NIOS Class 10 Question Paper 2022 (Apr) Maths

This Question Paper consists of 36 questions and 12 printed pages + Graph Sheet.
Bg àíZ-nÌ _| 36 àíZ VWm 12 ‘w{ÐV n¥ð h¢ + J«m\$ {eQ>&
Sl. No.

Roll No. Code No.
AZw H « $ _m§ H $ H$mo S > Z§ .
63/OS/1
MATHEMATICS
Set / go Q > A
(J{UV)
(211)
Day and Date of Examination :
(narjm H$m {XZ d {XZm§ H $)
Signature of Invigilators : 1.
({ZarjH$m| Ho $ hñVmja)
2.

General Instructions :

1. Candidate must write his/her Roll Number on the first page of the Question Paper.

2. Please check the Question Paper to verify that the total pages and the total number of questions
contained in the Question Paper are the same as those printed on the top of the first page. Also check
to see that the questions are in sequential order.

3. For the objective type of questions, you have to choose any one of the four alternatives given in the
question i.e. (A), (B), (C) and (D) and indicate your correct answer in the Answer-Book given to you.

4. All the questions including objective type questions are to be answered within the allotted time and
no separate time limit is fixed for answering objective type questions.

5. Making any identification mark in the Answer-Book or writing Roll Number anywhere other than
the specified places will lead to disqualification of the candidate.

6. Write your Question Paper Code No. 63/OS/1, Set - A on the Answer-Book.

7. (a) The Question Paper is in English/Hindi medium only. However, if you wish, you can answer
in any one of the languages listed below :

English, Hindi, Urdu, Punjabi, Bengali, Tamil, Malayalam, Kannada, Telugu, Marathi, Odia,
Gujarati, Konkani, Manipuri, Assamese, Nepali, Kashmiri, Sanskrit and Sindhi.

You are required to indicate the language you have chosen to answer in the box provided in
the Answer-Book.

(b) If you choose to write the answer in the language other than Hindi and English, the
responsibility for any errors/mistakes in understanding the questions will be yours only.

63/OS/1–211-A] G-925 1 [ Contd......

gm_mÝ` AZwXoe :

1. narjmWu àíZ-nÌ Ho$ nhbo n¥ð> na AnZm AZwH«$‘m§H$ Adí¶ {bI|&

2. H¥$n¶m àíZ-nÌ H$mo Om±M b| {H$ àíZ-nÌ Ho$ Hw$b n¥ð>m| VWm àíZm| H$s CVZr hr g§»¶m h¡ {OVZr àW‘ n¥ð> Ho$ g~go D$na N>nr h¡& Bg
~mV H$s Om±M ^r H$a b| {H$ àíZ H«${‘H$ ê$n ‘| h¢&

3. dñVw{Zð> àíZm| _| AmnH$mo Mma {dH$ënm| (A), (B), (C) VWm (D) _| go H$moB© EH$ CÎma MwZZm h¡ VWm Xr JB© CÎma-nwpñVH$m _| Amn
ghr CÎma {b{IE&

4. dñVw{Zð> àíZm| Ho$ gmW-gmW g^r àíZm| Ho$ CÎma {ZYm©[aV Ad{Y Ho$ ^rVa hr XoZo h¢& dñVw{Zð> àíZm| Ho$ {bE AbJ go g_` Zht {X`m
OmEJm&

5. CÎma-nwpñVH$m ‘| nhMmZ-{M• ~ZmZo AWdm {Z{X©ï> ñWmZm| Ho$ A{V[aº$ H$ht ^r AZwH«$‘m§H$ {bIZo na narjmWu H$mo A¶mo½¶ R>ham¶m
Om¶oJm&

6. AnZr CÎma-nwpñVH$m na àíZ-nÌ H$r H$moS> g§»¶m. 63/OS/1, goQ> - A {bI|&

7. (H$) àíZ-nÌ Ho$db A§J«oOr/qhXr ‘mܶ‘ ‘| h¡& {’$a ^r, ¶{X Amn Mmh| Vmo ZrMo Xr JB© {H$gr EH$ ^mfm ‘| CÎma Xo gH$Vo h¢ :
A§J«oOr, qhXr, CXÿ©, n§Om~r, ~§Jbm, V{‘b, ‘b¶mb‘, H$ÝZ‹S>, VobwJy, ‘amR>r, C{‹S>¶m, JwOamVr, H$m|H$Ur, ‘{Unwar, Ag{‘¶m,
Zonmbr, H$í‘rar, g§ñH¥$V Am¡a qgYr&

H¥$n¶m CÎma-nwpñVH$m ‘| {XE JE ~m°³g ‘| {bI| {H$ Amn {H$g ^mfm ‘| CÎma {bI aho h¢&

(I) ¶{X Amn qhXr Ed§ A§J«oOr Ho$ A{V[a³V {H$gr Aݶ ^mfm ‘| CÎma {bIVo h¢, Vmo àíZm| H$mo g‘PZo ‘| hmoZo dmbr Ìw{Q>¶m|/Jb{V¶m|
H$s {Oå‘oXmar Ho$db AmnH$s hmoJr&

63/OS/1–211-A] G-925 2 [ Contd......

MATHEMATICS
(J{UV)
(211)
Time : 2 ½ Hours] [Maximum Marks : 85
g_` : 2 ½ KÊQ>o] [nyUmªH$ : 85
Note : (1) Question Numbers (1-10) are Multiple Choice Questions. Each question carries one mark. For each
question, four alternative choices, (A), (B), (C) and (D) are provided, of which only one is correct.
You have to select the correct alternative and indicate it in the answer-book provided to you by
writing (A), (B), (C) or (D) as the case may be. Q. No. 11 to 15 also carry one mark each.
(2) Question Numbers (16-25) carry 2 marks each.
(3) Question Numbers (26-33) carry 4 marks each.
(4) Question Numbers (34-36) carry 6 marks each.
(5) All questions are compulsory.

{ZX} e : (1) àíZ g§»¶m 1 go 10 VH$ ~hþ{dH$ënr¶ àíZ (Multiple Choice Questions) h¢& à˶oH$ àíZ EH$ A§H$ H$m h¡& à˶oH$ àíZ ‘|
Mma {dH$ën (A), (B), (C) VWm (D) {XE J`o h¢, {OZ‘| go Ho$db EH$ ghr h¡& AmnH$mo ghr {dH$ën MwZZm h¡ VWm àË`oH$ àíZ Ho$ CÎma
AnZr CÎma-nwpñVH$m ‘| (A), (B), (C) AWdm (D) O¡gr ^r pñW{V hmo, {bIH$a Xem©Zm h¡& àíZ g§»`m 11 go 15 ^r EH$ A§H$ H$m h¡&
(2) àíZ g§»¶m (16 go 25) VH$ à˶oH$ àíZ Ho 2 A§H$ h¢&
(3) àíZ g§»¶m (26 go 33) VH$ à˶oH$ àíZ Ho 4 A§H$ h¢&
(4) àíZ g§»¶m (34 go 36) VH$ à˶oH$ àíZ Ho 6 A§H$ h¢&
(5) g^r àíZ A{Zdm¶© h¢&

1. Which of the following is a rational expression? [1]

{ZåZ _| go H$m¡Z gm EH$ n[a_o` ì`§OH$ h¡?

x2 + 2 y 2
(A) (B) 8 x + 6 y
3x − y

(C) 2 − 5 (D) 2π

63/OS/1–211-A] G-925 3 [ Contd......

2. Which of the following is a pure surd? [1]
{ZåZ _| go H$m¡Z gr EH$ ewÕ H$aUr h¡?
(A) 3 27 (B) 32
(C) 2 22 (D) 25

3. A zero of the polynomial x 2 − 3 x − 10 is [1]

~hþnX x 2 − 3x − 10 H$m EH$ ewÝ`H$ h¡ …
(A) 10 (B) – 2
(C) 3 (D) 4

4. The point ( −5,2 ) lie in the quadrant [1]

q~Xþ ( −5,2 ) {Og MVwWmªe _| pñWV h¡, dh h¡
(A) I (B) II
(C) III (D) IV

5. Two circles are always [1]
(A) Congruent
(B) Neither similar nor congruent
(C) Always similar but may not congruent
(D) Similar and congruent
Xmo d¥Îm gXm
(A) gdmªJg_ hmoVo h¢
(B) Z hr g_ê$n Am¡a Z hr gdmªJg_ hmoVo h¢&
(C) g_ê$n hmoVo h¢ naÝVw gdmªJg_ Zht ^r hmo gH$Vo h¢&
(D) g_ê$n hmoVo h¢ VWm gdmªJg_ hmoVo h¢&

63/OS/1–211-A] G-925 4 [ Contd......

