Bihar Board Class 10th Model Paper 2025 Maths

BIHAR
BOARD
Model
Paper 2025

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SECONDARY SCHOOL EXAMINATION-2025
ek/;fed Ldwy ijh{kk&2025
( ANNUAL/okf’kZd )
MATHEMATICS
( Compulsory )
xf.kr
¼ vfuok;Z ½
fo"k; dksM :
Subject Code:
110
dqy ç”u : 100+30+8 = 13
Total Questions : 100+30+8 = 138

¼ le; % 3 ?kaVs 15 feuV ½ ¼ iw.kkZad %100 ½
[ Time : 3 Hours 15 Minutes ] [Full Marks:100]
ijh{kkfFkZ;ksa ds fy, funsZ'k%
Instructions for the candidates:
1. ijh{kkFkhZ 𝑂𝑀𝑅 mÙkj i=d ij viuk ç'u iqfLrdk Øekad ¼10 vadks dk½ vo';
fy[ksaA
Candidates must enter his/her Question Booklet Serial No. (10 Digits) in the
OMR Answer Sheet.
2. ijh{kkFkhZ ;FkklaHko vius 'kCnksa esa gh mÙkj nsAa
Candidates are required to give their answers in their own words as far as
practicable.
3. nkfguh vksj gkf”k;s ij fn;s gq, vad iw.kkaZd fufnZ"V djrs gSaA
Figures in the right hand margin indicate full marks.
4. ç'uksa dks /;ku iwoZd i<+us ds fy, 15 feuV dk vfrfjä le; fn;k x;k gSA
An extra time of 15 minutes has been allotted for the candidates to read the
questions carefully.

5. ;g ç'u iqfLrdk nks [k.Mksa esa foHkkftr gS – [k.M&v ,oa [k.M&c
This question booklet is divided into two sections- Section-A and Section-B

Page 1 of 34

6. [k.M&v esa 100 oLrqfu"B ç'u gS]a ftuesa ls dsoy 50 ç'uksa dk mÙkj nsuk vfuok;Z
gSA ipkl ls vf/kd ç”uksa ds mÙkj nsus ij ÁFke 50 mÙkjksa dk gh ewY;kadu fd;k
tk,xkA çR;sd ç'u ds fy, 1 vad fu/kkZfjr gSA lgh mÙkj dks miyC/k djk;s x;s
OMR mÙkj i=d esa fn;s x;s lgh fodYi dks uhys@dkys c‚y isu ls izxk<+ djsaA
fdlh Hkh çdkj ds OgkbVuj@rjy inkFkZ@CysM@uk[kwu vkfn dk OMR
mÙkj&iqfLrdk esa ç;ksx djuk euk gS] vU;Fkk ijh{kk ifj.kke vekU; gksxkA
In Section-A, there are 100 objective type questions, out of which any 50
questions are to be answered. First 50 answers will be evaluated in case more
than 50 questions are answered. Each question carries 1 mark. For answering
these darken the circle with blue/black ball pen against the correct option on
OMR Answer Sheet provided to you. Do not use whitener/liquid/blade/nail
etc. on OMR-sheet otherwise the result will be treated invalid.
7. [k.M&c esa] 30 y?kq mÙkjh; ç'u gSa] ftuesa ls fdUgha 15 ç'uksa dk mÙkj nsuk vfuok;Z
gSA çR;sd ç”u ds fy, 2 vad fu/kkZfjr gSaA buds vfrfjDr] bl [k.M esa 8 nh?kZ
mÙkjh; ç'u fn;s x;s gSa] ftuesa ls fdUgha 4 ç'uksa dk mÙkj nsuk gSA çR;sd ç”u ds
fy, 5 vad fu/kkZfjr gSA
In SECTION-B, there are 30 short answer type questions, out of which any 15
questions are to be answered. Each question carries 2 marks. Apart from these,
there are 8 long answer type questions, out of which any 4 questions are to be
answered. Each question carries 5 marks.
8. fdlh izdkj ds bysDVªkWfud midj.k dk iz;ksx iw.kZr;k oftZr gSA
Use of any electronic appliances is strictly prohibited.

Page 2 of 34

[k.M & v / SECTION-A
oLrqfu"B ç'u / Objective Type Questions

ç'u la[;k 1 ls 100 rd ds ç”u ds lkFk pkj fodYi fn;s x, gSa] ftuesa ls ,d lgh
gSA fdUgha 50 ç'uksa ds dk mÙkj vius }kjk pqus x, lgh fodYi dks 𝑂𝑀𝑅 “khV ij
fpfºur djsAa 50 × 1 = 50
Questions Nos. 1 to 100 have four options, out of which only one is correct.
Answer any 50 questions. You have to mark your selected option on the OMR-
Sheet. 50 × 1 = 50
1. fuEufyf[kr esa dkSu ifjes; la[;k gS\

(A) √7 + √7 (B) √25 + √3
(C) (D) √9 × √3
√

Which of the following is a rational number?
(A) √7 + √7 (B) √25 + √3
(C) (D) √9 × √3
√

2. ;fn 𝑚 ,d iw.kkaZd gS rks çR;sd fo"ke iw.kkaZd dk :i gksrk gS&
(A) 𝑚+1 (B) 𝑚
(C) 2𝑚 (D) 2𝑚 + 1
If 𝑚 is an integer then the form of every odd integer is –
(A) 𝑚+1 (B) 𝑚
(C) 2𝑚 (D) 2𝑚 + 1
3. fuEufyf[kr esa fdldk n'keyo çlkj Lkkar gS\

(A) (B)

(C) (D)

Which of the following has terminating decimal expansion?
(A) (B)

(C) (D)

Page 3 of 34

4. 0.87 =
(A) (B)

(C) (D)

5. ;fn 540 = 2 × 3 × 5 gks rks 𝑥 + 𝑦 − 𝑧 =
(A) 4 (B) 5
(C) 3 (D) 6
If 540 = 2 × 3 × 5 then 𝑥 + 𝑦 − 𝑧 =
(A) 4 (B) 5
(C) 3 (D) 6
6. fuEufyf[kr esa dkSu vifjes; la[;k gS\
(A) 2. 3 (B) √13 × √13
(C) √441 (D)

Which of the following is an irrational number?
(A) 2. 3 (B) √13 × √13
(C) √441 (D)

7. ;fn 𝑚 vkSj 𝑛 nks vHkkT; la[;k,¡ gSa rks mudk egÙke lekioÙkZd gksxk&
(A) 0 (B) 1
(C) 2 (D) 3
If 𝑚 and 𝑛 are two prime numbers then their highest common factor
will be –
(A) 0 (B) 1
(C) 2 (D) 3
8. nks la[;kvksa dk xq.kuQy 2366 gS vkSj mudk y?kqre lekioR;Z 182 gS] rks
egÙke lekioÙkZd gksxk&

Page 4 of 34

(A) 13 (B) 23
(C) 3 (D) 16
The product of two numbers is 2366 and their Lowest Common
Multiple is 182 then Highest Common Factor will be
(A) 13 (B) 23
(C) 3 (D) 16
9. fuEufyf[kr esa fdldk n'keyo çlkj vlkar gS\

(A) (B)

(C) (D)

Which of the following has non-terminating decimal expansion?
(A) (B)

(C) (D)

