Ó˚ ï˛y!°Ü˛yÎ˚ ˆòGÎ˚y
•°
ç#ÓlÎyeyÓ˚ áÓ˚ˆÏã˛Ó˚ §)ã˛Ü˛ §ÆyˆÏ•Ó˚ §Çáƒy
140 – 150 5
150–160 10
160–170 20
170–180 09
180–190 06
190–200 02
í˛z˛õˆÏÓ˚Ó˚ Ó˚y!¢ï˛Ìƒ !òˆÏÎ˚ ~ܲ!ê˛ xyÎ˚ï˛ˆÏ°á xAܲl ܲˆÏÓ˚y–
40ä ˆÜ˛yˆÏly Ó,ˆÏ_Ó˚ ~ܲ!ê˛ ã˛y˛õ myÓ˚y ˆÜ˛ˆÏw à!ë˛ï˛ ˆÜ˛yîñ Ó,ˆÏ_Ó˚ xÓ!¢T˛ xLjϢÓ˚ í˛z˛õ!Ó˚!fiÌï˛ ˆÎ ˆÜ˛yˆÏly !Ó®%ˆÏï˛ í˛zͲõߨ ˆÜ˛yˆÏîÓ˚
!mà%î •Î˚–
D x!ï˛!Ó˚=˛ ≤ß¿yÓ°#
ܲy˛õí˛¸!ê˛Ó˚ ˜òâ≈ƒ !lî≈ΠܲˆÏÓ˚y– Î!ò ≤Ã!ï˛ !Ùê˛yÓ˚ ܲy˛õˆÏí˛¸Ó˚ òyÙ 14 ê˛yܲy •Î˚ ï˛ˆÏÓ ï˛yÓ%!ê˛ ˜ï˛!Ó˚ ܲÓ˚ˆÏï˛ ˆÙyê˛ Ü˛ï˛ ê˛yܲy áÓ˚ã˛ ˛õí˛¸ˆÏÓ⁄
D xÌÓy
~ܲ!ê˛ ôyï˛Ó ӈϰÓ˚ Óƒy§ 4.2cm Î!ò ôyï%˛Ó˚ âlc 8.9g/cm3 •Î˚ ï˛ˆÏÓ Ó°!ê˛Ó˚ ˲Ó˚ !lî≈Î˚ ܲˆÏÓ˚y–
39ä ˆÜ˛ylG ~ܲ!ê˛ ¢•ˆÏÓ˚ ç#ÓlÎyeyÓ˚ áÓ˚ˆÏã˛Ó˚ §)ã˛Ü˛ !Ó£ÏÎ˚ܲ ~ܲ!ê˛ xôƒÎ˚ˆÏl ˛õyGÎ˚y §yÆy!•Ü˛ ˛õÎ≈ˆÏÓ«˛î !lˆÏã˛Ó˚ ï˛y!°Ü˛yÎ˚ ˆòGÎ˚y
•°
ç#ÓlÎyeyÓ˚ áÓ˚ˆÏã˛Ó˚ §)ã˛Ü˛ §ÆyˆÏ•Ó˚ §Çáƒy
140 – 150 5
150–160 10
160–170 20
170–180 09
180–190 06
190–200 02
í˛z˛õˆÏÓ˚Ó˚ Ó˚y!¢ï˛Ìƒ !òˆÏÎ˚ ~ܲ!ê˛ xyÎ˚ï˛ˆÏ°á xAܲl ܲˆÏÓ˚y–
40ä ˆÜ˛yˆÏly Ó,ˆÏ_Ó˚ ~ܲ!ê˛ ã˛y˛õ myÓ˚y ˆÜ˛ˆÏw à!ë˛ï˛ ˆÜ˛yîñ Ó,ˆÏ_Ó˚ xÓ!¢T˛ xLjϢÓ˚ í˛z˛õ!Ó˚!fiÌï˛ ˆÎ ˆÜ˛yˆÏly !Ó®%ˆÏï˛ í˛zͲõߨ ˆÜ˛yˆÏîÓ˚
!mà%î •Î˚–
D x!ï˛!Ó˚=˛ ≤ß¿yÓ°#
Page 5
Model Question
Class - IX : Mathemaitcs : 80 Marks : 2020-2021
Group-A Each Question Carries 1 Mark 1 x 20= 20
Answer the following questions
1. Write down two rational number between 3 and 4.
2. Divide 8 15 by 2 3 .
3. Write down rationalising factor of (2+ 5 ) .
4. Write the degree of the polynomial x3 – 3x5+x2 .
5. Write two different solutions of the equation x+2y = 6 .
6. If the point (3,4) lies on the straight line 3y = ax+7 , find the value of a.
7. Write down prependicular distance of the point ˛ P(4,3) from y-axis.
8. Write down complement angle of 590 .
9. In ∆ ABC, AB = AC and ∠ B = 650 . Determine ∠ C and ∠ A .
A B
10. In the adjacent figure, AP and DP are the internal
)
1300
angle bisectors of the angle A and D respectively of the x P
quadrilatersal ABCD. Determine the value of x
600 )
D C
11. If QR = 7cm and ∠ Q= 600 then for what value of PQ + QR , construction of ∆ PQR is possible.
12. Find the area of an equilatral triangle of perimeter 36 3 cm ˛
13. Find the are of an is oscels triangle each of whose equal sides is 13 cm and whose perimeter is 36
cm and atttude 12 cm.