6. The ratio of areas of two similar triangles is 25:16, then the ratio of their
corresponding sides is [1]
Xmo g_ê$n {Ì^wOm| Ho$ joÌ\$bm| H$m AZwnmV 25:16 h¡, Vmo CZH$s g§JV ^wOmAm| H$m AZwnmV h¡ …
(A) 625:256 (B) 4:5
(C) 5:4 (D) 16:25

7. The value of cos 2 75° − sin 2 15° is [1]
cos 2 75° − sin 2 15° H$m _mZ h¡
(A) 1 (B) 2

3
(C) (D) 0
2

1 1
8. sin 2 A − 2
+ cos 2 A + is equal to [1]
cos A cot 2 A
1 1
sin 2 A − + cos 2
A + ~am~a h¡
cos 2 A cot 2 A
(A) 1 (B) cos 2 A
(C) 0 (D) sin 2 A

9. The area of an equilateral triangle each of whose sides is of length 2 m is [1]
(A) 4 3 m2 (B) 2 3 m2

(C) 4 m2 (D) 3 m2
EH$ g_~mhþ {Ì^wO {OgH$s àË`oH$ ^wOm H$s b§~mB© 2 _r h¡, H$m joÌ\$b h¡ …
(A) 4 3 dJ© _r (B) 2 3 dJ© _r

(C) 4 dJ© _r (D) 3 dJ© _r

63/OS/1–211-A] G-925 5 [ Contd......

10. 0.025 in terms of rate percent is [1]

Xa à{VeV Ho$ ê$n _| 0.025 ~am~a h¡ …

(A) 25%

(B) 2.5%

(C) 0.25%

(D) 37½%

11. Simplify the following [1]

{ZåZ H$mo gab H$s{OE …

3 6
2  4 
  ÷ 
 11   22 

12. The total simple interest of a principal P at r% in n years is H xnr . Find the
25
principal (P). [1]

{H$gr _ybYZ P H$m r% Xa go n dfm] Ho$ {bE ã`mO H xnr h¡, Vmo _ybYZ (P) kmV H$s{OE&
25

13. If the perimeter of a closed semicircle is 36 cm, then find its radius. [1]

EH$ ~ÝX AY©d¥Îm H$s n[a_mn 36 go_r h¡, Vmo BgH$s {ÌÁ`m kmV H$s{OE&

63/OS/1–211-A] G-925 6 [ Contd......

14. In the given figure, sides QP and RQ of ΔPQR are produced to points S & T
respectively. If ∠ SPR = 135° and ∠ PQT = 110 ° , find ∠ PRQ . [1]
Xr JB© AmH¥${V _| ΔPQR H$s ^wOmAm| QP VWm RQ H$mo H«$_e… {~ÝXþAm| S VWm T VH$ ~‹T>m`m J`m h¡&
`{X ∠ SPR = 135° VWm ∠ PQT = 110 ° h¡, Vmo ∠ PRQ kmV H$s{OE&

15. In the given figure, if PT is tangent to the circle with centre O and ∠ TPO = 25° ,
then find x. [1]
Xr JB© AmH¥${V _|, `{X PT H|$Ð O dmbo d¥Îm H$s ñne© aoIm h¡ VWm ∠ TPO = 25° h¡, Vmo x kmV H$s{OE&

5
16. Rationalise the denominator of . [2]
3− 5
5
Ho$ ha H$m n[a_o`H$aU H$s{OE&
3− 5

17. If sin ( A + B ) = 1, cos ( A − B ) = 1 , where 0° ≤ ( A + B ) ≤ 90° and A > B, find A and B.
[2]
`{X sin ( A + B ) = 1, cos ( A − B ) = 1 h¡, Ohm± 0° ≤ ( A + B ) ≤ 90° VWm A > B h¡, Vmo A VWm B
kmV H$s{OE&

63/OS/1–211-A] G-925 7 [ Contd......

18. Evaluate : [2]
_mZ kmV H$s{OE …
cos 47° ⋅ cot 79° − sin 43° ⋅ tan11°

19. Find the volume of a right circular cylinder whose height is 13.5 cm and radius
of the base is 7 cm. [2]
13.5 go_r D±$MmB© VWm 7 go_r AmYma {ÌÁ`m Ho$ b§~d¥Îmr` ~obZ H$m Am`VZ kmV H$s{OE&

2
20. Rehana got rd the answers correct in an examination. What percent of her
3
answers were correct? [2]

2
aohmZm Zo EH$ narjm _| àíZm| Ho$ ghr CÎma {XE& CgHo$ {H$VZo à{VeV CÎma ghr Wo?
3

21. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord
of the larger circle which touches the smaller circle. [2]
Xmo g§H|$Ðr` d¥Îmm| H$s {ÌÁ`mE± 5 go_r VWm 3 go_r h¢& ~‹S>o d¥Îm H$s Cg Ordm H$s b§~mB© kmV H$s{OE Omo N>moQ>o d¥V
H$mo ñne© H$aVr h¡&

22. Find the value of x for which DE || AB in the given figure. [2]

Xr JB© AmH¥${V _| DE || AB h¡ Vmo x H$m _mZ kmV H$s{OE&

63/OS/1–211-A] G-925 8 [ Contd......

23. ABCD is a rhombus in which ∠ ABC = 68° . Find the measure of ∠ ACD . [2]
EH$ g_MVw^w©O ABCD _| ∠ ABC = 68° h¡, Vmo ∠ ACD H$s _mn kmV H$s{OE&

24. If two different dice are rolled together, then find the probability of getting an
even number on both dice. [2]
Xmo {^Þ nmgm| H$mo EH$ gmW CN>mbm J`m& XmoZm| nmgm| na g_g§»`m AmZo H$s àm{`H$Vm kmV H$s{OE&

25. If Mean of a grouped data is 27 and Mode is 45, then what is the value of
Median? [2]
`{X {H$Ýht dJuH¥$V Am§H$‹S>mo| H$m _mÜ` 27 VWm ~hþbH$ 45 h¡, Vmo BZHo$ _mÜ`H$ H$m _mZ Š`m h¡?

26. How many terms of the AP: 9, 17, 25, ---- must be taken to give a sum of 636?
[4]
g_m§Va lo‹T>r (AP): 9, 17, 25, ---- Ho$ {H$VZo nXm| H$m `moJ 636 h¡?

27. Solve the following system of linear equations graphically : [4]
{ZåZ a¡{IH$ g_rH$aU {ZH$m` H$mo AmboI Ûmam hb H$s{OE …
x + y = 6; x − y = 4

OR/AWdm
(For visually impaired learners only)
Solve the following system of linear equations:

3 x − y = 5; 4 x + 3 y = 11

(Ñ{ï> ~m{YV {dÚm{W©`m| Ho$ {bE àíZ 27 Ho$ ñWmZ na àíZ)
{ZåZ a¡{IH$ g_rH$aU {ZH$m` H$mo hb H$s{OE …
3 x − y = 5; 4 x + 3 y = 11

63/OS/1–211-A] G-925 9 [ Contd......

28. Draw a right ΔABC in which BC = 12 cm, AB = 5 cm and ∠ B = 90° . Construct
2
a triangle similar to it and of scale factor . [4]
3

EH$ g_H$moU {Ì^wO ABC It{ME {Og_| BC = 12 go_r, AB = 5 go_r VWm ∠ B = 90° h¡& A~ Bg
2
{Ì^wO Ho$ g_ê$n EH$ AÝ` {Ì^wO H$s aMZm H$s{OE {OgH$m ñHo$b JwUH$ h¡&
3
OR/AWdm
(For visually impaired learners only)
Write the steps of the above construction.
(Ñ{ï> ~m{YV {dÚm{W©`m| Ho$ {bE d¡H$pënV àíZ)
Cnamoº$ aMZm Ho$ nX (MaU) {b{IE&

29. Find the value of m if the co-ordinates (3, 1), (–2, –3) and (8, 2m) are collinear.
[4]
`{X q~Xþ (3, 1), (–2, –3) VWm (8, 2m) g§ aoI h¡ Vmo m H$m _mZ kmV H$s{OE&

30. Marks out of 100 obtained by 50 students of class X in Mathematics are given.
[4]
Marks 70-75 75-80 80-85 85-90 90-95 95-100
Number of students 12 18 6 7 5 2
Draw a frequency polygon for the data.
H$jm X Ho$ 50 {dÚm{W©`m| Ûmam J{UV H$s narjm _| 100 _| go àmá A§H$ {ZåZ gm[aUr _| {XE JE h¢&
àmám§H$ 70-75 75-80 80-85 85-90 90-95 95-100
{dÚm{W©`m| H$s g§»`m 12 18 6 7 5 2
Cnamoº$ Am§H$S>m| Ho$ {bE EH$ ~ma§~maVm ~hþ^wO It{ME&
OR/AWdm

63/OS/1–211-A] G-925 10 [ Contd......

