TBSE Class 10 Model Question Paper 2021 Maths Standard

Model Question
Class - X : Mathematics (Standard) : 80 Marks : 2020-2021
!Ó˲yàÈüÈܲ : ≤Ã!ï˛!ê˛ ≤Èϟ¿Ó˚ ÙylÈüÈ1 : 1 x 20 = 20
I) Choose the correct answer : 1x5 1x10
1. k ~Ó˚ ˆÜ˛yl ÙyˆÏlÓ˚ çlƒ kx(x–2)+6 =0 !mâyï˛ §Ù#ܲÓ˚ˆÏîÓ˚ Ó#çmÎ˚ §Ùyl •ˆÏÓ û
a) k= 6 (b) k=2 (c) k = –6 (d) k=4
2. y = 0, y = – 4 ˜ÏÓ˚!áܲ §Ù#ܲÓ˚î Î%àˆÏ°Ó˚ xyˆÏSÈ
a) ~ܲ!ê˛ §Ùyôyl (b) ò%!ê˛ §Ùyôyl (c) x§#Ù §ÇáƒÜ˛ §Ùyôyl(d) ˆÜ˛yˆÏly §Ùyôyl ˆl•z–
3. §Ùyhs˝Ó˚ ≤Ãà!ï˛ 3, 8, 13, 18, .... ~Ó˚ ˆÜ˛yl ˛õò 78 ?
a) 14 (b) 15 (c) 16 (d) 17
4. x x«˛ ˆÌˆÏܲ P(3, –5) !Ó®%Ó˚ ò)Ó˚c å~ܲˆÏÜ˛ä •°
a) 3 b) –5 (c) 5 (d) –3
5. ˆÏÎ ˆày°ˆÏܲÓ˚ xyÎ˚ï˛l 36π ˆ§!Ù3ñ ï˛yÓ˚ Óƒy§yô≈ 刧!Ùä •° û
1
(a) 3 (b) 3 3 (c) 3 3 (d) 3
II) Answer the following questions : 1x5
6. ≤Ãò_ !ã˛ˆÏe PQ •° Ó,ˆÏ_Ó˚ ~ܲ!ê˛ flõ¢≈ܲ ~ÓÇ ∠ QOP = 700 ñ ï˛y•ˆÏ° ∠ QPO = ?

O
) 0 P
70
Q

3
7. ˆòGÎ˚y xyˆÏSÈ sin α ~ÓÇ cos β =0 ñ ï˛y•ˆÏ° β − α ~Ó˚ Ùyl •° û
2

AD 3
8.≤Ãò_ !ã˛ˆÏe DE || BC– Î!ò = ~ÓÇ AE = 2.7 ˆ§!Ù •Î˚ñ ï˛ˆÏÓ EC •° û
BD 2
A
2.7cm

D E

B C

9. P(–6, 10) ~ÓÇ Q (–2, 4) !Ó®%mˆÏÎ˚Ó˚ §ÇˆÏÎyçܲ ˆÓ˚áyLjϢÓ˚ Ùôƒ!Ó®% Î!ò A (m,7) •Î˚ñ ï˛ˆÏÓ m ~Ó˚ Ùyl Ü˛ï˛ ⁄

10. Î!ò ~ܲ!ê˛ Ó˚y!¢ï˛ˆÏ̃Ó˚ àí˛¸ Ùyl 27 ~ÓÇ ÙôƒÙy 33 •° ï˛ˆÏÓ ï˛yÓ˚ §Çáƒyà%Ó˚% Ùyl •ˆÏÓ û
III) Fill in the blanks :
11. Î!ò x –3 myÓ˚y 4x2 – 6x – m §¡õ)î≈ Ó˚)ˆÏ˛õ !Ó˲yçƒ •Î˚ñ ï˛ˆÏÓ m ~Ó˚ Ùyl •ˆÏÓ ______.
12. AOBC •° ~ܲ!ê˛ xyÎ˚ï˛ˆÏ«˛eñ ÎyÓ˚ !ï˛l!ê˛ ¢#£Ï≈!Ó®% •° A (O,–3), O (0,0) ~ÓÇ B (4,0) – ï˛yÓ˚ ܲˆÏî≈Ó˚ ˜òâ≈ƒ •°
______.