10. ;fn 𝑝 = 𝑎𝑏 rFkk 𝑞 = 𝑎 𝑏] tgk¡ 𝑝, 𝑞 /kukRed iw.kkaZd rFkk 𝑎, 𝑏 vHkkT;

la[;k,¡ gS]a rks (𝑝, 𝑞) dk y?kqÙke lekioR;Z gS&
(A) 𝑎𝑏 (B) 𝑎 𝑏
(C) 𝑎 𝑏 (D) 𝑎 𝑏
If 𝑝 = 𝑎𝑏 and 𝑞 = 𝑎 𝑏, where 𝑝, 𝑞 positive integer and 𝑎, 𝑏 are prime
numbers then the Lowest Common Multiple of (𝑝, 𝑞) is
(A) 𝑎𝑏 (B) 𝑎 𝑏
(C) 𝑎 𝑏 (D) 𝑎 𝑏
11.fuEufyf[kr esa ls dkSu&lk ;qXe lg&vHkkT; gS\
(A) (15, 45) (B) (9, 16)
(C) (21, 105) (D) (14, 84)
Which of the following pair is Co-prime?
(A) (15, 45) (B) (9, 16)
(C) (21, 105) (D) (14, 84)

Page 5 of 34

12. 0.3125 dks ds :i esa fy[kk tk ldrk gS&

(A) (B)

(C) (D)

0.3125 can be written in the form of as-

(A) (B)

(C) (D)

13.fuEufyf[kr esa ls dkSu&lk cgqin gS\
(A) 𝑥 + √2𝑥 + 1 (B) 𝑥+

(C) 𝑥 − 3𝑥 + √121 (D) 2𝑥 + √4𝑥

Which of the following is a polynomial?
(A) 𝑥 + √2𝑥 + 1 (B) 𝑥+

(C) 𝑥 − 3𝑥 + √121 (D) 2𝑥 + √4𝑥

14.cgqin (𝑥 + 3) (𝑥 − 8) dk ?kkr gS&
(A) 2 (B) 5
(C) 6 (D) 4
The degree of the polynomial (𝑥 + 3) (𝑥 − 8) is
(A) 2 (B) 5
(C) 6 (D) 4
15. cgqin 2𝑥 − 6 ds “kwU;d gS&
a
(A) √3, −√3 (B) √3, √3
(C) −√3, −√3 (D) (3, −3)

The zeroes of the polynomial 2𝑥 − 6 are
(A) √3, −√3 (B) √3, √3
(C) −√3, −√3 (D) (3, −3)

Page 6 of 34

16. cgqin 𝑝(𝑥) = 2𝑥 − 8𝑥 − 12, rks 𝑝(2) dk eku gS&
(A) 20 (B) –20
(C) 36 (D) –28
The polynomial 𝑝(𝑥) = 2𝑥 − 8𝑥 − 12, then the value of 𝑝(2) is –
(A) 20 (B) –20
(C) 36 (D) –28
17.;fn cgqin 3𝑦 + 7𝑦 − 𝐾 ds 'kwU;d ,d nwljs ds O;qRØe gks] rks 𝐾 dk eku
gksxk&
(A) (B) −

(C) 3 (D) −3
If zeroes of the polynomial 3𝑦 + 7𝑦 − 𝐾 are reciprocal to each other,
then the value of 𝐾 will be−
(A) (B) −

(C) 3 (D) −3
18.'kwU;d &2]&5 okys cgqinksa dh la[;k gksxh&
(A) 2 (B) 3
(C) 5 (D) vufxur
The number of polynomial with zeroes −2, −5 will be−
(A) 2 (B) 3
(C) 5 (D) Infinite
19.;fn cgqin 𝑝(𝑥) = 5𝑥 + 7𝑥 − 12, ds 'kwU;d 𝛼 vkSj 𝛽 gks]a rks 5(𝛼 + 𝛽)
dk eku gS&
(A) –7 (B) 7
(C) 35 (D) 60
If 𝛼 and 𝛽 are zeroes of the polynomial 𝑝(𝑥) = 5𝑥 + 7𝑥 − 12, then the
value of 5(𝛼 + 𝛽) is –
(A) –7 (B) 7

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(C) 35 (D) 60
20. ;fn 𝛼, 𝛽, 𝛾 f=?kkr cgqin 𝑎𝑥 + 𝑏𝑥 + 𝑐𝑥 + 𝑑 ds 'kwU;d gkas] rks 𝛼 ∙ 𝛽 ∙ 𝛾
dk eku gksxk
(A) (B) −

(C) (D) −

If 𝛼, 𝛽, 𝛾 are zeroes of the Cubic polynomial 𝑎𝑥 + 𝑏𝑥 + 𝑐𝑥 + 𝑑, then
the value of 𝛼 ∙ 𝛽 ∙ 𝛾 is
(A) (B) −

(C) (D) −

21.;fn js[kk,¡ 5𝑥 + 𝑝𝑦 = 6 vkSj 15𝑥 + 9𝑦 = 12 lekUrj gSa] rks 𝑝 dk eku
gksxk
(A) 3 (B)

(C) 2 (D) 9
If the lines 5𝑥 + 𝑝𝑦 = 6 and 15𝑥 + 9𝑦 = 12 are parallel, then the value
of 𝑝 will be
(A) 3 (B)

(C) 2 (D) 9
22.;fn nks pjksa esa nks jSf[kd lehdj.kksa ds vkys[k çfrPNsnh js[kk,¡ gks] rks gyksa dh
la[;k gksxh&
(A) dksbZ gy ugha (B) flQZ ,d
(C) vuUr gy (D) buesa ls dksbZ ugha

If the graph of two linear equations in two variables is intersecting lines,
then the number of solutions will be
(A) no solution (B) only one
(C) infinite solution (D) none of these
23. ;fn 5𝑥 − 8𝑦 = 0 rFkk 10𝑥 − 18𝑦 = 0 rks 𝑥 rFkk 𝑦 ds eku gSa–

Page 8 of 34

(A) 𝑥 = 5, 𝑦 = 0 (B) 𝑥 = 0, 𝑦 = 8
(C) 𝑥 = 0, 𝑦 = 0 (D) 𝑥 = 1, 𝑦 = 1
If 5𝑥 − 8𝑦 = 0 and 10𝑥 − 18𝑦 = 0 then the values of 𝑥 and 𝑦 are–
(A) 𝑥 = 5, 𝑦 = 0 (B) 𝑥 = 0, 𝑦 = 8
(C) 𝑥 = 0, 𝑦 = 0 (D) 𝑥 = 1, 𝑦 = 1
24. ;fn lehdj.k 𝑎𝑥 + 𝑏𝑥 + 𝑐 = 0, 𝑎 ≠ 0, dk ewy leku gks] rks 𝑐 =

(A) − (B)

(C) (D) −

If the equation 𝑎𝑥 + 𝑏𝑥 + 𝑐 = 0, 𝑎 ≠ 0, has equal roots, then 𝑐 =

(A) − (B)

(C) (D) −

25. fuEufyf[kr esa ls dkSu lk f}?kkr lehdj.k ugha gS\
(A) (𝑥 + 2) = 3(𝑥 − 4) (B) 4𝑥 − 𝑥 = 𝑥 + 7

(C) √2𝑥 − 3 = 2𝑥 + 4 (D) (𝑥 − 1) = 3𝑥 − 2𝑥 + 4

Which of the following is not a quadratic equation?
(A) (𝑥 + 2) = 3(𝑥 − 4) (B) 4𝑥 − 𝑥 = 𝑥 + 7