(For visually impaired learners only)
Find the mean of the following distribution.
Class 0-6 6-12 12-18 18-24 24-30
Frequency 5 4 1 6 4
(Ñ{ï> ~m{YV {dÚm{W©`m| Ho$ {bE d¡H$pënV àíZ)
{ZåZ ~ma§~maVm ~§Q>Z H$m _mÜ` kmV H$s{OE …
dJ© 0-6 6-12 12-18 18-24 24-30
~ma§~maVm 5 4 1 6 4

31. One card is drawn at random from a well-shuffled deck of 52 cards. Find the
probability of getting [4]
(i) A king of red colour.
(ii) The queen of diamonds.
52 nÎmm| H$s AÀN>r àH$ma go \|$Q>r JB© Vme H$s JÈ>r _| go `mÑÀN>`m EH$ nÎmm {ZH$mbm J`m& {ZåZ Ho$ AmZo H$s
àm{`H$Vm kmV H$s{OE …
(i) bmb a§J H$m ~mXemh&
(ii) BªQ> H$s ~oJ_&

32. In an election 75% of the total voters cast their votes. The winning candidates
gets 51% of the cast votes. If the winning person gets 1530 votes, find the total
number of voters in the polling station. [4]
EH$ MwZmd _| Hw$b _VXmVmAm| Ho$ 75% Zo dmoQ> S>mbo& OrVZo dmbo àË`mer H$mo S>mbo JE dmoQ>m| H$m 51% dmoQ>
{_bo `{X OrVZo dmbo H$mo 1530 dmoQ> {_bo hm|, Vmo Cg MwZmd H|$Ð Ho$ Hw$b dmoQ>am| H$s g§»`m kmV H$s{OE&

33. A straight tree is broken due to storm. The broken part is bent in such a way that
the peak of the tree touches the ground at an angle 60º at distance of 2 3 m .
Find the initial height of the tree. [4]
EH$ grYm I‹S>m no‹S> Vy\$mZ AmZo na Qy>Q> H$a {Ja n‹S>m& no‹S> H$m Qy>Q>m hþAm ^mJ Bg àH$ma {Jam {H$ BgH$m erf©
60º Ho$ H$moU na ^y{_ H$mo ñne© H$aZo bJm {OgH$s no‹S> H$s O‹S> go Xÿar 2 3 _r h¡& no‹S> H$s Ama§{^H$ D±$MmB©
kmV H$s{OE&

63/OS/1–211-A] G-925 11 [ Contd......

34. A natural number, when increased by 12, equals 160 times its reciprocal. Find
the number. [6]

EH$ àmH¥$V g§»`m H$mo 12 go ~‹T>mZo na `h AnZo ì`wËH«$_ Ho$ 160 JwUm Ho$ g_mZ hmo OmVr h¡& g§»`m kmV
H$s{OE&

35. A square of side 4 cm is inscribed in a circle. Find the area enclosed between the
 22 
circle and the square.  Use π =  [6]
 7

EH$ d¥Îm Ho$ A§VJ©V EH$ 4 go_r ^wOm H$m dJ© ItMm J`m& d¥Îm VWm dJ© Ho$ ~rM H$m n[a~Õ joÌ\$b kmV
 22 
H$s{OE& π = {b{OE 
 7 

36. Prove that parallelograms on the same or equal bases and between the same
parallels are equal in area. [6]

{gÕ H$s{OE {H$ g_m§Va MVw^w©O, Omo g_mZ `m EH$ hr AmYmam| na hm| Am¡a EH$ hr g_m§Va aoImAm| Ho$ ~rM pñWV
hm|, joÌ\$b _| ~am~a h¢&



63/OS/1–211-A] G-925 12

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This Question Paper consists of 36 questions and 12 printed pages + Graph Sheet.
Bg àíZ-nÌ _| 36 àíZ VWm 12 ‘w{ÐV n¥ð h¢ + J«m\$ {eQ>&
Sl. No.

Roll No. Code No.
AZw H « $ _m§ H $ H$mo S > Z§ .
63/OS/1
MATHEMATICS
Set / go Q > B
(J{UV)
(211)
Day and Date of Examination :
(narjm H$m {XZ d {XZm§ H $)
Signature of Invigilators : 1.
({ZarjH$m| Ho $ hñVmja)
2.

General Instructions :

1. Candidate must write his/her Roll Number on the first page of the Question Paper.

2. Please check the Question Paper to verify that the total pages and the total number of questions
contained in the Question Paper are the same as those printed on the top of the first page. Also check
to see that the questions are in sequential order.

3. For the objective type of questions, you have to choose any one of the four alternatives given in the
question i.e. (A), (B), (C) and (D) and indicate your correct answer in the Answer-Book given to you.

4. All the questions including objective type questions are to be answered within the allotted time and
no separate time limit is fixed for answering objective type questions.

5. Making any identification mark in the Answer-Book or writing Roll Number anywhere other than
the specified places will lead to disqualification of the candidate.

6. Write your Question Paper Code No. 63/OS/1, Set - B on the Answer-Book.

7. (a) The Question Paper is in English/Hindi medium only. However, if you wish, you can answer
in any one of the languages listed below :

English, Hindi, Urdu, Punjabi, Bengali, Tamil, Malayalam, Kannada, Telugu, Marathi, Odia,
Gujarati, Konkani, Manipuri, Assamese, Nepali, Kashmiri, Sanskrit and Sindhi.

You are required to indicate the language you have chosen to answer in the box provided in
the Answer-Book.

(b) If you choose to write the answer in the language other than Hindi and English, the
responsibility for any errors/mistakes in understanding the questions will be yours only.

63/OS/1–211-B] G-925 1 [ Contd......

gm_mÝ` AZwXoe :

1. narjmWu àíZ-nÌ Ho$ nhbo n¥ð> na AnZm AZwH«$‘m§H$ Adí¶ {bI|&

2. H¥$n¶m àíZ-nÌ H$mo Om±M b| {H$ àíZ-nÌ Ho$ Hw$b n¥ð>m| VWm àíZm| H$s CVZr hr g§»¶m h¡ {OVZr àW‘ n¥ð> Ho$ g~go D$na N>nr h¡& Bg
~mV H$s Om±M ^r H$a b| {H$ àíZ H«${‘H$ ê$n ‘| h¢&

3. dñVw{Zð> àíZm| _| AmnH$mo Mma {dH$ënm| (A), (B), (C) VWm (D) _| go H$moB© EH$ CÎma MwZZm h¡ VWm Xr JB© CÎma-nwpñVH$m _| Amn
ghr CÎma {b{IE&

4. dñVw{Zð> àíZm| Ho$ gmW-gmW g^r àíZm| Ho$ CÎma {ZYm©[aV Ad{Y Ho$ ^rVa hr XoZo h¢& dñVw{Zð> àíZm| Ho$ {bE AbJ go g_` Zht {X`m
OmEJm&

5. CÎma-nwpñVH$m ‘| nhMmZ-{M• ~ZmZo AWdm {Z{X©ï> ñWmZm| Ho$ A{V[aº$ H$ht ^r AZwH«$‘m§H$ {bIZo na narjmWu H$mo A¶mo½¶ R>ham¶m
Om¶oJm&

6. AnZr CÎma-nwpñVH$m na àíZ-nÌ H$r H$moS> g§»¶m. 63/OS/1, goQ> - B {bI|&

7. (H$) àíZ-nÌ Ho$db A§J«oOr/qhXr ‘mܶ‘ ‘| h¡& {’$a ^r, ¶{X Amn Mmh| Vmo ZrMo Xr JB© {H$gr EH$ ^mfm ‘| CÎma Xo gH$Vo h¢ :
A§J«oOr, qhXr, CXÿ©, n§Om~r, ~§Jbm, V{‘b, ‘b¶mb‘, H$ÝZ‹S>, VobwJy, ‘amR>r, C{‹S>¶m, JwOamVr, H$m|H$Ur, ‘{Unwar, Ag{‘¶m,
Zonmbr, H$í‘rar, g§ñH¥$V Am¡a qgYr&

H¥$n¶m CÎma-nwpñVH$m ‘| {XE JE ~m°³g ‘| {bI| {H$ Amn {H$g ^mfm ‘| CÎma {bI aho h¢&

(I) ¶{X Amn qhXr Ed§ A§J«oOr Ho$ A{V[a³V {H$gr Aݶ ^mfm ‘| CÎma {bIVo h¢, Vmo àíZm| H$mo g‘PZo ‘| hmoZo dmbr Ìw{Q>¶m|/Jb{V¶m|
H$s {Oå‘oXmar Ho$db AmnH$s hmoJr&

63/OS/1–211-B] G-925 2 [ Contd......