D xÌÓy
x xˆÏ«˛Ó˚ í˛z˛õÓ˚ ˆÎ !Ó®%!ê˛ (–6, 0) ~ÓÇ (4, 0) ˆÌˆÏܲ §Ùò)Ó˚Óï˛#≈ ï˛y •° ______–
13. Î!ò (P–1), (P+3), (3P–1) §Ùyhs˝Ó˚ ≤Ãà!ï˛ˆÏï˛ ÌyˆÏܲ ï˛ˆÏÓ P ~Ó˚ Ùyl •ˆÏÓ _____–

○ ○ ○ ○ ○ ○ ○ ○ ○ ○
14. ≤Ãò_ âl Ó›!ê˛Ó˚ §Ù@˝Ã ï˛ˆÏ°Ó˚ ˆ«˛eÊ˛° •° ______–
15. Î!ò sin θ − cos θ = 3 cos θ (θ ≠ 90) •Î˚ñ l
ï˛ˆÏÓ tan θ ~Ó˚ Ùyl •ˆÏÓ _____–
IV) Answer to the following questions r
16. x2 – 6x+2=0 §Ù#ܲÓ˚ˆÏîÓ˚ Ó#çmˆÏÎ˚Ó˚ §Ù!T˛ !lî≈Î˚ ܲˆÏÓ˚y–
17. y xˆÏ«˛Ó˚ §yˆÏ˛õˆÏ«˛ (3, –5) !Ó®%Ó˚ ≤Ã!ï˛!ӈϡ∫Ó˚ fiÌylyAܲ !lî≈Î˚ ܲˆÏÓ˚y–
18. ~ܲ!ê˛ ˆày°ˆÏܲÓ˚ ÓƒÎ˚ 14ˆ§!Ù– ~!ê˛Ó˚ ˛õ,¤˛ï˛ˆÏ°Ó˚ ˆ«˛eÊ˛° !lî≈Î˚ ܲˆÏÓ˚y–
xÌÓy
~ܲ!ê˛ xô≈ ˆày°ˆÏܲÓ˚ Óƒy§ 4.2 ˆ§!Ù– ~!ê˛Ó˚ xyÎ˚ï˛l !lî≈Î˚ ܲˆÏÓ˚y–
19. ≤Ãò_ !ã˛ˆÏe AB || CD, AB=4 ˆ§!Ùñ AE=3 ˆ§!Ù ~ÓÇ CD=10 ˆ§!Ù– DE ~Ó˚ ˜òâ≈ƒ !lî≈Î˚ ܲˆÏÓ˚y–

D

B
→

E
→

A C

20. ˛Î!ò ~ܲ!ê˛ âê˛ly E âê˛yÓ˚ §Ω˛yÓly 0.023 •Î˚ ï˛ˆÏÓ P (E) !lî≈Î˚ ܲˆÏÓ˚y–
!Ó˲yàÈüÈá : Each Question Carries 2 Marks : 2x6=12
21. k ~Ó˚ Ùyl !lî≈Î˚ ܲˆÏÓ˚y ÎyÓ˚ çlƒ ˜Ó˚!áܲ §Ù#ܲÓ˚î ï˛sf 2x+5y=3 ~ÓÇ (k+1)x + 2(k+2)y=2k ~Ó˚ x§#Ù §ÇáƒÜ˛
§Ùyôyl ÌyˆÏܲ–
1 1
22. Ó•%˛õò Ó˚y!¢Ùy°y 2y2 + 7y + 5 ~Ó˚ ¢)lƒmÎ α ~ÓÇ β •ˆÏ° +
α β ~Ó˚ Ùyl !lî≈Î˚ ܲˆÏÓ˚y–
xÌÓy
Î!ò Ó•%˛õò Ó˚y!¢Ùy°y 5x2+13x–p ~Ó˚ ~ܲ!ê˛ ¢)lƒ x˛õÓ˚!ê˛Ó˚ xˆÏlylƒÜ˛ •Î˚ñ ï˛ˆÏÓ p !lî≈Î˚ ܲˆÏÓ˚y–
23. ~ܲ!ê˛ !ÙlyˆÏÓ˚Ó˚ (AB) ˛õyòˆÏòˆÏ¢ ˆÌˆÏܲ 30 !Ùê˛yÓ˚ ò)Ó˚Óï˛#≈ ˆÜ˛yˆÏly !Óò%ƒÍ (P) ˆÏ̈Ïܲ !ÙlyˆÏÓ˚Ó˚ ¢#ˆÏ£Ï≈Ó˚ í˛zߨ!ï˛ ˆÜ˛yî 300–
!ÙlyˆÏÓ˚Ó˚ í˛zFã˛ï˛y !lî≈Î˚ ܲˆÏÓ˚y–
A