(C) √2𝑥 − 3 = 2𝑥 + 4 (D) (𝑥 − 1) = 3𝑥 − 2𝑥 + 4

26. ;fn f}?kkr lehdj.k 𝑥 − 7𝑥 + 12 = 0 dk ,d ewy 3 gks] rks bldk nwljk
ewy gksxk&
(A) –3 (B) 4
(C) –4 (D) 2
If one root of the quadratic equation 𝑥 − 7𝑥 + 12 = 0 is 3 then its other
root will be –
(A) –3 (B) 4
(C) –4 (D) 2
27. ;fn f}?kkr lehdj.k 𝑥 + 𝑝𝑥 + 𝑞 = 0 ds ewy 𝑝 rFkk 𝑞 gks] rks 𝑝 + 𝑞 =

Page 9 of 34

(A) 1 (B) –1
(C) 2 (D) –2
If 𝑝 and 𝑞 are roots of the quadratic equation 𝑥 + 𝑝𝑥 + 𝑞 = 0, then
𝑝+𝑞 =
(A) 1 (B) –1
(C) 2 (D) –2
28. f}?kkr lehdj.k 3𝑥 − 13𝑥 + 10 = 0 dk fofoDrdj gS&
(A) 49 (B) –49
(C) 13 (D) 169
The discriminant of the quadratic equation 3𝑥 − 13𝑥 + 10 = 0 is –
(A) 49 (B) –49
(C) 13 (D) 169
29.f}?kkr lehdj.k 𝑥(2𝑥 + 5) = 0 ds ewyksa dk xq.kuQy gS&

(A) (B) 0

(C) − (D)

The product of the roots of the quadratic equation 𝑥(2𝑥 + 5) = 0 is

(A) (B) 0

(C) − (D)

30. fuEufyf[kr esa dkSu&lk lekarj Js<+h esa gS\
(A) 0.2, 0.22, 0.222, 0.2222, …
(B) √7, √28, √63, √112, …
(C) 2, 4, 8, 16, …
(D) 1, , , 2, …

Which of the following is an arithmetic progression?
(A) 0.2, 0.22, 0.222, 0.2222, …
(B) √7, √28, √63, √112, …
(C) 2, 4, 8, 16, …
Page 10 of 34

(D) 1, , , 2, …

31. lekarj Js<+h 12] 10] 8] --- dk dkSu&lk in 0 gS\
(A) 7ok¡ (B) 8ok¡
(C) 9ok¡ (D) 10ok¡
Which term of the arithmetic progression 12, 10, 8, … is 0?
(A) 7th (B) 8th
(C) 9th (D) 10th
32. lekarj Js<h+ &5]&1]3]7]--- dk lkoZvarj gS&
(A) 4 (B) −4
(C) 3 (D) –6
The Common difference of the arithmetic progression −5, −1, 3, 7, … is –
(A) 4 (B) –4
(C) 3 (D) –6
33.;fn lekarj Js<h+ dk igyk in ′𝑎′ vkSj lkoZvarj ′𝑑′ gS] rks çFke 𝑛 inksa dk
;ksxQy gksxk&
(A) 𝑛{2𝑎 + (𝑛 − 1) × 𝑑} (B)
( )

(C) {2𝑎 + (𝑛 − 1) × 𝑑} (D) {𝑎 + (𝑛 − 1) × 𝑑}

If the first term of an arithmetic progression is ′𝑎′ and Common
difference is ′𝑑′ then the sum of first 𝑛 terms of the arithmetic
progression will be
(A) 𝑛{2𝑎 + (𝑛 − 1) × 𝑑} (B)
( )

(C) {2𝑎 + (𝑛 − 1) × 𝑑} (D) {𝑎 + (𝑛 − 1)𝑑}

34.;fn lekarj Js<h+ dk 𝑛 ok¡ in 𝑡 = 3 − 4𝑛 rks 𝑡 =
(A) –17 (B) 17
(C) 20 (D) –20
If the 𝑛𝑡ℎ term of an arithmetic progression, 𝑡 = 3 − 4𝑛 then 𝑡 =

Page 11 of 34

(A) –17 (B) 17
(C) 20 (D) –20

35.;fn lekarj Js<h+ dk lkekU; in (17 − 5𝑛) gS] rks bldk lkoZvarj gksxk&
(A) 5 (B) –5
(C) 12 (D) 0
If the general term of an arithmetic progression is (17 − 5𝑛) then its
Common difference will be–
(A) 5 (B) –5
(C) 12 (D) 0
36.çFke 𝑛 fo"ke çk—r la[;kvksa dk ;ksxQy gS&
(A) 𝑛 −1 (B) 𝑛+1
(C) 2𝑛 − 1 (D) 𝑛
The sum of first n odd natural numbers is
(A) 𝑛 −1 (B) 𝑛+1
(C) 2𝑛 − 1 (D) 𝑛
37. ;fn 18, 𝑥, 𝑦, −3 lekarj Js<+h esa gSa rks 𝑥 + 𝑦 =
(A) 7 (B) 13
(C) 21 (D) 15
If 18, 𝑥, 𝑦, −3 are in arithmetic progression then 𝑥 + 𝑦 =
(A) 7 (B) 13
(C) 21 (D) 15
38. ;fn 𝐴 rFkk 𝐵 iwjd dks.k gSa] rks
(A) 𝑠𝑖𝑛𝐵 = 𝑠𝑖𝑛𝐵 (B) 𝑠𝑒𝑐𝐴 = 𝑐𝑜𝑠𝑒𝑐𝐵
(C) 𝑐𝑜𝑡𝐴 = 𝑐𝑜𝑡𝐵 (D) 𝑡𝑎𝑛𝐴 = 𝑡𝑎𝑛𝐵
If 𝐴 and 𝐵 are complementary angles, then
(A) 𝑠𝑖𝑛𝐵 = 𝑠𝑖𝑛𝐵 (B) 𝑠𝑒𝑐𝐴 = 𝑐𝑜𝑠𝑒𝑐𝐵
(C) 𝑐𝑜𝑡𝐴 = 𝑐𝑜𝑡𝐵 (D) 𝑡𝑎𝑛𝐴 = 𝑡𝑎𝑛𝐵
39.cos(90 − 𝜙) =

Page 12 of 34

(A) 𝑠𝑖𝑛𝜙 (B) 𝑐𝑜𝑠𝜙
(C) −𝑠𝑖𝑛𝜙 (D) −𝑐𝑜𝑠𝜙
40. cos 27 − sin 63 =
(A) –1 (B) 0
(C) 1 (D)

41.𝑠𝑖𝑛2𝜃 = 2𝑠𝑖𝑛𝜃 lR; gS tc 𝜃 =
(A) 60 (B) 45
(C) 30 (D) 0
𝑠𝑖𝑛2𝜃 = 2𝑠𝑖𝑛𝜃 is true when 𝜃 =
(A) 60 (B) 45
(C) 30 (D) 0
4
42.;fn 𝑠𝑖𝑛𝜃 = rks tan 𝜃 =
5

(A) (B)

(C) (D)

If 𝑠𝑖𝑛𝜃 = then tan 𝜃 =

(A) (B)

(C) (D)

43.;fn 𝑡𝑎𝑛𝜃 = rks sec 𝜃 − tan 𝜃 =
√

(A)
√ (B) 2√ 2

(C) √7 (D) 1

If 𝑡𝑎𝑛𝜃 = then sec 𝜃 − tan 𝜃 =
√

(A)
√ (B) 2√ 2

(C) √7 (D) 1

44. =
Page 13 of 34

(A) 0 (B) 1
(C) 2 (D)