14. How much water in litre can a rectangular watertank hold whose length is 6m, breadth 5m and
depth 4.5m.
15. Find the diameter of base of a right circular cylinder whose curved surface area in 88 cm2 and
height 14cm .
16. The circumference of the base of a cone is 44cm and slant height is 10 cm. Find the curved
surface area of the cone.
17. Find the total surface area of a hemisphere whose diameter is 2 cm.
18. Find the average of first seven prime numbers.
19. In a statistical distribution, find the median of the class interval 140-150.
20. An unbiased die is thrown once. What is the probability of getting a composite number.
Section - B : Each Question Carries 2 Marks : 6 x 2 = 12
21. Rationalise the denominator
5
5− 6
22. If P(x) = x3–x2+x–1 , evaluate P(–2) .
23. Write two equations of straight line passing through the point (2,10).
Class - IX : Mathemaitcs : 80 Marks : 2020-2021
Group-A Each Question Carries 1 Mark 1 x 20= 20
Answer the following questions
1. Write down two rational number between 3 and 4.
2. Divide 8 15 by 2 3 .
3. Write down rationalising factor of (2+ 5 ) .
4. Write the degree of the polynomial x3 – 3x5+x2 .
5. Write two different solutions of the equation x+2y = 6 .
6. If the point (3,4) lies on the straight line 3y = ax+7 , find the value of a.
7. Write down prependicular distance of the point ˛ P(4,3) from y-axis.
8. Write down complement angle of 590 .
9. In ∆ ABC, AB = AC and ∠ B = 650 . Determine ∠ C and ∠ A .
A B
10. In the adjacent figure, AP and DP are the internal
)
1300
angle bisectors of the angle A and D respectively of the x P
quadrilatersal ABCD. Determine the value of x
600 )
D C
11. If QR = 7cm and ∠ Q= 600 then for what value of PQ + QR , construction of ∆ PQR is possible.
12. Find the area of an equilatral triangle of perimeter 36 3 cm ˛
13. Find the are of an is oscels triangle each of whose equal sides is 13 cm and whose perimeter is 36
cm and atttude 12 cm.
14. How much water in litre can a rectangular watertank hold whose length is 6m, breadth 5m and
depth 4.5m.
15. Find the diameter of base of a right circular cylinder whose curved surface area in 88 cm2 and
height 14cm .
16. The circumference of the base of a cone is 44cm and slant height is 10 cm. Find the curved
surface area of the cone.
17. Find the total surface area of a hemisphere whose diameter is 2 cm.
18. Find the average of first seven prime numbers.
19. In a statistical distribution, find the median of the class interval 140-150.
20. An unbiased die is thrown once. What is the probability of getting a composite number.
Section - B : Each Question Carries 2 Marks : 6 x 2 = 12
21. Rationalise the denominator
5
5− 6
22. If P(x) = x3–x2+x–1 , evaluate P(–2) .
23. Write two equations of straight line passing through the point (2,10).
Page 6
24. ˛In the adjacent figure, X and Y are the mid points
of the sides AD and BC of the trapezium ABCD A 12cm B
→
respectively. If AB=12cm, XY=14cm,
X Y
find the value of DC. 14cm
→
D C
25. In the adjacent figure, PQ || ST, ∠ PQR=1100, S → T
)
0
0
∠ RST=130 , find ∠ QRS . Q 130
P →
)
1100
R
26. ˛In the figure along side ∠ DAB= ∠ ABC, A
)
If AD=BC , Show that BD=AC
B ) D
C
Group-C : Each Question Carries 3 Marks : 3x8=24
p
27. Express 2.1234 in the form of form.
q
28. Using factor theorem factorise y2–2y+6 .
* OR
Using suitable identity evaluate (101)3 .
29. Draw the graph of the equation 3x–4y =12. Write the co-ordinates of the point where this line
intersects the x-axis and y - axis.