0
) 30
P B
30 !Ù

24. ~ܲ!ê˛ !¢¢%Ó˚ ܲyˆÏSÈ ~ܲ!ê˛ SÈE˛y xyˆÏSÈñ ÎyÓ˚ SÈÎ˚!ê˛ ï˛ˆÏ° !l¡¨!°!áï˛ x«˛Ó˚à%ˆÏ°y Ó˚ˆÏÎ˚ˆÏSÈ ı

A B C D E A

SÈE˛y!ê˛ ~ܲÓyÓ˚ !lˆÏ«˛˛õ ܲÓ˚y •°– ï˛y•ˆÏ° (i) A ~ÓÇ (ii) D ˛õyGÎ˚yÓ˚ §Ω˛yÓly ܲ# •ˆÏÓ⁄
D xÌÓy
í˛z_ÙÓ˚)ˆÏ˛õ ˆÙ¢yˆÏly 52!ê˛ ï˛yˆÏ§Ó˚ ~ܲ!ê˛ ˛õƒyˆÏÜ˛ê˛ ˆÌˆÏܲ ~ܲ!ê˛ ï˛y§ ˆï˛y°y •°– ˆï˛y°y ï˛y§!ê˛ (i) •zflÒyÓl Óy ~ܲ!ê˛ ˆê˛E˛y
(ii) ~ܲ!ê˛ Ü˛yˆÏ°y §yˆÏ•Ó •GÎ˚yÓ˚ §Ω˛yÓly !lî≈Î˚ ܲˆÏÓ˚y–

25. x2 – 7x +10 Ó•%˛õò Ó˚y!¢Ùy°yÓ˚ ¢)lƒà%ˆÏ°y !lî≈Î˚ ܲˆÏÓ˚y–
26. ≤ÃÙyî ܲˆÏÓ˚y ˆÎñ tan 100. tan750. tan 150.tan800=1˛
!Ó˲yàÈüÈà / Each Question Carries 3 Marks : 3x8=24
27. ˆÎyàÊ˛° !lî≈Î˚ ܲˆÏÓ˚y 34 + 32+30+...+10
28. A (15,5) ~ÓÇ B (9,20) !Ó®%mˆÏÎ˚Ó˚ §ÇˆÏÎyçܲ ˆÓ˚áyÇ¢ˆÏܲ P(11,y) !Ó®%!ê˛ ˆÎ xl%˛õyˆÏï˛ !Ó˲=˛ ܲˆÏÓ˚ ï˛y !lî≈Î˚ ܲˆÏÓ˚y–
y ~Ó˚ ÙylG !lî≈Î˚ ܲˆÏÓ˚y–