45. 3 cot 60 =
(A) (B) 1

(C) 3 (D) √3
46.𝑐𝑜𝑠1 ∙ 𝑐𝑜𝑠2 ∙ cos 3 … 𝑐𝑜𝑠180 =
(A) 1 (B) –1
(C) 0 (D) −

47.2 − 2𝑐𝑜𝑠𝑒𝑐 𝐴 =
(A) − cot 𝐴 (B) cot 𝐴
(C) 2 cot 𝐴 (D) −2cot 𝐴
48. ;fn 𝑎𝑠𝑖𝑛𝑥 = 1 vkSj 𝑏𝑐𝑜𝑠𝑥 = 1 rks 𝑐𝑜𝑡𝑥 =
(A) 1 (B)

(C) (D)

If 𝑎𝑠𝑖𝑛𝑥 = 1 and 𝑏𝑐𝑜𝑠𝑥 = 1 then 𝑐𝑜𝑡𝑥 =
(A) 1 (B)

(C) (D)

49. sin 45 + cos 45 − 1 =
(A) 0 (B)

(C) 1 (D) −1

50.− tan 𝐴 + =

(A) 0 (B) 1
(C) –1 (D) 2 tan 𝐴

51. − =

(A) 1 (B) 2

Page 14 of 34

(C) 0 (D) 4

52. × 𝑡𝑎𝑛60 =

(A) 0 (B) 1
(C) √3 (D) 2

53. ;fn 𝑐𝑜𝑠𝑒𝑐𝜙 − 𝑐𝑜𝑡𝜙 = 𝑦 rks 𝑐𝑜𝑡𝜙 =

(A) (B)

(C) (D)

If 𝑐𝑜𝑠𝑒𝑐𝜙 − 𝑐𝑜𝑡𝜙 = 𝑦 then 𝑐𝑜𝑡𝜙 =

(A) (B)

(C) (D)

54.𝑐𝑜𝑠𝑒𝑐30 =
(A) 𝑠𝑖𝑛30 (B) 𝑠𝑒𝑐60
(C) 𝑐𝑜𝑠𝑒𝑐60 (D) 𝑠𝑒𝑐30
55.;fn 2𝑐𝑜𝑠3𝜃 = 1 rks 𝜃 =
(A) 10 (B) 20
(C) 30 (D) 60

If 2𝑐𝑜𝑠3𝜃 = 1 then 𝜃 =
(A) 10 (B) 20
(C) 30 (D) 60
56.;fn 𝑠𝑖𝑛𝐵 = rks 𝑐𝑜𝑠𝐵 =

(A)
√ (B)
√

(C) (D)
√

If 𝑠𝑖𝑛𝐵 = then 𝑐𝑜𝑠𝐵 =

Page 15 of 34

(A)
√ (B)
√

(C) (D)
√

57.;fn 𝑡𝑎𝑛𝐴 + 𝑐𝑜𝑡𝐴 = 2 rks tan 𝐴 + cot 𝐴 =
(A) 0 (B) 1
(C) 2 (D) 4
If 𝑡𝑎𝑛𝐴 + 𝑐𝑜𝑡𝐴 = 2 then tan 𝐴 + cot 𝐴 =
(A) 0 (B) 1
(C) 2 (D) 4
58.fdl prqFkkaZ'k esa Hkqt vkSj dksfV nksuksa _.kkRed gksrs gSa\
(A) çFke (B) f}rh;
(C) r`rh; (D) prqFkZ
In which quadrant are both abscissa and ordinate negative?
(A) First (B) Second
(C) Third (D) Fourth
59.fcUnqvksa 𝐴(8, 0) vkSj 𝐵(−6, 2) ds chp dh nwjh gS&
(A) 2√10 bdkbZ;k¡ (B) 10√2 bdkbZ;k¡

(C) 10 bdkbZ;k¡ (D) 16 bdkbZ;k¡
The distance between the point 𝐴(8, 0) and 𝐵(−6, 2) is
(A) 2√10 𝑢𝑛𝑖𝑡𝑠 (B) 10√2 𝑢𝑛𝑖𝑡𝑠
(C) 10 𝑢𝑛𝑖𝑡𝑠 (D) 16 𝑢𝑛𝑖𝑡𝑠
60.𝑥-v{k vkSj 𝑦-v{k ds çfrPNsnu fcUnq dks dgk tkrk gS
(A) dsUæd (B) fcUnq
(C) yEcdsUæ (D) ifjdsUæ
The point of intersection of 𝑥 -axis and 𝑦-axis is said to be
(A) Centroid (B) Origin
(C) Orthocentre (D) Circumcentre

Page 16 of 34

61.fcUnqvksa 𝑃¼4]&5½ vkSj 𝑄¼8]7½ dks feykus okyh js[kk [kaM ds e/;-fcUnq ds
fu;ked gSa
(A) (2, 6) (B) (6, −1)
(C) (6, 1) (D) (−2, −6)
The Co-ordinates of the mid-point of the line segment joining the points
𝑃(4, −5) and 𝑄(8, 7) are
(A) (2, 6) (B) (6, −1)
(C) (6, 1) (D) (−2, −6)
62.ewy fcUnq ls fcUnq 𝑅(−𝑥, 𝑦) dh nwjh gS

(A) 𝑥 −𝑦 bdkbZ;k¡ (B) 𝑥 +𝑦 bdkbZ;k¡
(C) (𝑥 + 𝑦 ) bdkbZ;k¡ (D) (𝑥 + 𝑦) bdkbZ;k¡
The distance of the point 𝑅(−𝑥, 𝑦) from the origin is
(A) 𝑥 − 𝑦 units (B) 𝑥 + 𝑦 units
(C) (𝑥 + 𝑦 ) units (D) (𝑥 + 𝑦) units
63.;fn fcUnq,¡ ¼1] 2½] ¼&5] 6½ rFkk (𝑎, −2) lajs[k gSa] rks 𝑎 =
(A) 7 (B) –7
(C) 6 (D) 2
If points (1, 2), (−5, 6) and (𝑎, −2) are collinear, then 𝑎 =
(A) 7 (B) –7
(C) 6 (D) 2
64.js[kk 𝑦 = 7 dk vkys[k fuEu esa ls fdl fcUnq ls gksdj xqtjsxh\
(A) (7, 3) (B) (7, −6)
(C) (5, 7) (D) (7, 1)
The graph of the line 𝑦 = 7 passes through which of the following point?
(A) (7, 3) (B) (7, −6)
(C) (5, 7) (D) (7, 1)

Page 17 of 34

65.𝑦-v{k ls fcUnq 𝑃(4,6) dh nwjh gS&
(A) 6 bdkbZ;k¡ (B) 4 bdkbZ;k¡
(C) 2 bdkbZ;k¡ (D) 10 bdkbZ;k¡
The distance of the point 𝑃(4, 6) from 𝑦-axis is
(A) 6 units (B) 4 units
(C) 2 units (D) 10 units
66.fcUnq 𝐴(𝑎, 𝑏) vkSj 𝐵(𝑐, 𝑑) dks feykus okys js[kk[kaM 𝐴𝐵 dks 𝜆 ∶ 1 ds vuqikr
esa vUr% foHkkftr djus okys fcUnq dk 𝑦-funsZ”kkad gS&
(A) (B)

(C) (D)

The 𝑦-Co-ordinates of a point which divide the line segment 𝐴𝐵 joining
the points 𝐴(𝑎, 𝑏) and 𝐵(𝑐, 𝑑) in the ratio 𝜆 ∶ 1 internally is –

(A) (B)

(C) (D)

67.fdlh o`Ùk ds O;kl ds fljksa dk funsZ'kkad 𝑃(8, −6) vkSj 𝑄(−8, 6)gSa] rks blds
dsUæ dk funsZ'kkad gS&
(A) (4, −3) (B) (−4, 3)
(C) (1, 1) (D) (0, 0)
The Co-ordinates of the ends of diameter of a circle are 𝑃(8, −6) and
𝑄(−8, 6), then Co-ordinate of its centre is–
(A) (4, −3) (B) (−4, 3)
(C) (1, 1) (D) (0, 0)
68.,d f=Hkqt dk dsUæd ¼4]0½ gS vkSj mlds nks 'kh"kZ ¼3]4½ vkSj ¼5]&6½ gSa] rks
rhljk 'kh"kZ gS
(A) (2, 4) (B) (4, 2)
(C) (0, 2) (D) (2, 0)

Page 18 of 34

The Centroid of a triangle is (4, 0) and its two vertices are (3, 4) and
(5, −6), then the third vertex is
(A) (2, 4) (B) (4, 2)
(C) (0, 2) (D) (2, 0)

69. fcUnq − , 4 fdl ikn esa fLFkr gS\

(A) çFke (B) f}rh;
(C) r`rh; (D) prqFkZ
In which quadrant does the point − , 4 lie?