MATHEMATICS
(J{UV)
(211)
Time : 2 ½ Hours] [Maximum Marks : 85
g_` : 2 ½ KÊQ>o] [nyUmªH$ : 85
Note : (1) Question Numbers (1-10) are Multiple Choice Questions. Each question carries one mark. For each
question, four alternative choices, (A), (B), (C) and (D) are provided, of which only one is correct.
You have to select the correct alternative and indicate it in the answer-book provided to you by
writing (A), (B), (C) or (D) as the case may be. Q. No. 11 to 15 also carry one mark each.
(2) Question Numbers (16-25) carry 2 marks each.
(3) Question Numbers (26-33) carry 4 marks each.
(4) Question Numbers (34-36) carry 6 marks each.
(5) All questions are compulsory.

{ZX} e : (1) àíZ g§»¶m 1 go 10 VH$ ~hþ{dH$ënr¶ àíZ (Multiple Choice Questions) h¢& à˶oH$ àíZ EH$ A§H$ H$m h¡& à˶oH$ àíZ ‘|
Mma {dH$ën (A), (B), (C) VWm (D) {XE J`o h¢, {OZ‘| go Ho$db EH$ ghr h¡& AmnH$mo ghr {dH$ën MwZZm h¡ VWm àË`oH$ àíZ Ho$ CÎma
AnZr CÎma-nwpñVH$m ‘| (A), (B), (C) AWdm (D) O¡gr ^r pñW{V hmo, {bIH$a Xem©Zm h¡& àíZ g§»`m 11 go 15 ^r EH$ A§H$ H$m h¡&
(2) àíZ g§»¶m (16 go 25) VH$ à˶oH$ àíZ Ho 2 A§H$ h¢&
(3) àíZ g§»¶m (26 go 33) VH$ à˶oH$ àíZ Ho 4 A§H$ h¢&
(4) àíZ g§»¶m (34 go 36) VH$ à˶oH$ àíZ Ho 6 A§H$ h¢&
(5) g^r àíZ A{Zdm¶© h¢&

1. 0.025 in terms of rate percent is [1]

Xa à{VeV Ho$ ê$n _| 0.025 ~am~a h¡ …

(A) 25%

(B) 2.5%

(C) 0.25%

(D) 37½%

63/OS/1–211-B] G-925 3 [ Contd......

2. The area of an equilateral triangle each of whose sides is of length 2 m is [1]
(A) 4 3 m2 (B) 2 3 m2

(C) 4 m2 (D) 3 m2
EH$ g_~mhþ {Ì^wO {OgH$s àË`oH$ ^wOm H$s b§~mB© 2 _r h¡, H$m joÌ\$b h¡ …
(A) 4 3 dJ© _r (B) 2 3 dJ© _r

(C) 4 dJ© _r (D) 3 dJ© _r

1 1
3. sin 2 A − + cos 2
A + is equal to [1]
cos 2 A cot 2 A

1 1
sin 2 A − + cos 2
A + ~am~a h¡
cos 2 A cot 2 A
(A) 1 (B) cos 2 A
(C) 0 (D) sin 2 A

4. The value of cos 2 75° − sin 2 15° is [1]

cos 2 75° − sin 2 15° H$m _mZ h¡
(A) 1 (B) 2

3
(C) (D) 0
2

5. The lengths of sides of a triangle (in cm) are given below, in which case
construction of a triangle is possible? [1]
{Ì^wO H$s ^wOmAm| H$s b§~mB`m± (go_r _|) ZrMo Xr JB© h¢& {H$g Ho$g _| {Ì^wO H$s aMZm g§^d h¡?
(A) 1, 2, 3 (B) 4, 4, 8
(C) 5, 3, 9 (D) 8, 7, 3

63/OS/1–211-B] G-925 4 [ Contd......

6. The point ( −5,2 ) lie in the quadrant [1]

q~Xþ ( −5,2 ) {Og MVwWmªe _| pñWV h¡, dh h¡
(A) I (B) II
(C) III (D) IV

7. The ratio of areas of two similar triangles is 25:16, then the ratio of their
corresponding sides is [1]
Xmo g_ê$n {Ì^wOm| Ho$ joÌ\$bm| H$m AZwnmV 25:16 h¡, Vmo CZH$s g§JV ^wOmAm| H$m AZwnmV h¡ …
(A) 625:256 (B) 4:5
(C) 5:4 (D) 16:25

8. A zero of the polynomial x 2 − 3 x − 10 is [1]
~hþnX x 2 − 3x − 10 H$m EH$ ewÝ`H$ h¡ …
(A) 10 (B) – 2
(C) 3 (D) 4

9. Which of the following is a pure surd? [1]
{ZåZ _| go H$m¡Z gr EH$ ewÕ H$aUr h¡?
(A) 3 27 (B) 32
(C) 2 22 (D) 25

10. Which of the following is a rational expression? [1]
{ZåZ _| go H$m¡Z gm EH$ n[a_o` ì`§OH$ h¡?

x2 + 2 y 2
(A) (B) 8 x + 6 y
3x − y

(C) 2 − 5 (D) 2π

63/OS/1–211-B] G-925 5 [ Contd......

11. In the given figure, if PT is tangent to the circle with centre O and ∠ TPO = 25° ,
then find x. [1]
Xr JB© AmH¥${V _|, `{X PT H|$Ð O dmbo d¥Îm H$s ñne© aoIm h¡ VWm ∠ TPO = 25° h¡, Vmo x kmV H$s{OE&

12. In the given figure, sides QP and RQ of ΔPQR are produced to points S & T
respectively. If ∠ SPR = 135° and ∠ PQT = 110 ° , find ∠ PRQ . [1]
Xr JB© AmH¥${V _| ΔPQR H$s ^wOmAm| QP VWm RQ H$mo H«$_e… {~ÝXþAm| S VWm T VH$ ~‹T>m`m J`m h¡&
`{X ∠ SPR = 135° VWm ∠ PQT = 110 ° h¡, Vmo ∠ PRQ kmV H$s{OE&

13. The total simple interest of a principal P at r% in n years is H xnr . Find the
25
principal (P). [1]

{H$gr _ybYZ P H$m r% Xa go n dfm] Ho$ {bE ã`mO H xnr h¡, Vmo _ybYZ (P) kmV H$s{OE&
25

14. If the perimeter of a closed semicircle is 36 cm, then find its radius. [1]
EH$ ~ÝX AY©d¥Îm H$s n[a_mn 36 go_r h¡, Vmo BgH$s {ÌÁ`m kmV H$s{OE&

63/OS/1–211-B] G-925 6 [ Contd......

15. Simplify the following [1]
{ZåZ H$mo gab H$s{OE …

3 6
2  4 
  ÷ 
 11   22 

16. If two different dice are rolled together, then find the probability of getting an
even number on both dice. [2]
Xmo {^Þ nmgm| H$mo EH$ gmW CN>mbm J`m& XmoZm| nmgm| na g_g§»`m AmZo H$s àm{`H$Vm kmV H$s{OE&

17. If Mean of a grouped data is 27 and Mode is 45, then what is the value of
Median? [2]
`{X {H$Ýht dJuH¥$V Am§H$‹S>mo| H$m _mÜ` 27 VWm ~hþbH$ 45 h¡, Vmo BZHo$ _mÜ`H$ H$m _mZ Š`m h¡?