3 1
29. Ùyl !lî≈Î˚ ܲˆÏÓ˚y Èü/ Cot2300 – 2cos2300– sec2450+ cosec2300
4 4
xÌÓy
1
Î!ò tan (A+B)= 3 ~ÓÇ tan (A–B) = •Î˚ñ ˆÎáyˆÏl 00 < A + B < 900 G A > B ï˛ˆÏÓñ A ~ÓÇ B ~Ó˚ Ùyl !lî≈Î˚
3
ܲˆÏÓ˚y–
30. 14 ˆÏ§!Ù Óƒy§yô≈ !Ó!¢T˛ ~ܲ!ê˛ Ó,ˆÏ_Ó˚ ~ܲ!ê˛ çƒy Ó,ˆÏ_Ó˚ ˆÜ˛ˆÏw §ÙˆÏܲyî í˛zͲõߨ ܲˆÏÓ˚– Ó,_!ê˛Ó˚ xl%Ó˚)˛õ í˛z˛õÓ,_yLjϢÓ˚ ˆ«˛e
Ê˛° !lî≈Î˚ ܲˆÏÓ˚y–
xÌÓy
~ܲ!ê˛ â!í˛¸Ó˚ !Ù!lˆÏê˛Ó˚ ÜÑ˛yê˛y!ê˛ 12 ˆ§!Ù °¡∫y– 35 !Ù!lê˛ §ÙˆÏÎ˚ !Ù!lˆÏê˛Ó˚ ÜÑ˛yê˛y!ê˛ â!í˛¸Ó˚ §¡ø%á ˲yˆÏàÓ˚ ˆÎ ˆ«˛e x!ï˛Ü˛Ù ܲˆÏÓ˚ ï˛yÓ˚
ˆ«˛eÊ˛° !lî≈Î˚ ܲˆÏÓ˚y–
31. §Ùyôyl ܲˆÏÓ˚y / 2 x2 + 7 x + 5 2 = 0
D xÌÓy
1 1
− = 3, x ≠ 0, 2
x x−2

32. ~ܲ!ê˛ ˆá°yÎ˚ ~ܲ ê˛yܲyÓ˚ Ù%oy 3 ÓyÓ˚ ê˛§‰ ܲÓ˚y •° ~ÓÇ ≤Ã!ï˛ ˆ«˛ˆÏe ï˛yÓ˚ Ê˛°yÊ˛° !°!˛õÓÂô ܲÓ˚y •Î˚– Ó˚yç% !çï˛ˆÏÓ Î!ò ê˛§‰
ܲÓ˚y ≤Ã!ï˛!ê˛ Ê˛° ~ܲ•z •Î˚– Ó˚yç%Ó˚ ˆá°yˆÏï˛ •yÓ˚yÓ˚ §Ω˛yÓly !lî≈Î˚ ܲˆÏÓ˚y– ˆá°yÓ˚ §Ü˛° §Ω˛yÓƒ Ê˛°yÊ˛°à%ˆÏ°yG ˆ°ˆÏáy–

33. !l¡¨!°!áï˛ Ó˚y!¢ï˛ˆÏ̃Ó˚ §Çáƒyà%Ó˚% Ùyl !lî≈Î˚ ܲˆÏÓ˚y /

ˆ◊!î!Ó˲yà 0-20 20-40 40-6 60-80 80-100 100-120 120-140

˛õ!Ó˚§Çáƒy 6 8 10 12 6 5 3

34.150 !Ùê˛yÓ˚ ÓƒÓôyˆÏl xÓ!fiÌï˛ ò%!ê˛ hflψÏΩ˛Ó˚ ~ܲ!ê˛Ó˚ í˛zFã˛ï˛y x˛õÓ˚!ê˛Ó˚ !mà%l ~ÓÇ ï˛yˆÏòÓ˚ ˛õyòˆÏòˆÏ¢Ó˚ §ÇˆÏÎyçܲ ˆÓ˚áyLjϢÓ˚
G˛õÓ˚ xÓ!fiÌï˛ ˆÜ˛yˆÏly !Ó®% ˆÌˆÏܲ í˛zFã˛ï˛Ó˚ hflÏΩ˛ G x˛õÓ˚ hflψÏΩ˛Ó˚ í˛zߨ!ï˛ˆÏܲyî ÎÌyܲˆÏÙ 600 ~ÓÇ 300– hflÏΩ˛ ò%!ê˛Ó˚ í˛zFã˛ï˛y !lî≈Î˚
ܲˆÏÓ˚y–
!Ó˲yàÈüÈâ : Each Question Carries 4 Marks : 4x6=24
3
35. §Ùyôyl ܲˆÏÓ˚y / 2 x − =9
y
7
3x − =2 y ≠0
y