(A) First (B) Second
(C) Third (D) Fourth
70.𝑥-v{k ij lHkh fcUnqvksa dk dksfV gksrk gS &
(A) 0 (B) 1
(C) 2 (D) –1
Ordinate of all the points on 𝑥-axis is –
(A) 0 (B) 1
(C) 2 (D) –1

71.;fn Δ𝐴𝐵𝐶 vkSj ΔPQR le:i gSa rFkk 𝐴 = 42 , Q= 84 rks 𝐶 =

(A) 48 (B) 54
(C) 96 (D) 42

If Δ𝐴𝐵𝐶 and ΔPQR are similar and 𝐴 = 420 , Q = 840 then 𝐶 =

(A) 48 (B) 54
(C) 96 (D) 42

72.;fn Δ𝑃𝑄𝑅 esa 𝑃𝑅 = 𝑃𝑄 + 𝑄𝑅 rks 𝑄 =

(A) 45 (B) 60
(C) 75 (D) 90

In Δ𝑃𝑄𝑅 if 𝑃𝑅 = 𝑃𝑄 + 𝑄𝑅 then 𝑄 =

Page 19 of 34

(A) 45 (B) 60
(C) 75 (D) 90
73.;fn 𝛥𝐴𝐵𝐶 ,d leckgq f=Hkqt gS tSls 𝐴𝐷 ⊥ 𝐵𝐶 rks 𝐴𝐷 =
(A) 2𝐷𝐶 (B) 𝐷𝐶

(C) 4𝐷𝐶 (D) 3𝐶𝐷
If Δ𝐴𝐵𝐶 is an equilateral triangle such that 𝐴𝐷 ⊥ 𝐵𝐶, then 𝐴𝐷 =
(A) 2𝐷𝐶 (B) 𝐷𝐶

(C) 4𝐷𝐶 (D) 3𝐶𝐷

74. Δ𝐴𝐵𝐶 esa] fcUnq 𝐷 vkSj 𝐸 Øe”k% Hkqtkvksa 𝐴𝐵 rFkk 𝐴𝐶 ij bl çdkj gS fd

𝐷𝐸 || 𝐵𝐶 A ;fn = vkSj 𝐴𝐶 = 18 lsehŒ rks 𝐴𝐸 =

(A) 8 lsehŒ (B) 9 lsehŒ
(C) 12 lsehŒ (D) 4 lsehŒ
In Δ𝐴𝐵𝐶, 𝐷 and E are points on the sides 𝐴𝐵 and AC respectively such
that 𝐷𝐸 ∥ 𝐵𝐶. If = and 𝐴𝐶 = 18 cm. then 𝐴𝐸 =

(A) 8 cm. (B) 9 cm.
(C) 12 cm. (D) 4 cm.
75.lef}ckgq ledks.k f=Hkqt esa çR;sd U;wudks.k dh eki gksxh
(A) 60 (B) 90
(C) 45 (D) 30
In isosceles right triangle the measure of each acute angle will be
(A) 60 (B) 90
(C) 45 (D) 30
76.nks le:i f=Hkqtksa dh laxr Å¡pkbZ;k¡ 7 lsehŒ vkSj 10 lsehŒ gS] rks muds
{ks=Qyksa dk vuqikr gksxk
(A) 49 ∶ 100 (B) 100 ∶ 49
(C) √10 : √7 (D) √7 : √10

Page 20 of 34

The Corresponding heights of two similar triangles are 7 cm. and 10 cm. ,
then the ratio of their areas will be
(A) 49 ∶ 100 (B) 100 ∶ 49
(C) √10 : √7 (D) √7 : √10
77.4-5 lsehŒ f=T;k okys o`Ùk ij [khaph xbZ nks lekarj Li”kZ js[kkvksa ds chp dh
nwjh gksxh
(A) 4.5 lsehŒ (B) 1.5 lsehŒ
(C) 9 lsehŒ (D) 6 lsehŒ
The distance between two parallel tangents drawn on a circle of radius
4.5 𝑐𝑚 is–
(A) 4.5 𝑐𝑚. (B) 1.5 𝑐𝑚.
(C) 9 𝑐𝑚. (D) 6 𝑐𝑚.
78.fdlh ckº; fcUnq ls o`Ùk ij fdruh Li'kZ js[kk,¡ [khaph tk ldrh gSa \
(A) nks (B) ,d
(C) rhu (D) vufxur

How many tangents can be drawn to a circle from an external point?

(A) Two (B) One
(C) Three (D) Infinitely many
79.;fn 𝑂 dsUæ okys o`Ùk ij 𝑃𝐴 rFkk 𝑃𝐵 nks Li'kZ js[kk,¡ bl çdkj gSa fd

𝐴𝑃𝐵 = 500 rks 𝐴𝑂𝐵 =
(A) 50 (B) 25
(C) 90 (D) 130

If 𝑃𝐴 and 𝑃𝐵 are two tangents to a circle with centre 𝑂 such that

𝐴𝑃𝐵 = 500 then ∠𝐴𝑂𝐵 =
(A) 50 (B) 25
(C)
Page 21 of 34

(D) 90 (E) 130

80.nh xbZ vk—fr esa] fcUnq 𝑂 o`Ùk dk dsUæ gS rFkk 𝐴𝑂𝐵 = 300 gS] rks 𝑂𝐵𝐴
dk eku gS
(A) 30
30
(B) 60
A B
(C) 75
(D) 90

In the given figure point 𝑂 is the centre of the circle and 𝐴𝑂𝐵 = 300
then the value of 𝑂𝐵𝐴 is
(A) 30
(B) 60 30

(C) 75 A B
(D) 90
81. 8 lsehŒ f=T;k okys o`Ùk ds dsUæ ls 17 lsehŒ nwj fLFkr ,d fcUnq ls o`Ùk ij
[khaph xbZ Li'kZ js[kk dh yEckbZ gksxh&
(A) 15 lsehŒ (B) 8 lsehŒ
(C) √353 lsehŒ (D) 25 lsehŒ
The length of the tangent drawn from a point 17 𝑐𝑚 away from the centre
of a circle of radius 8 cm. is –
(A) 15 𝑐𝑚. (B) 8 𝑐𝑚.
(C) √353 𝑐𝑚. (D) 25 𝑐𝑚.