30. Taking a suitable unit plot the following points (x,y) given in the following table
x –2 –1 0
y 8 7 –1.5
31. Prove that sum of the interior angles of a triangle is 1800.
32. Construct ∆ ABC where BC= 7cm, ∠ B=750, and AB + AC = 13cm.
33. A field in the shape of rapezium whose parallel sides are 25m and 10m. The non parrallel sides are
14m and 13m. Find the area of the field.
of the sides AD and BC of the trapezium ABCD A 12cm B
→
respectively. If AB=12cm, XY=14cm,
X Y
find the value of DC. 14cm
→
D C
25. In the adjacent figure, PQ || ST, ∠ PQR=1100, S → T
)
0
0
∠ RST=130 , find ∠ QRS . Q 130
P →
)
1100
R
26. ˛In the figure along side ∠ DAB= ∠ ABC, A
)
If AD=BC , Show that BD=AC
B ) D
C
Group-C : Each Question Carries 3 Marks : 3x8=24
p
27. Express 2.1234 in the form of form.
q
28. Using factor theorem factorise y2–2y+6 .
* OR
Using suitable identity evaluate (101)3 .
29. Draw the graph of the equation 3x–4y =12. Write the co-ordinates of the point where this line
intersects the x-axis and y - axis.
30. Taking a suitable unit plot the following points (x,y) given in the following table
x –2 –1 0
y 8 7 –1.5
31. Prove that sum of the interior angles of a triangle is 1800.
32. Construct ∆ ABC where BC= 7cm, ∠ B=750, and AB + AC = 13cm.
33. A field in the shape of rapezium whose parallel sides are 25m and 10m. The non parrallel sides are
14m and 13m. Find the area of the field.
Page 7
34. 50 seeds were selected at random from each of 5 bags of seeds and were kept under standardised
conditions favourable to germination. After 20 days, the number of seeds which had germinated in
each collection were counted and recorded as follows :
Bag 1 2 3 4 5
Number of seeds 40 48 42 39 41
germinate
What is the probability of germination of (i) more than 40 seeds in a bag ?
(ii) 49 seeds in a bag ? (iii) more than 35 seeds in a bag ?
Section- D : Each Question Carries 4 Marks : 4x6=24
35. Without actual division show that polynomial x3–3x2–13x+15 is divisible by˛ x2+2x–3.
* OR
Find the remainder obtained by dividing polynomial 3x4–4x3–3x–1 by˛ (x–1) .
36. If two isosceles triangle lie on same base BC , prove that ∠ ABD = ∠ ACD
36. In the figure along side, PS and RT are two medians of the triangle PQR and SM || RT
1
Prove that QM= PQ P
4
T
→
R
M →
S
Q
OR
In figure alongside, in trspezium ABCD, AB||CD and AD=BC. prove that
A B (i) A= B (ii) ABC
∠ ∠ ∆ ≅ ∆ BAD
(iii) AC=BD
D C
conditions favourable to germination. After 20 days, the number of seeds which had germinated in
each collection were counted and recorded as follows :
Bag 1 2 3 4 5
Number of seeds 40 48 42 39 41
germinate
What is the probability of germination of (i) more than 40 seeds in a bag ?
(ii) 49 seeds in a bag ? (iii) more than 35 seeds in a bag ?
Section- D : Each Question Carries 4 Marks : 4x6=24
35. Without actual division show that polynomial x3–3x2–13x+15 is divisible by˛ x2+2x–3.
* OR
Find the remainder obtained by dividing polynomial 3x4–4x3–3x–1 by˛ (x–1) .
36. If two isosceles triangle lie on same base BC , prove that ∠ ABD = ∠ ACD
36. In the figure along side, PS and RT are two medians of the triangle PQR and SM || RT
1
Prove that QM= PQ P
4
T
→
R
M →
S
Q
OR
In figure alongside, in trspezium ABCD, AB||CD and AD=BC. prove that
A B (i) A= B (ii) ABC
∠ ∠ ∆ ≅ ∆ BAD
(iii) AC=BD
D C
Page 8
38. What length of cloth 1.1m wide will be required to make a comical tent of height 12m and base
diameter 16m ? Find the cost of the cloth to make the conical tent at Rs. 14 per meter.
OR
The diameter of a metal ball in 4.2 cm. If the deusity of the metal is 8.9g/cm3 , find the mass of the ball.
39. In a city, the weekly observations made in a study on the cost of living index are given in the
following tables.
Cost of living index No. of weeks
140 – 150 5
150–160 10
160–170 20
170–180 09
180–190 06
190–200 02
Draw a histogram for the data above.
40.Prove that the angle subtended by an are at the centre is double the angle subtended by it at any point
on the remaining part of the circle.
* Additional Questions
diameter 16m ? Find the cost of the cloth to make the conical tent at Rs. 14 per meter.
OR
The diameter of a metal ball in 4.2 cm. If the deusity of the metal is 8.9g/cm3 , find the mass of the ball.
39. In a city, the weekly observations made in a study on the cost of living index are given in the
following tables.
Cost of living index No. of weeks
140 – 150 5
150–160 10
160–170 20
170–180 09
180–190 06
190–200 02
Draw a histogram for the data above.
40.Prove that the angle subtended by an are at the centre is double the angle subtended by it at any point
on the remaining part of the circle.
* Additional Questions