D xÌÓy
l#ˆÏã˛Ó˚ §Ù#ܲÓ˚î ï˛ˆÏsfÓ˚ ˜°!áܲ Ó˚)ˆÏ˛õ 到á!ã˛ˆÏeÓ˚ §y•yˆÏÎƒä §Ùyôyl ܲˆÏÓ˚y /
3x+2y=4
2x–3y=7
36. ≤ÃÙyî ܲˆÏÓ˚y ˆÎñ Ó!•ıfiÌ ˆÜ˛yˆÏly !Ó®% ˆÌˆÏܲ Ó,ˆÏ_Ó˚ í˛z˛õÓ˚ x!AÜ˛ï˛ flõ¢≈ܲà%ˆÏ°yÓ˚ ˜òâ≈ƒ §Ùyl ~ÓÇ ~Ó˚y ˆÜ˛ˆÏw §Ùyl ˆÜ˛yî
í˛zͲõߨ ܲˆÏÓ˚–
37. 4 ˆ§!Ù Óƒy§yô≈ !Ó!¢T˛ Ó,ˆÏ_Ó˚ Ó!•ıfiÌ ˆÜ˛yˆÏly !Ó®% ˆÌˆÏܲ ò%!ê˛ flõ¢≈ܲ xAܲl ܲˆÏÓ˚yñ ÎyÓ˚y ˛õÓ˚flõÓ˚ 600 ˆÜ˛yˆÏî lï˛– å¢%ô%Ùye
xAܲl ≤Ãîy°# !°áˆÏÓñ ≤ÃÙyî !òˆÏï˛ •ˆÏÓ ly– xAܲl !ã˛•´à%ˆÏ°y §%flõT˛ •ˆÏï˛ •ˆÏÓ–ä
38. ∆ ABC ~Ó˚ Óy•%mÎ˚ AB G BC ~ÓÇ ÙôƒÙy AD ÎÌyܲˆÏÙ PQR ~Ó˚ Óy•%mÎ˚ PQ G QR ~ÓÇ ÙôƒÙy PM ~Ó˚ §yˆÏÌ
§Ùyl%˛õy!ï˛Ü˛– ˆòáyG ˆÎ ∆ ABC ∼ ∆ PQR P

A

B C R
D Q
M

D xÌÓy
∆ ABC ~Ó˚ ∠ BAC §ÙˆÏܲyî ~ÓÇ BL G CM •° ò%!ê˛ ÙôƒÙy– A
≤ÃÙyÙ Ü˛ˆÏÓ˚y ˆÎñ 4 (BL2+CM2)= 5BC2
L
M

B C

39. ~ܲ!ê˛ ÊÑ˛y˛õy xô≈ˆÏày°ˆÏܲÓ˚ G˛õÓ˚ §ÙÓƒy§yô≈ §¡õߨ ÊÑ˛y˛õy ˆã˛y. Ó!§ˆÏÎ˚ ~ܲ!ê˛ ˛õye ˜ï˛!Ó˚ ܲÓ˚y •ˆÏÎ˚ˆÏSÈ – Î!ò xô≈ˆÏày°Ü˛!ê˛Ó˚
Óƒy§ 14 ˆ§!Ù ~ÓÇ §¡õ)î≈ ˛õyˆÏeÓ˚ í˛zFã˛ï˛y 13 ˆ§!Ù •Î˚ñ ï˛ˆÏÓ ˛õye!ê˛Ó˚ xyÎ˚ï˛l ~ÓÇ ˆË˛ï˛ˆÏÓ˚Ó˚ ˛õ,¤˛ï˛ˆÏ°Ó˚ ˆ«˛eÊ˛° !lî≈Î˚ ܲˆÏÓ˚y–
D xÌÓy
12 ˆ§!Ù í˛zFã˛ï˛y G 5ˆ§!Ù Ë)˛!ÙÓ˚ Óƒy§yô≈ !Ó!¢T˛ ~ܲ!ê˛ !lˆÏÓ˚ê˛ °¡∫Ó,_yܲyÓ˚ ˆã˛y. ˆÌˆÏܲ §Ù í˛zFã˛ï˛y G §ÙË)˛!Ù Óƒy§yô≈ !Ó!¢T˛
~ܲ!ê˛ !lˆÏÓ˚ê˛ ¢AÜ%˛ ˆÜÑ˛ˆÏê˛ §!Ó˚ˆÏÎ˚ ˆlGÎ˚y •°– xÓ!¢T˛ âl Ó›!ê˛Ó˚ xyÎ˚ï˛l ~ÓÇ §Ù@˝Ã ˛õ,¤˛ï˛ˆÏ°Ó˚ ˆ«˛eÊ˛° !lî≈Î˚ ܲˆÏÓ˚y–
[ π = 3.14]
40. !l¡¨!°!áï˛ ˛õ!Ó˚§Çáƒy !Ó˲yçl!ê˛Ó˚ ÙôƒÜ˛ Óy àí˛¸Ùyl 57.6 ~ÓÇ ˆÙyê˛ ˛õ!Ó˚§Çáƒy 50–