82.,d ?ku ds fod.kZ dh yEckbZ 5√3 lsehŒ gS] rks bldk lEiw.kZ i`"B dk {ks=Qy
gksxk&
(A) 125 lseh2Œ (B) 150 lseh2Œ

(C) 75 lseh2Œ (D) 250 lseh2Œ

The length of the diagonal of a cube is 5√3 cm., then its total surface area
will be

Page 22 of 34

(A) 125 𝑐𝑚. (B) 150 𝑐𝑚.
(C) 75 𝑐𝑚. (D) 250 𝑐𝑚.
83.;fn ,d csyu vkSj 'kadq ds f=T;k vkSj Å¡pkbZ leku gksa] rks muds vk;ruksa dk
vuqikr gksxk
(A) 1∶3 (B) 3∶1
(C) 3∶4 (D) 2∶3
If the radius and height of a cylinder and a cone be equal then the ratio of
their volumes will be–
(A) 1∶3 (B) 3∶1
(C) 3∶4 (D) 2∶3
84.lqjkgh dk la;kstu gS&
(A) xksyk rFkk csyu (B) csyu rFkk 'kadq
(C) nks v/kZxksysa (D) v/kZxksyk rFkk csyu
A surahi is the combination of
(A) a sphere and a cylinder (B) a cylinder and a cone
(C) two hemispheres (D) a hemisphere and a
cylinder
85.,d ?kM+h ds feuV okyh lwbZ }kjk 45 feuV esa cuk;k x;k dks.k gS
(A) 180 (B) 270
(C) 90 (D) 135
Angle described by minute hand of a watch in 45 minutes is
(A) 180 (B) 270
(C) 90 (D) 135
86.10 lsehŒ f=T;k okys v/kZo`Ùk dh dqy ifjfefr gksxh&
(A) (𝜋 + 2)10 lsehŒ (B) (𝜋 + 1)10 lsehŒ
(C) 10𝜋 lsehŒ (D) (𝜋 + 5)10 lsehŒ
Total perimeter of a semi-circle of radius 10 𝑐𝑚 is –
(A) (𝜋 + 2)10 𝑐𝑚. (B) (𝜋 + 1)10 𝑐𝑚.

Page 23 of 34

(C) 10𝜋 𝑐𝑚. (D) (𝜋 + 5)10 𝑐𝑚.
87. 6 lsehΠO;kl ds ,d xksys }kjk foLFkkfir gok dk vk;ru gS&
(A) 36 ?ku lsehŒ (B) 108 𝜋 ?ku lsehŒ
(C) 36 𝜋 ?ku lsehŒ (D) 144 𝜋 ?ku lsehŒ
The volume of air displaced by a sphere of diameter 6 cm. is
(A) 36 𝑐𝑢𝑏𝑖𝑐 𝑐𝑚. (B) 108 𝜋 𝑐𝑢𝑏𝑖𝑐 𝑐𝑚.
(C) 36 𝜋 𝑐𝑢𝑏𝑖𝑐 𝑐𝑚. (D) 144 𝜋 𝑐𝑢𝑏𝑖𝑐 𝑐𝑚.
88. 𝑝 f=T;k okys o`Ùk esa dks.k 𝜃 ds f=T;[kaM dk {ks=Qy gS

(A) oxZ bdkbZ (B) oxZ bdkbZ

(C) oxZ bdkbZ (D) oxZ bdkbZ
The arc of a sector of an angle 𝜃 in the circle with radius 𝑝 is

(A) square unit (B) square unit

(C) square unit (D) square unit

89.;fn fdlh v/kZxksys ds lEiw.kZ i`"B dk {ks=Qy 462 lseh2Πgks] rks mldh f=T;k
gksxh&
(A) 14 lsehŒ (B) 7 lsehŒ
(C) 6 lsehŒ (D) 3.5 lsehŒ

If the total surface area of a hemisphere is 462 𝑐𝑚. then its radius will
be–

(A) 14 cm. (B) 7 𝑐𝑚.
(C) 6 𝑐𝑚. (D) 3.5 𝑐𝑚.
90.,d leckgq f=Hkqt dk {ks=Qy 81√3 lsehŒ2 gS] rks bldh Hkqtk gS

(A) 9√3 lsehŒ (B) 9 lsehŒ

(C) 3√3 lsehŒ (D) 18 lsehŒ

The area of an equilateral triangle is 81√3 𝑐𝑚. , then its side is

Page 24 of 34

(A) 9√3 𝑐𝑚. (B) 9 𝑐𝑚.

(C) 3√3 𝑐𝑚. (D) 18 𝑐𝑚.
91.rhu iklsa dh mNky esa laHko ifj.kkeksa dh la[;k gksxh &
(A) 216 (B) 136
(C) 128 (D) 18
In tossing of three dice the number of possible outcomes is –
(A) 216 (B) 136
(C) 128 (D) 18
92.;fn dksbZ ?kVuk ?kfVr ugha gks ldrh gS rks mldh çkf;drk gksxh

(A) 0 (B)

(C) 1 (D)

If an event cannot occur then its probability is –
(A) 0 (B)

(C) 1 (D)

93.,d iklk ,d ckj Qsadk tkrk gSA vHkkT; la[;k vkus dh çkf;drk gksxh

(A) (B)

(C) (D)

A dice is thrown once. The probability of getting a prime number will be
(A) (B)

(C) (D)

94.vPNh çdkj ls QsVh xbZ ,d rk'k dh xM~Mh esa ls ,d iÙkk ;k–PN;k fudkyk
tkrk gS] rks blds dkyk jax dk jkuh gksus dh çkf;drk gS&
(A) (B)

(C) (D)

Page 25 of 34

One card is drawn at random from a well-shuffled deck of playing cards
then its probability of getting a black queen is
(A) (B)

(C) (D)

95.nks flDdksa dh mNky esa ,d Hkh “kh’kZ ugha vkus dh çkf;drk gksxh&

(A) (B)

(C) (D)

The probability of getting no head in tossing two coins will be –
(A) (B)

(C) (D)

96.23]20]22]37]24]23]19]22]17]23 dk cgqyd gS
(A) 23 (B) 22
(C) 19 (D) 37
Mode of 23, 20, 22, 37, 24, 23, 19, 22, 17, 23 is
(A) 23 (B) 22
(C) 19 (D) 37
97. ;fn ik¡p vk¡dM+ksa 𝑥, 𝑥 + 1, 𝑥 + 2, 𝑥 + 3 rFkk 𝑥 + 4 dk ek/; 14 gks rks 𝑥 =
(A) 10 (B) 14
(C) 12 (D) 11
If the mean of the five data 𝑥, 𝑥 + 1, 𝑥 + 2, 𝑥 + 3 and 𝑥 + 4 is 14 then
𝑥=
(A) 10 (B) 14
(C) 12 (D) 11
98.fuEufyf[kr esa ls dkSu dsUæh; ço`fÙk dh eki ugha gS\
(A) ifjlj (B) cgqyd
(C) ek/; (D) ekf/;dk

Page 26 of 34

Which of the following is not a measure of central tendency?
(A) Range (B) Mode
(C) Mean (D) Median
99.çFke 8 vHkkT; la[;kvksa dk ekf/;dk gS&
(A) 13 (B) 11
(C) 9 (D) 7
The median of first 8 prime numbers is
(A) 13 (B) 11
(C) 9 (D) 7
100. fuEufyf[kr forj.k ds fy,
oxZ&varjky 0-10 10-20 20-30 30-40 40-50
ckjackjrk 8 12 20 6 4
cgqyd oxZ dk mPp&lhek gS&

(A) 20 (B) 30
(C) 25 (D) 50
For the following distribution
Class-interval 0-10 10-20 20-30 30-40 40-50
Frequency 8 12 20 6 4
The upper limit of the modal class is-