18. Find the value of x for which DE || AB in the given figure. [2]

Xr JB© AmH¥${V _| DE || AB h¡ Vmo x H$m _mZ kmV H$s{OE&

19. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord
of the larger circle which touches the smaller circle. [2]
Xmo g§H|$Ðr` d¥Îmm| H$s {ÌÁ`mE± 5 go_r VWm 3 go_r h¢& ~‹S>o d¥Îm H$s Cg Ordm H$s b§~mB© kmV H$s{OE Omo N>moQ>o d¥V
H$mo ñne© H$aVr h¡&

63/OS/1–211-B] G-925 7 [ Contd......

20. Find the volume of a right circular cylinder whose height is 13.5 cm and radius
of the base is 7 cm. [2]
13.5 go_r D±$MmB© VWm 7 go_r AmYma {ÌÁ`m Ho$ b§~d¥Îmr` ~obZ H$m Am`VZ kmV H$s{OE&

2
21. Rehana got rd the answers correct in an examination. What percent of her
3
answers were correct? [2]

2
aohmZm Zo EH$ narjm _| àíZm| Ho$ ghr CÎma {XE& CgHo$ {H$VZo à{VeV CÎma ghr Wo?
3

22. Evaluate : [2]
_mZ kmV H$s{OE …
cos 47° ⋅ cot 79° − sin 43° ⋅ tan11°

23. In figure AB || CD, ∠ BOD = 127°, ∠ OAB = 68° , find ∠ ABO . [2]

Xr JB© AmH¥${V _| AB || CD, ∠ BOD = 127° VWm ∠ OAB = 68° h¡, Vmo ∠ ABO kmV H$s{OE&

5
24. Rationalise the denominator of . [2]
3− 5

5
Ho$ ha H$m n[a_o`H$aU H$s{OE&
3− 5

63/OS/1–211-B] G-925 8 [ Contd......

25. If sin ( A + B ) = 1, cos ( A − B ) = 1 , where 0° ≤ ( A + B ) ≤ 90° and A > B, find A and B.
[2]

`{X sin ( A + B ) = 1, cos ( A − B ) = 1 h¡, Ohm± 0° ≤ ( A + B ) ≤ 90° VWm A > B h¡, Vmo A VWm B
kmV H$s{OE&

26. The number 42 divided into two parts such that one part is equal to square of
another part, then find the two parts. [4]
g§»`m 42 H$mo Xmo ^mJm| _| Bg àH$ma ~m§Q>m J`m {H$ EH$ ^mJ, Xÿgao ^mJ Ho$ dJ© Ho$ g_mZ h¡& XmoZmo§ ^mJ kmV
H$s{OE&

27. The shadow of a tower becomes longer by 10 m, when the angle of elevation of
sun changes from 60° to 45°. Find the height of the tower. [4]
gy`© H$m CÞ`Z H$moU 60° go 45° hmoZo na EH$ _rZma H$s N>m`m 10 _r ~‹T> OmVr h¡& _rZma H$s D±$MmB© kmV
H$s{OE&

28. In an election 75% of the total voters cast their votes. The winning candidates
gets 51% of the cast votes. If the winning person gets 1530 votes, find the total
number of voters in the polling station. [4]
EH$ MwZmd _| Hw$b _VXmVmAm| Ho$ 75% Zo dmoQ> S>mbo& OrVZo dmbo àË`mer H$mo S>mbo JE dmoQ>m| H$m 51% dmoQ>
{_bo `{X OrVZo dmbo H$mo 1530 dmoQ> {_bo hm|, Vmo Cg MwZmd H|$Ð Ho$ Hw$b dmoQ>am| H$s g§»`m kmV H$s{OE&

29. One card is drawn at random from a well-shuffled deck of 52 cards. Find the
probability of getting [4]
(i) A king of red colour.
(ii) The queen of diamonds.
52 nÎmm| H$s AÀN>r àH$ma go \|$Q>r JB© Vme H$s JÈ>r _| go `mÑÀN>`m EH$ nÎmm {ZH$mbm J`m& {ZåZ Ho$ AmZo H$s
àm{`H$Vm kmV H$s{OE …
(i) bmb a§J H$m ~mXemh&
(ii) BªQ> H$s ~oJ_&

63/OS/1–211-B] G-925 9 [ Contd......

30. Find the value of m if the co-ordinates (3, 1), (–2, –3) and (8, 2m) are collinear.
[4]

`{X q~Xþ (3, 1), (–2, –3) VWm (8, 2m) g§ aoI h¡ Vmo m H$m _mZ kmV H$s{OE&

31. Marks out of 100 obtained by 50 students of class X in Mathematics are given.
[4]

Marks 70-75 75-80 80-85 85-90 90-95 95-100
Number of students 12 18 6 7 5 2
Draw a frequency polygon for the data.

H$jm X Ho$ 50 {dÚm{W©`m| Ûmam J{UV H$s narjm _| 100 _| go àmá A§H$ {ZåZ gm[aUr _| {XE JE h¢&

àmám§H$ 70-75 75-80 80-85 85-90 90-95 95-100

{dÚm{W©`m| H$s g§»`m 12 18 6 7 5 2

Cnamoº$ Am§H$S>m| Ho$ {bE EH$ ~ma§~maVm ~hþ^wO It{ME&

OR/AWdm

(For visually impaired learners only)
Find the mean of the following distribution.
Class 0-6 6-12 12-18 18-24 24-30
Frequency 5 4 1 6 4

(Ñ{ï> ~m{YV {dÚm{W©`m| Ho$ {bE d¡H$pënV àíZ)

{ZåZ ~ma§~maVm ~§Q>Z H$m _mÜ` kmV H$s{OE …

dJ© 0-6 6-12 12-18 18-24 24-30

~ma§~maVm 5 4 1 6 4

63/OS/1–211-B] G-925 10 [ Contd......

32. Draw a right ΔABC in which BC = 12 cm, AB = 5 cm and ∠ B = 90° . Construct
2
a triangle similar to it and of scale factor . [4]
3

EH$ g_H$moU {Ì^wO ABC It{ME {Og_| BC = 12 go_r, AB = 5 go_r VWm ∠ B = 90° h¡& A~ Bg
2
{Ì^wO Ho$ g_ê$n EH$ AÝ` {Ì^wO H$s aMZm H$s{OE {OgH$m ñHo$b JwUH$ h¡&
3

OR/AWdm
(For visually impaired learners only)
Write the steps of the above construction.

(Ñ{ï> ~m{YV {dÚm{W©`m| Ho$ {bE d¡H$pënV àíZ)
Cnamoº$ aMZm Ho$ nX (MaU) {b{IE&

33. Solve the following system of linear equations graphically : [4]

{ZåZ a¡{IH$ g_rH$aU {ZH$m` H$mo AmboI Ûmam hb H$s{OE …

x + y = 6; x − y = 4

OR/AWdm
(For visually impaired learners only)
Solve the following system of linear equations:

3 x − y = 5; 4 x + 3 y = 11

(Ñ{ï> ~m{YV {dÚm{W©`m| Ho$ {bE àíZ 27 Ho$ ñWmZ na àíZ)
{ZåZ a¡{IH$ g_rH$aU {ZH$m` H$mo hb H$s{OE …
3 x − y = 5; 4 x + 3 y = 11

63/OS/1–211-B] G-925 11 [ Contd......

34. Find LCM and HCF of a2 + b2 − c2 + 2ab, c2 + a2 − b2 + 2ca and b 2 + c 2 − a 2 + 2bc .
[6]

a 2 + b2 − c2 + 2ab, c2 + a 2 − b2 + 2ca VWm b 2 + c 2 − a 2 + 2bc H$m b.g. (LCM) VWm _.g.
(HCF) kmV H$s{OE&

35. Prove that parallelograms on the same or equal bases and between the same
parallels are equal in area. [6]

{gÕ H$s{OE {H$ g_m§Va MVw^w©O, Omo g_mZ `m EH$ hr AmYmam| na hm| Am¡a EH$ hr g_m§Va aoImAm| Ho$ ~rM pñWV
hm|, joÌ\$b _| ~am~a h¢&

36. A square of side 4 cm is inscribed in a circle. Find the area enclosed between the

 22 
circle and the square.  Use π =  [6]
 7

EH$ d¥Îm Ho$ A§VJ©V EH$ 4 go_r ^wOm H$m dJ© ItMm J`m& d¥Îm VWm dJ© Ho$ ~rM H$m n[a~Õ joÌ\$b kmV

 22 
H$s{OE& π = {b{OE 
 7 



63/OS/1–211-B] G-925 12

=f' . -t-t+t+ :~1 'E:~-::J:::- ::+ -'.-:;f:l:j:;:;

+r'. .::t :~. :
"+ ..
_:.:-_ :, ..:;.~-t:-, T-'B#
it: ••: fo. -:-;:- .. ::cc:.. ..+' :'}L:~~';': [:1':. ~ '.