ˆ◊!î!Ó˲yà 0–20 20–40 40–60 60–80 80–100 100–120

˛õ!Ó˚§Çáƒy 7 f1 12 f2 8 5

f1~ÓÇ f2 !lî≈Î˚ ܲˆÏÓ˚y–

D x!ï˛!Ó˚=˛ ≤ß¿yÓ°#

Model Question
Class - X : Mathematics (Standard) : 80 Marks : 2020-2021
Group-A : Each Question Carries È1 Mark : 1 x 20 = 20
I. Choose the correct answer : 1x5
1. The value of k for which the quadratic equation kx(x–2)+6 =0 has equal roots
a) k= 6 (b) k=2 (c) k = –6 (d) k=4
2. The pair of linear equations y = 0, y = – 4 has
a) one solution (b) two solutions (c) infinitely many solutions (d) no solution.
3. Which term of the A P : 3, 8, 13, 18, .... is 78 ?
a) 14 (b) 15 (c) 16 (d) 17
4. The distance of the point P(3, –5) from x-axis (in units) is
a) 3 b) –5 (c) 5 (d) –3
5. The radius of a sphere (in cm) whose volume is 36π cm3ñ is
1
(a) 3 (b) 3 3 (c) 3 3 (d) 3
II. Answer the following question : 1x5
6. In the given figure PQ is a tangent to the circle and ∠ QOP = 700
then ∠ QPO = ?

O
) 0 P
70
Q

3
7. Given than È sin α = and cos β =0 ñ then the value of β − α is
2

AD 3
8. In the given figure DE || BC . If = and AE = 2.7 cm,
BD 2
then EC is equal to ______. A
2.7cm

D E

B C
9. If A (m,7) is the mid point of the line segment joining the points P(–6, 10) and Q (–2, 4) then the
value of m is ________.

10. If the mean of a data is 27 and its median is 33 then the mode is _______.
III. Fill in the blanks :
11.If 4x2 – 6x – m is exactly divisible by x – 3, then the value of m is_____.
12. AOBC is a rectangle whose three vertices are A (O,–3), O (0,0) and B (4,0) – The length of its
diagonel is ______.

* OR
The point on the x-axis which is equdistant from (–6, 0) and (4, 0) is ______–
13. If (P–1), (P+3), (3P–1) are in AP, then P is equal to _____–

○ ○ ○ ○ ○ ○ ○ ○ ○ ○
14. The total surface area of the given solid figure is ______– l

r
15. If sin θ − cos θ = 3 cos θ , (θ ≠ 900 )
then the value of tan θ is _____–
IV. Answer to the following questions
16. Find the sum of the roots of the equation x2 – 6x+2=0
17. Find the coordinate of the image of a point (3, –5) with respect to the Y-axis.
18. The diameter of a sphere is 14 cm. Find its surface area.
* OR
The diameter of a hemisphere is 4.2 cm. Find its valume.
19. In the adjoining figure, AB || CD, AB=4 cm, AE=3 cm and CD=10 cm. Find the value of DE.