(A) 20 (B) 30
(C) 25 (D) 50

[k.M&c @ SECTION-B

Page 27 of 34

y?kq mÙkjh; ç'u @Short Answer Type Questions

ç'u la[;k 1 ls 30 rd y?kq mÙkjh; ç'u gSAa buesa ls fdUgha 15 ç'uksa ds mÙkj nsaA
çR;sd ç'u ds fy, 2 vad fu/kkZfjr gSA 𝟏𝟓 × 𝟐 = 𝟑𝟎
Question Nos. 1 to 30 are Short Answer Type Questions. Answer any 15
questions. Each question carries 2 marks. 15 × 2 = 30
1. fl) djsa fd 2√3 ,d vifjes; la[;k gSA 2
Prove that 2√3 is an irrational number.
2. la[;k 12]144 vkSj 240 dk y?kqÙke lekioR;Z vHkkT; xq.ku[kaM fof/k ls Kkr
djsaA 2
Find the Lowest Common Multiple of the numbers 12, 144 and 240 by
prime factorization.
3. ;wfDyM ds foHkktu ,YxksfjFe dk mi;ksx dj] 135 vkSj 225 dk egÙke
lekioÙkZd Kkr djsaA 2
Using Euclid’s division algorithm, find the Highest Common Factor of
135 and 225.
4. f}?kkr cgqin 6𝑦 − 3 − 7𝑦 ds 'kwU;dksa dks Kkr djsAa 2
Find the zeroes of the quadratic polynomial 6𝑦 − 3 − 7𝑦.
( )
5. ;fn 𝑝(𝑥) = 𝑥 − 18𝑥 + 81 rFkk 𝑞(𝑥) = (𝑥 − 9) rks dk ?kkr Kkr
( )

djsaA 2
If 𝑝(𝑥) = 𝑥 − 18𝑥 + 81 and 𝑞(𝑥) = (𝑥 − 9) then find the degree of
( )
.
( )

6. ;fn cgqin 𝑓(𝑥) = 5𝑥 − 7𝑥 + 1 ds 'kwU;kad 𝛼 rFkk 𝛽 gSaA 𝛼 + 𝛽 dk
eku Kkr djsaA 2
If 𝛼 and 𝛽 are zeros of the polynomial 𝑓(𝑥) = 5𝑥 − 7𝑥 + 1. Find the
value of 𝛼 + 𝛽 .
7. lehdj.k ;qXe 𝑥 − 2𝑦 = 0 rFkk 3𝑥 + 4𝑦 − 20 = 0 dks gy djsaA 2

Page 28 of 34

Solve the pair of equation 𝑥 − 2𝑦 = 0 and 3𝑥 + 4𝑦 − 20 = 0.
8. f}?kkr lehdj.k 3𝑦 − 2√6𝑦 + 2 = 0 dk fofoDrdj Kkr djsa ,oa fQj
dh ç—fr Kkr crk,¡A 2
Find the discriminant of the quadratic equation 3𝑦 − 2√6𝑦 + 2 = 0 and
hence find the nature of the roots.
9. f}?kkr lw= dk mi;ksx dj lehdj.k 𝑥 + 7𝑥 − 60 = 0 dk ewy fudkysaA 2
Using quadratic formula find the roots of the equation 𝑥 + 7𝑥 − 60 = 0.
10.D;k la[;kvksa dh lwph 5]11]17]23----- dk dksbZ in 301 gS\ 2
Check Whether 301 is a term of the list of numbers 5, 11, 17, 23, … ?
11.fdlh lekarj Js<h+ dk 17 ok¡ in mlds 10 osa in ls 14 vf/kd gSA bldk
lkoZvarj Kkr djsaA 2
The 17th term of an arithmetic progression exceeds its 10 th term by 14.
Find the Common difference.
12.;ksxQy fudkysa% 7 + 10 + 14 + ⋯ + 84. 2

Find the sum: 7 + 10 + 14 + ⋯ + 84.

13.0 vkSj 50 ds chp dh fo"ke la[;kvksa dk ;ksx Kkr djsaA 2
Find the sum of the odd numbers between 0 and 50.

14. ;fn 5 cot 𝐴 = 3 rks dk eku fudkysaA 2

If 5 cot 𝐴 = 3 then find the value of .

15. fl) djsa fd (sin 𝜃 − cos 𝜃 + 1) 𝑐𝑜𝑠𝑒𝑐 𝜃 = 2. 2
Prove that (sin 𝜃 − cos 𝜃 + 1) 𝑐𝑜𝑠𝑒𝑐 𝜃 = 2.

16. dk eku fudkysAa 2

Find the value of .

17. 𝑠𝑖𝑛35 ∙ 𝑐𝑜𝑠55 + 𝑐𝑜𝑠35 𝑠𝑖𝑛55 dk eku fudkysaA 2
Find the value 𝑠𝑖𝑛35 ∙ 𝑐𝑜𝑠55 + 𝑐𝑜𝑠35 𝑠𝑖𝑛55 .
18.ml f=Hkqt dk {ks=Qy Kkr djsa ftlds 'kh"kZ ¼4]&3½]¼&9] 7½ vkSj ¼8] 8½ gSaA 2
Page 29 of 34

Find the area of the triangle whose vertices are (4, −3), (−9, 7) and
(8, 8).
19.fcUnqvksa ¼5]&6½ vkSj ¼&1]&4½ dks tksM+us okys js[kk[kaM dks 𝑥-v{k fdl vuqikr
esa foHkkftr djrh gS\ 2
Find the ratio in which the 𝑥-axis divides the line segment joining the
points (5, −6) and (−1, −4)?
20.𝑥 dk eku Kkr djsa] ftlds fy, fcUnq 𝑃(𝑥, 2) vkSj 𝑄(3, 4) ds chp dh nwjh
8 bdkbZ gSA 2
Find the value of 𝑥 for which the distance between the points 𝑃(𝑥, 2) and
𝑄(3, 4) is 8 units.
21.fcUnqvksa ¼8] 10½ vkSj ¼4] 6½ dks feykus okys js[kk[kaM ds e/; fcUnq dh nwjh
fcUnq ¼2] 4½ ls Kkr djsaA 2
Find the distance of the midpoint of the line segment joining the points
(8, 10) and (4, 6) from the point (2, 4).
22.;fn ∆𝐴𝐵𝐶, 𝐵 = 𝐶 vkSj fcUnq 𝐷 rFkk 𝐸 Øe'k% Hkqtkvksa 𝐴𝐵 rFkk 𝐴𝐶
ij bl çdkj gSa fd 𝐵𝐷 = 𝐶𝐸 rks fl) djsa fd 𝐷𝐸 ∥ 𝐵𝐶. 2
If in ∆𝐴𝐵𝐶, 𝐵 = 𝐶 and points 𝐷 and 𝐸 are on the sides 𝐴𝐵 and 𝐴𝐶
respectively such that 𝐵𝐷 = 𝐶𝐸 then prove that 𝐷𝐸 ∥ 𝐵𝐶.
23.nh xbZ vkÑfr esa 𝑆𝑇 ∥ 𝑄𝑅 ] ;fn 𝑆𝑇 = 3lsehŒ] 𝑄𝑅 = 6 lsehŒ rFkk
{ksŒ(∆𝑃𝑆𝑇) = 15 lsehŒ2] rks ∆𝑃𝑄𝑅 dk {ks=Qy Kkr djssAa 2
P