'L .. H- erF' ':f:::"~::-' ..-:: ::f

: + - -;: h,::;: :c.: '~'1:tE:F£..: .'.:: . , ::
":;' ~.- .r:~ ri:~
:-<: :+:-:::' .n
+:- •.. t: '.;.::E'h
. -.,:' - cC.;. .~~

~:::+:Cc'

." ...- 4' .,.:
~.

'.:~.
:,' ': f·, ,. -t+ -:- +++, +f+-fJ+t- ..
......
- _.: - -T

t +. + .•.~_,' <4 +" ::.,;. i-:,. -.
','
.,
:!. .
. ,-:
t_.'·

..',.':"_:.!T et::.' i =::r~-. -::. t::.'-!:I .. ±:::-:- ...
:t c_ t. fi:' ....

· ,~' ~. t:.+ c.. ! .;:': , ._:: t+.:.:
:,..

. .+:
.+' :;: .. 1-"
:rt
-.-' ". -l"
'\.-
t.'-' .:c,

...
r 1-+

.. '

1:1:: .

.!- - +'-t : HT ~. -; p-1=j:

Ft JJ.1ifut J: -, +- '- '_Ft ~.

.: : ....• ~t
, ,. I. - +4+Ii .': fi:'1Ett't:., .....
..f-,.. +:

~- ':.j.
.. .
h+i..;+H+t++,:13:
•. !
:,~ ... ' ..,. .
.,.

~ .r :t
. "IT ,,' ~ ..
IL ~•• . r:

':.1+: ':+il::.!: cc - :F=t.[' ~:
.. : :q., .: F . ,-- -+<-"
V rcr' t:::t-i M: _
,e:-

+: -t-
' ..
;±:;:;t -:~ '"m is:', . ++-
t+- :tt:
.. ::L.
~_tt-t-:;:::E=I+
.•
r .
-i';" ~Ti. m:...:· - -
":-:fi': F"I.i:§iE'
:;:

;: iI

_:t
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':1='

Fr,·....J:' •.• .::,+,-,rt;t-.:
. fi-1=..4 et' ~.
.+ : .: rr+ +t;: r. ".
.+'

'_ ". i+
.. - -;.+1 d 'f'-.~'
~ .. +,
~::t -+ iH+- ,. t'" ..

,+++ ~r,:: f--'-
.= '

This Question Paper consists of 36 questions and 12 printed pages + Graph Sheet.
Bg àíZ-nÌ _| 36 àíZ VWm 12 ‘w{ÐV n¥ð h¢ + J«m\$ {eQ>&
Sl. No.

Roll No. Code No.
AZw H « $ _m§ H $ H$mo S > Z§ .
63/OS/1
MATHEMATICS
Set / go Q > C
(J{UV)
(211)
Day and Date of Examination :
(narjm H$m {XZ d {XZm§ H $)
Signature of Invigilators : 1.
({ZarjH$m| Ho $ hñVmja)
2.

General Instructions :

1. Candidate must write his/her Roll Number on the first page of the Question Paper.

2. Please check the Question Paper to verify that the total pages and the total number of questions
contained in the Question Paper are the same as those printed on the top of the first page. Also check
to see that the questions are in sequential order.

3. For the objective type of questions, you have to choose any one of the four alternatives given in the
question i.e. (A), (B), (C) and (D) and indicate your correct answer in the Answer-Book given to you.

4. All the questions including objective type questions are to be answered within the allotted time and
no separate time limit is fixed for answering objective type questions.

5. Making any identification mark in the Answer-Book or writing Roll Number anywhere other than
the specified places will lead to disqualification of the candidate.

6. Write your Question Paper Code No. 63/OS/1, Set - C on the Answer-Book.

7. (a) The Question Paper is in English/Hindi medium only. However, if you wish, you can answer
in any one of the languages listed below :

English, Hindi, Urdu, Punjabi, Bengali, Tamil, Malayalam, Kannada, Telugu, Marathi, Odia,
Gujarati, Konkani, Manipuri, Assamese, Nepali, Kashmiri, Sanskrit and Sindhi.

You are required to indicate the language you have chosen to answer in the box provided in
the Answer-Book.

(b) If you choose to write the answer in the language other than Hindi and English, the
responsibility for any errors/mistakes in understanding the questions will be yours only.

63/OS/1–211-C] G-925 1 [ Contd......

gm_mÝ` AZwXoe :

1. narjmWu àíZ-nÌ Ho$ nhbo n¥ð> na AnZm AZwH«$‘m§H$ Adí¶ {bI|&

2. H¥$n¶m àíZ-nÌ H$mo Om±M b| {H$ àíZ-nÌ Ho$ Hw$b n¥ð>m| VWm àíZm| H$s CVZr hr g§»¶m h¡ {OVZr àW‘ n¥ð> Ho$ g~go D$na N>nr h¡& Bg
~mV H$s Om±M ^r H$a b| {H$ àíZ H«${‘H$ ê$n ‘| h¢&

3. dñVw{Zð> àíZm| _| AmnH$mo Mma {dH$ënm| (A), (B), (C) VWm (D) _| go H$moB© EH$ CÎma MwZZm h¡ VWm Xr JB© CÎma-nwpñVH$m _| Amn
ghr CÎma {b{IE&

4. dñVw{Zð> àíZm| Ho$ gmW-gmW g^r àíZm| Ho$ CÎma {ZYm©[aV Ad{Y Ho$ ^rVa hr XoZo h¢& dñVw{Zð> àíZm| Ho$ {bE AbJ go g_` Zht {X`m
OmEJm&

5. CÎma-nwpñVH$m ‘| nhMmZ-{M• ~ZmZo AWdm {Z{X©ï> ñWmZm| Ho$ A{V[aº$ H$ht ^r AZwH«$‘m§H$ {bIZo na narjmWu H$mo A¶mo½¶ R>ham¶m
Om¶oJm&

6. AnZr CÎma-nwpñVH$m na àíZ-nÌ H$r H$moS> g§»¶m. 63/OS/1, goQ> - C {bI|&

7. (H$) àíZ-nÌ Ho$db A§J«oOr/qhXr ‘mܶ‘ ‘| h¡& {’$a ^r, ¶{X Amn Mmh| Vmo ZrMo Xr JB© {H$gr EH$ ^mfm ‘| CÎma Xo gH$Vo h¢ :
A§J«oOr, qhXr, CXÿ©, n§Om~r, ~§Jbm, V{‘b, ‘b¶mb‘, H$ÝZ‹S>, VobwJy, ‘amR>r, C{‹S>¶m, JwOamVr, H$m|H$Ur, ‘{Unwar, Ag{‘¶m,
Zonmbr, H$í‘rar, g§ñH¥$V Am¡a qgYr&

H¥$n¶m CÎma-nwpñVH$m ‘| {XE JE ~m°³g ‘| {bI| {H$ Amn {H$g ^mfm ‘| CÎma {bI aho h¢&

(I) ¶{X Amn qhXr Ed§ A§J«oOr Ho$ A{V[a³V {H$gr Aݶ ^mfm ‘| CÎma {bIVo h¢, Vmo àíZm| H$mo g‘PZo ‘| hmoZo dmbr Ìw{Q>¶m|/Jb{V¶m|
H$s {Oå‘oXmar Ho$db AmnH$s hmoJr&

63/OS/1–211-C] G-925 2 [ Contd......

MATHEMATICS
(J{UV)
(211)
Time : 2 ½ Hours] [Maximum Marks : 85
g_` : 2 ½ KÊQ>o] [nyUmªH$ : 85
Note : (1) Question Numbers (1-10) are Multiple Choice Questions. Each question carries one mark. For each
question, four alternative choices, (A), (B), (C) and (D) are provided, of which only one is correct.
You have to select the correct alternative and indicate it in the answer-book provided to you by
writing (A), (B), (C) or (D) as the case may be. Q. No. 11 to 15 also carry one mark each.
(2) Question Numbers (16-25) carry 2 marks each.
(3) Question Numbers (26-33) carry 4 marks each.
(4) Question Numbers (34-36) carry 6 marks each.
(5) All questions are compulsory.