D

B
→

E
→

A C

20. ˛If the probability of an event E happening is 0.023, then find P (E) .
Group- B : Each Question Carries 2 Marks : 2x6=12
21. Find the value of k for which the system of the linear equations 2x+5y=3 and (k+1)x + 2(k+2)y=2k
will have infinite number of soultion.
1 1
22. If α and β are the zeros of the polynomial 2y2 + 7y + 5, then find the value +
α β.
OR
If one zero of the polynomial 5x2+13x–p is reciprocal of the other, then find p.
23. In the given figure the angle of elevation of the top of a tower (AB) ˛from a point (P) on the ground,
which is 30 m away from the foot of the tower is 300. Find the height of the tower.
A

0
) 30
P B
30m

24. A child has a die whose 6 faces show the letters given below :

A B C D E A

The die is thrown once. What is the probability of getting (i)A, (ii) D ?
* OR
A card in drawn at random from a well shuffled deck of 52 playing cards. Find the probability that
the card drawn is (i) a card of spade or an ace, (ii) a black king.

25. Find the zeros of the polynomial x2 – 7x +10.
26. Prove that tan 100. tan750. tan 150.tan800=1˛
Section- C : Each Question Carries 3 Marks : 3x8=24
27. Find the sum : 34 + 32+30+...+10
28. Find the ratio in which the point P(11,y) divides the line segment joining the points A (15, 5) and
B (9,20). Also find the value of y.

3 1
29. Evaluate / Cot2300 – 2cos2300– sec2450+ cosec2300
4 4
* OR
1
If tan (A+B)= 3 and tan (A–B) = , 00 < A + B < 900 and A > B find the value of A and B.
3
30. A chord of a circle of radius 14cm makes a right angle at the centre. Find the area of the minor
segment of the circle.
* OR
The minute hand of a clock is 12cm long. Find the area of the face of the clock described by the minute
hand in 35 minutes.
31. Slove / 2 x2 + 7 x + 5 2 = 0
OR
1 1
− = 3, x ≠ 0, 2
x x−2

32. A game consists of tossing a one rupee coin three times and noting its outcome each time. Raju
wins if all the three tosses give the same result. Calculate the probability that Raju will loss the game.
Write all the possible outcomes also.

33. Find the mode of the following data :

Class 0-20 20-40 40-60 60-80 80-100 100-120 120-140

Frequency 6 8 10 12 6 5 3

34. Of two towers, 150 meters apart, the height of one is double the other. From a point on the line
joining the bottoms of the two towers, the angle of elevation of the taller tower and the other tower are
found to be 600 and 300 respectively. Find the height of the two towers.
Section D : Each Question Carries 4 Marks : 4x6=24

3
35. Solve / 2x − =9
y
7
3x + =2 , y ≠0
y
OR
Solve the following system of equations graphically :
3x+2y=4
2x–3y=7
36. Prove that the lengths of tangents drawn from an external point to a circle are equal and they
subtand equal angles at the centre.
37. From an exterior point draw a pair of tangents to a circle of radius 4cm, which are inclined to each
other at an angle of 600. (Write only the constructional procedure but no proof is to be given. Traces of
construction must be clear.)
38. Side AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ
and QR and median PM of another triangle PQR. Prove that ∆ ABC ∼ ∆ PQR
P

A

B C R
D Q
M

OR
A

BL and CM are medians of a ∆ ABC,
right angled at A. Prove that 4 (BL2+CM2)= 5BC2 L
M

B C

39. A vessel is in the form of a hemisperical bowl mounted by a hollow cylinder. The diameter of the
hemispere is 14 cm and total height of the vessel is 13cm. Find the capapcity and inner surface area of
the vessel.
* OR
From a solid right circular cylinder with height 12cm and vadius of the base 5cm, a right circular cone
of the same height and the same base radius is removed. Find the volume and total surface area of the
remaining solid. [ π = 3.14 ]
40. The mean of the following frequency distribution is 57.6 and the total number of boservation is 50.

Class 0–20 20–40 40–60 60–80 80–100 100–120

Frequency 7 f1 12 f2 8 5

Find f1and f2 .

* Additional Questions