S T
3 lsehŒ

Q R
6 lsehŒ

Page 30 of 34

In the given figure 𝑆𝑇 ∥ 𝑄𝑅. If 𝑆𝑇 = 3 𝑐𝑚., 𝑄𝑅 = 6 𝑐𝑚. and
𝑎𝑟. (∆𝑃𝑆𝑇) = 15 𝑐𝑚 then find the area of ∆𝑃𝑄𝑅.
P

S T
3 cm.-

Q R
6 cm.
-
24.fdlh o`Ùk ds dsUæ ls 13 lsehŒ dh nwjh ij fdlh fcUnq 𝑃 ls [khaph xbZ Li'kZ
js[kk dh yEckbZ 12 lsehŒ gSA o`Ùk dh f=T;k Kkr djsaA 2
The length of a tangent drawn from a point 𝑃 which is at a distance 13
𝑐𝑚. from the centre of a circle, is 12 cm. Find the radius of the circle.
25. fdlh fHkUu ds va'k vkSj gj esa 2 tksM+ nsus ij og 5 ds cjkcj gks tkrk gS
vkSj ;fn mlds va'k vkSj gj esa ls 1 ?kVk ns rks og 7 ds cjkcj gks tkrk gS
bu dFkuksa ds fy, lehdj.k fy[ksa 2
If 2 is added to the numerator and denominator of a fraction it becomes to
5 and if 1 is subtracted from its numerator and denominator it becomes 7.
Write the equations for these statements.
26.fuEufyf[kr caVu dk ek/; Kkr djsa% 2
oxZ&varjky 0-10 10-20 20-30 30-40 40-50
ckjackjrk 8 15 12 16 9

Find the mean of the following distribution:
Class-interval 0-10 10-20 20-30 30-40 40-50
Frequency 8 15 12 16 9

27.;fn 14 lsehŒ f=T;k okys o`Ùk dk ,d pki dsUæ ij 120 dk dks.k varfjr
djrk gS] rks pki dh yEckbZ Kkr djsaA 2
If the arc of a circle of radius 14 𝑐𝑚. subtends 120 at the centre then
find the length of the arc.

Page 31 of 34

28.;fn fdlh yaco`Ùkh; csyu dh Å¡pkbZ mlds vk/kkj dh f=T;k dh nqxquh gS ,oa
mlds oØ i`"B dk {ks=Qy 616 lsehŒ2 gS] rks mlds vk/kkj dh f=T;k fudkysaA2
If the height of a right circular cylinder is twice the radius of its base and
its curved surface area is 616 𝑐𝑚 , find the radius of its base.
29.;fn rhu flDdksa dks ,d lkFk mNkyk tkrk gS rks rhuksa ij ,d gh ifj.kke
vkus dh çkf;drk Kkr djsaA 2
If three coins are tossed simultaneously then find the probability of
getting the same outcome in all three coins.
30.;fn nks iklksa dks ,d lkFk Qsd
a us ij nksuksa ij vkus okys vadks dk varj 3 vkus
dh çkf;drk fudkysaA 2
If two dice are thrown simultaneously, find the probability that the
difference between the numbers on both the dice is 3.

nh?kZ mÙkjh; ç'u @ Long Answer Type Questions
ç'u la[;k 31 ls 38 nh?kZ mÙkjh; ç'u gSa A buesa ls fdUgh 4 ç'uksa ds mÙkj nsa A
çR;sd ç'.0u ds fy, 5 vad fu/kkZfjr gSA 𝟒 × 𝟓 = 𝟐𝟎
Question Nos. 31 to 38 are Long Answer Type Questions. Answer any 4 questions.
Each question carries 5 marks. 4 × 5 = 20
31. xzkQh; fof/k ls jSf[kd lehdj.k ;qXe 𝑥 − 𝑦 + 1 = 0 rFkk 2𝑥 + 3𝑦 − 12 = 0
dks gy djsa A 5
Using graphical method, solve the pair of linear equations
𝑥 − 𝑦 + 1 = 0 and 2𝑥 + 3𝑦 − 12 = 0.
32. ,d vk;rkdkj [ksr dk fod.kZ mldh NksVh Hkqtk ls 60ehVj vf/kd yack gSA
;fn cM+h Hkqtk NksVh Hkqtk ls 30ehVj vf/kd gks] rks [ksr dh Hkqtk,¡ Kkr djsaA 5
The diagonal of a rectangular field is 60 metres more than the shorter side.
If the longer side is 30 metres more than the shorter side, find the sides of
the field.
33.fl) djsa fd ,d ledks.k f=Hkqt esa d.kZ dk oxZ vU; nks Hkqtkvksa ds oxksaZ ds

Page 32 of 34

;ksxQy ds cjkcj gksrk gSA 5
Prove that in a right triangle, the square of the hypotenuse is equal to the
sum of the squares of the other two sides.

34.,d f=Hkqt 𝑃𝑄𝑅 cuk,¡ ftlesa 𝑄𝑅 = 8 lsehŒA 𝑄 = 450 ] 𝑃 = 1050 gS]

fQj ∆𝑃𝑄𝑅 ds le:i ,d f=Hkqt dk jpuk djsa ftldh Hkqtk,¡ ∆𝑃𝑄𝑅 dh

laxr Hkqtkvksa dh xquh gksaA 5

Draw a triangle 𝑃𝑄𝑅 in which 𝑄𝑅 = 8 𝑐𝑚. 𝑄 = 450 , 𝑃 = 1050 .

Then construct a triangle similar to ∆𝑃𝑄𝑅. Whose sides are times

the corresponding sides of ∆𝑃𝑄𝑅.
35.,d O;fDr] tks unh ds ,d fdukjs ij [kM+k gS unh ds nwljs fdukjs ij fLFkr
,d isM+ ds f”k[kj dk mUu;u dks.k 60 ikrk gSA tc og O;fDr fdukjs ls 36
ehVj ihNs gV tkrk gS] rks og mUu;u dks.k 30 dk gks tkrk gSA isM+ dh
Å¡pkbZ rFkk unh dh pkSMk+ bZ Kkr djsaA 5
A person standing on the bank of a river observes that the angle of
elevation of the top of a tree standing on the opposite bank is 60 . When
he moves 36 metres away from the bank, he finds the angle of elevation to
be 30 . Find the height of the tree and the width of the river.
36.fl) djsa fd 5
+ = 2 sec 𝐴.
( ) ( )

Prove that

𝑐𝑜𝑠𝑒𝑐𝐴 𝑐𝑜𝑠𝑒𝑐𝐴
+ = 2 sec 𝐴.
(𝑐𝑜𝑠𝑒𝑐𝐴 − 1) (𝑐𝑜𝑠𝑒𝑐𝐴 + 1)

37. fuEufyf[kr vk¡dM+s dk ekf/;dk Kkr djsa 5
çkIrkad 70% 60% 50% 40% 30% 20%
ls vf/kd ls vf/kd ls vf/kd ls vf/kd ls vf/kd ls vf/kd

Page 33 of 34

Nk= la[;k 7 18 40 42 53 60

Find the median of the following data
Marks More More than More More than More than More
obtained than 60% than 40% 30% than 20%
70% 50%
No. of 7 18 40 42 53 60
Students

38.,d yac o`Ùkh; 'kadq ds vk/kkj dh f=T;k vkSj Å¡pkbZ Øe'k% 5 ehVj rFkk 12 ehVj
gSA ml “kadq dk vk;ru ,oa dqy i`"Bh; {ks=Qy Kkr djsaA 5
The base radius and height of a right circular cone are 5 meter and 12 meters
respectively. Find its volume and total surface area.

Page 34 of 34

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