{ZX} e : (1) àíZ g§»¶m 1 go 10 VH$ ~hþ{dH$ënr¶ àíZ (Multiple Choice Questions) h¢& à˶oH$ àíZ EH$ A§H$ H$m h¡& à˶oH$ àíZ ‘|
Mma {dH$ën (A), (B), (C) VWm (D) {XE J`o h¢, {OZ‘| go Ho$db EH$ ghr h¡& AmnH$mo ghr {dH$ën MwZZm h¡ VWm àË`oH$ àíZ Ho$ CÎma
AnZr CÎma-nwpñVH$m ‘| (A), (B), (C) AWdm (D) O¡gr ^r pñW{V hmo, {bIH$a Xem©Zm h¡& àíZ g§»`m 11 go 15 ^r EH$ A§H$ H$m h¡&
(2) àíZ g§»¶m (16 go 25) VH$ à˶oH$ àíZ Ho 2 A§H$ h¢&
(3) àíZ g§»¶m (26 go 33) VH$ à˶oH$ àíZ Ho 4 A§H$ h¢&
(4) àíZ g§»¶m (34 go 36) VH$ à˶oH$ àíZ Ho 6 A§H$ h¢&
(5) g^r àíZ A{Zdm¶© h¢&

1. The value of cos 2 75° − sin 2 15° is [1]

cos 2 75° − sin 2 15° H$m _mZ h¡
(A) 1
(B) 2

3
(C)
2
(D) 0

63/OS/1–211-C] G-925 3 [ Contd......

1 1
2. sin 2 A − 2
+ cos 2 A + is equal to [1]
cos A cot 2 A

1 1
sin 2 A − 2
+ cos 2 A + ~am~a h¡
cos A cot 2 A

(A) 1 (B) cos 2 A

(C) 0 (D) sin 2 A

3. The ratio of areas of two similar triangles is 25:16, then the ratio of their
corresponding sides is [1]

Xmo g_ê$n {Ì^wOm| Ho$ joÌ\$bm| H$m AZwnmV 25:16 h¡, Vmo CZH$s g§JV ^wOmAm| H$m AZwnmV h¡ …
(A) 625:256 (B) 4:5

(C) 5:4 (D) 16:25

4. The distance of the point P(–6, 8) from the origin is [1]

q~Xþ P(–6, 8) H$s _ybq~Xþ go Xÿar h¡

(A) 8 (B) 2 7

(C) 10 (D) 6

5. A zero of the polynomial x 2 − 3 x − 10 is [1]

~hþnX x 2 − 3x − 10 H$m EH$ ewÝ`H$ h¡ …
(A) 10 (B) – 2

(C) 3 (D) 4

63/OS/1–211-C] G-925 4 [ Contd......

6. Which of the following is a pure surd? [1]
{ZåZ _| go H$m¡Z gr EH$ ewÕ H$aUr h¡?

(A) 3 27 (B) 32

(C) 2 22 (D) 25

7. Which of the following is a rational expression? [1]
{ZåZ _| go H$m¡Z gm EH$ n[a_o` ì`§OH$ h¡?

x2 + 2 y 2
(A) (B) 8 x + 6 y
3x − y

(C) 2 − 5 (D) 2π

8. The area of an equilateral triangle each of whose sides is of length 2 m is [1]

(A) 4 3 m2 (B) 2 3 m2

(C) 4 m2 (D) 3 m2
EH$ g_~mhþ {Ì^wO {OgH$s àË`oH$ ^wOm H$s b§~mB© 2 _r h¡, H$m joÌ\$b h¡ …

(A) 4 3 dJ© _r (B) 2 3 dJ© _r

(C) 4 dJ© _r (D) 3 dJ© _r

9. 0.025 in terms of rate percent is [1]

Xa à{VeV Ho$ ê$n _| 0.025 ~am~a h¡ …
(A) 25% (B) 2.5%

(C) 0.25% (D) 37½%

63/OS/1–211-C] G-925 5 [ Contd......

10. Two circles are always [1]
(A) Congruent
(B) Neither similar nor congruent
(C) Always similar but may not congruent
(D) Similar and congruent
Xmo d¥Îm gXm
(A) gdmªJg_ hmoVo h¢
(B) Z hr g_ê$n Am¡a Z hr gdmªJg_ hmoVo h¢&
(C) g_ê$n hmoVo h¢ naÝVw gdmªJg_ Zht ^r hmo gH$Vo h¢&
(D) g_ê$n hmoVo h¢ VWm gdmªJg_ hmoVo h¢&

11. The total simple interest of a principal P at r% in n years is H xnr . Find the
25
principal (P). [1]

{H$gr _ybYZ P H$m r% Xa go n dfm] Ho$ {bE ã`mO H xnr h¡, Vmo _ybYZ (P) kmV H$s{OE&
25

12. If the perimeter of a closed semicircle is 36 cm, then find its radius. [1]
EH$ ~ÝX AY©d¥Îm H$s n[a_mn 36 go_r h¡, Vmo BgH$s {ÌÁ`m kmV H$s{OE&

13. In the given figure, sides QP and RQ of ΔPQR are produced to points S & T
respectively. If ∠ SPR = 135° and ∠ PQT = 110 ° , find ∠ PRQ . [1]
Xr JB© AmH¥${V _| ΔPQR H$s ^wOmAm| QP VWm RQ H$mo H«$_e… {~ÝXþAm| S VWm T VH$ ~‹T>m`m J`m h¡&
`{X ∠ SPR = 135° VWm ∠ PQT = 110 ° h¡, Vmo ∠ PRQ kmV H$s{OE&

63/OS/1–211-C] G-925 6 [ Contd......

14. In the given figure, if PT is tangent to the circle with centre O and ∠ TPO = 25° ,
then find x. [1]
Xr JB© AmH¥${V _|, `{X PT H|$Ð O dmbo d¥Îm H$s ñne© aoIm h¡ VWm ∠ TPO = 25° h¡, Vmo x kmV H$s{OE&

15. Simplify the following [1]
{ZåZ H$mo gab H$s{OE …

3 6
2  4 
  ÷ 
 11   22 

16. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord
of the larger circle which touches the smaller circle. [2]
Xmo g§H|$Ðr` d¥Îmm| H$s {ÌÁ`mE± 5 go_r VWm 3 go_r h¢& ~‹S>o d¥Îm H$s Cg Ordm H$s b§~mB© kmV H$s{OE Omo N>moQ>o d¥V
H$mo ñne© H$aVr h¡&

2
17. Rehana got rd the answers correct in an examination. What percent of her
3
answers were correct? [2]
2
aohmZm Zo EH$ narjm _| àíZm| Ho$ ghr CÎma {XE& CgHo$ {H$VZo à{VeV CÎma ghr Wo?
3

18. Find the volume of a right circular cylinder whose height is 13.5 cm and radius
of the base is 7 cm. [2]
13.5 go_r D±$MmB© VWm 7 go_r AmYma {ÌÁ`m Ho$ b§~d¥Îmr` ~obZ H$m Am`VZ kmV H$s{OE&

63/OS/1–211-C] G-925 7 [ Contd......

19. Evaluate : [2]
_mZ kmV H$s{OE …
cos 47° ⋅ cot 79° − sin 43° ⋅ tan11°

20. If sin ( A + B ) = 1, cos ( A − B ) = 1 , where 0° ≤ ( A + B ) ≤ 90° and A > B, find A and B.
[2]
`{X sin ( A + B ) = 1, cos ( A − B ) = 1 h¡, Ohm± 0° ≤ ( A + B ) ≤ 90° VWm A > B h¡, Vmo A VWm B
kmV H$s{OE&

5
21. Rationalise the denominator of . [2]
3− 5
5
Ho$ ha H$m n[a_o`H$aU H$s{OE&
3− 5

22. In the given figure, AD is the bisector of ∠ A intersecting BC at D. If AB = 4.2 cm,
BD = 4 cm and DC = 6 cm, then find x. [2]

Xr JB© AmH¥${V _| AD H$moU A H$m g_{Û^mOH$ h¡ VWm BC H$mo D na H$mQ>Vm h¡& `{X AB = 4.2 go_r,
BD = 4 go_r VWm DC = 6 go_r h¡, Vmo x kmV H$s{OE&

o_r
g
4.2

4 go_r 6 go_r

63/OS/1–211-C] G-925 8 [ Contd......

23. If two different dice are rolled together, then find the probability of getting an
even number on both dice. [2]
Xmo {^Þ nmgm| H$mo EH$ gmW CN>mbm J`m& XmoZm| nmgm| na g_g§»`m AmZo H$s àm{`H$Vm kmV H$s{OE&

24. If Mean of a grouped data is 27 and Mode is 45, then what is the value of
Median? [2]
`{X {H$Ýht dJuH¥$V Am§H$‹S>mo| H$m _mÜ` 27 VWm ~hþbH$ 45 h¡, Vmo BZHo$ _mÜ`H$ H$m _mZ Š`m h¡?

25. ABCD is a rhombus in which ∠ ABC = 68° . Find the measure of ∠ ACD . [2]
EH$ g_MVw^w©O ABCD _| ∠ ABC = 68° h¡, Vmo ∠ ACD H$s _mn kmV H$s{OE&

26. Factorise : [4]
JwUZIÊS>Z H$s{OE …
x 2 + x − ( a + 1)( a + 2 )

27. Find the lengths of sides of a triangle ABC whose vertices are A (4, 3), B (3, –2)
and C (5, –7). [4]
Cg {Ì^wO ABC H$s ^wOmAm| H$s b§~mB©`m± kmV H$s{OE {OgHo$ erf© A (4, 3), B (3, –2) VWm C (5, –7)
h¢&

28. A straight tree is broken due to storm. The broken part is bent in such a way that
the peak of the tree touches the ground at an angle 60º at distance of 2 3 m .
Find the initial height of the tree. [4]
EH$ grYm I‹S>m no‹S> Vy\$mZ AmZo na Qy>Q> H$a {Ja n‹S>m& no‹S> H$m Qy>Q>m hþAm ^mJ Bg àH$ma {Jam {H$ BgH$m erf©
60º Ho$ H$moU na ^y{_ H$mo ñne© H$aZo bJm {OgH$s no‹S> H$s O‹S> go Xÿar 2 3 _r h¡& no‹S> H$s Ama§{^H$ D±$MmB©
kmV H$s{OE&

29. In an election 75% of the total voters cast their votes. The winning candidates
gets 51% of the cast votes. If the winning person gets 1530 votes, find the total
number of voters in the polling station. [4]
EH$ MwZmd _| Hw$b _VXmVmAm| Ho$ 75% Zo dmoQ> S>mbo& OrVZo dmbo àË`mer H$mo S>mbo JE dmoQ>m| H$m 51% dmoQ>
{_bo `{X OrVZo dmbo H$mo 1530 dmoQ> {_bo hm|, Vmo Cg MwZmd H|$Ð Ho$ Hw$b dmoQ>am| H$s g§»`m kmV H$s{OE&

63/OS/1–211-C] G-925 9 [ Contd......

30. One card is drawn at random from a well-shuffled deck of 52 cards. Find the
probability of getting [4]
(i) A king of red colour.
(ii) The queen of diamonds.
52 nÎmm| H$s AÀN>r àH$ma go \|$Q>r JB© Vme H$s JÈ>r _| go `mÑÀN>`m EH$ nÎmm {ZH$mbm J`m& {ZåZ Ho$ AmZo H$s
àm{`H$Vm kmV H$s{OE …
(i) bmb a§J H$m ~mXemh&
(ii) BªQ> H$s ~oJ_&

31. Marks out of 100 obtained by 50 students of class X in Mathematics are given.
[4]
Marks 70-75 75-80 80-85 85-90 90-95 95-100
Number of students 12 18 6 7 5 2
Draw a frequency polygon for the data.
H$jm X Ho$ 50 {dÚm{W©`m| Ûmam J{UV H$s narjm _| 100 _| go àmá A§H$ {ZåZ gm[aUr _| {XE JE h¢&
àmám§H$ 70-75 75-80 80-85 85-90 90-95 95-100
{dÚm{W©`m| H$s g§»`m 12 18 6 7 5 2
Cnamoº$ Am§H$S>m| Ho$ {bE EH$ ~ma§~maVm ~hþ^wO It{ME&
OR/AWdm
(For visually impaired learners only)
Find the mean of the following distribution.
Class 0-6 6-12 12-18 18-24 24-30
Frequency 5 4 1 6 4
(Ñ{ï> ~m{YV {dÚm{W©`m| Ho$ {bE d¡H$pënV àíZ)
{ZåZ ~ma§~maVm ~§Q>Z H$m _mÜ` kmV H$s{OE …
dJ© 0-6 6-12 12-18 18-24 24-30
~ma§~maVm 5 4 1 6 4

63/OS/1–211-C] G-925 10 [ Contd......

32. Solve the following system of linear equations graphically : [4]
{ZåZ a¡{IH$ g_rH$aU {ZH$m` H$mo AmboI Ûmam hb H$s{OE …

x + y = 6; x − y = 4

OR/AWdm

(For visually impaired learners only)

Solve the following system of linear equations:

3 x − y = 5; 4 x + 3 y = 11

(Ñ{ï> ~m{YV {dÚm{W©`m| Ho$ {bE àíZ 27 Ho$ ñWmZ na àíZ)

{ZåZ a¡{IH$ g_rH$aU {ZH$m` H$mo hb H$s{OE …

3 x − y = 5; 4 x + 3 y = 11

33. Draw a right ΔABC in which BC = 12 cm, AB = 5 cm and ∠ B = 90° . Construct
2
a triangle similar to it and of scale factor . [4]
3

EH$ g_H$moU {Ì^wO ABC It{ME {Og_| BC = 12 go_r, AB = 5 go_r VWm ∠ B = 90° h¡& A~ Bg
2
{Ì^wO Ho$ g_ê$n EH$ AÝ` {Ì^wO H$s aMZm H$s{OE {OgH$m ñHo$b JwUH$ h¡&
3

OR/AWdm

(For visually impaired learners only)

Write the steps of the above construction.

(Ñ{ï> ~m{YV {dÚm{W©`m| Ho$ {bE d¡H$pënV àíZ)

Cnamoº$ aMZm Ho$ nX (MaU) {b{IE&

63/OS/1–211-C] G-925 11 [ Contd......

34. A square of side 4 cm is inscribed in a circle. Find the area enclosed between the
 22 
circle and the square.  Use π =  [6]
 7

EH$ d¥Îm Ho$ A§VJ©V EH$ 4 go_r ^wOm H$m dJ© ItMm J`m& d¥Îm VWm dJ© Ho$ ~rM H$m n[a~Õ joÌ\$b kmV
 22 
H$s{OE& π = {b{OE 
 7 

35. A natural number, when increased by 12, equals 160 times its reciprocal. Find
the number. [6]

EH$ àmH¥$V g§»`m H$mo 12 go ~‹T>mZo na `h AnZo ì`wËH«$_ Ho$ 160 JwUm Ho$ g_mZ hmo OmVr h¡& g§»`m kmV
H$s{OE&

36. In a ΔABC, AD is perpendicular to BC, prove that AB2 + CD2 = AC2 + BD2 .[6]

EH$ {Ì^wO ABC _| AD ^wOm BC na b§~ h¡& {gÕ H$s{OE {H$ AB2 + CD2 = AC2 + BD2



63/OS/1–211-C] G-925 12

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_:.:-_ :, ..:;.~-t:-, T-'B#
it: ••: fo. -:-;:- .. ::cc:.. ..+' :'}L:~~';': [:1':. ~ '.

'L .. H- erF' ':f:::"~::-' ..-:: ::f

: + - -;: h,::;: :c.: '~'1:tE:F£..: .'.:: . , ::
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~.

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:,' ': f·, ,. -t+ -:- +++, +f+-fJ+t- ..
......
- _.: - -T

t +. + .•.~_,' <4 +" ::.,;. i-:,. -.
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t_.'·

..',.':"_:.!T et::.' i =::r~-. -::. t::.'-!:I .. ±:::-:- ...
:t c_ t. fi:' ....

· ,~' ~. t:.+ c.. ! .;:': , ._:: t+.:.:
:,..

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Ft JJ.1ifut J: -, +- '- '_Ft ~.

.: : ....• ~t
, ,. I. - +4+Ii .': fi:'1Ett't:., .....
..f-,.. +:

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h+i..;+H+t++,:13:
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IL ~•• . r:

':.1+: ':+il::.!: cc - :F=t.[' ~:
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~_tt-t-:;:::E=I+
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_:t
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Fr,·....J:' •.• .::,+,-,rt;t-.:
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