Class 10 Mathematics (Standard): Question Paper for 2023 (Set 2) | Mathematics (Maths) Class 10 PDF Download

 Page 1


30/4/2 1 [P.T.O. 
 
 
 
 
 
 
 
 
 
 
 
J{UV (_mZH$) - g¡ÕmpÝVH$ 
MATHEMATICS (STANDARD) - Theory 
{ZYm©[aV g_` … 3 KÊQ>o 
Time allowed : 3 hours 
A{YH$V_ A§H$ … 80 
Maximum Marks : 80 
ZmoQ> / NOTE :    
(i) H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _| _w{ÐV n¥ð> 15 h¢Ÿ& 
Please check that this question paper contains 15 printed pages. 
(ii) àíZ-nÌ _| Xm{hZo hmW H$s Amoa {XE JE àíZ-nÌ H$moS> H$mo N>mÌ CÎma-nwpñVH$m Ho$ _wI-n¥ð> na 
{bI|& 
Q.P. Code given on the right hand side of the question paper should be written on 
the title page of the answer-book by the candidate.  
(iii) H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _| 38 àíZ h¢& 
Please check that this question paper contains 38 questions. 
(iv) H¥$n`m àíZ H$m CÎma {bIZm ewê$ H$aZo go nhbo, CÎma-nwpñVH$m _| àíZ H$m H«$_m§H$ Adí` 
{bI|& 
Please write down the Serial Number of the question in the answer-book before 
attempting it. 
(v) Bg àíZ-nÌ H$mo n‹T>Zo Ho$ {bE 15 {_ZQ> H$m g_` {X`m J`m h¡& àíZ-nÌ H$m {dVaU nydm©• _| 
10.15 ~Oo {H$`m OmEJm& 10.15 ~Oo go 10.30 ~Oo VH$ N>mÌ Ho$db àíZ-nÌ H$mo n‹T>|Jo Am¡a 
Bg Ad{Y Ho$ Xm¡amZ do CÎma-nwpñVH$m na H$moB© CÎma Zht {bI|Jo& 
15 minute time has been allotted to read this question paper. The question paper 
will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will 
read the question paper only and will not write any answer on the answer-book 
during this period. 
 
30/4/2 
àíZ-nÌ H$moS> 
Q.P. Code 
 
narjmWu àíZ-nÌ H$moS> H$mo CÎma-nwpñVH$m Ho$ 
_wI-n¥ð> na Adí` {bI|Ÿ& 
Candidates must write the Q.P. Code 
on the title page of the answer-book. 
SET ~ 2 
Series WX1YZ/4 
 
amob Z§. 
Roll No. 
 
 
# 
Page 2


30/4/2 1 [P.T.O. 
 
 
 
 
 
 
 
 
 
 
 
J{UV (_mZH$) - g¡ÕmpÝVH$ 
MATHEMATICS (STANDARD) - Theory 
{ZYm©[aV g_` … 3 KÊQ>o 
Time allowed : 3 hours 
A{YH$V_ A§H$ … 80 
Maximum Marks : 80 
ZmoQ> / NOTE :    
(i) H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _| _w{ÐV n¥ð> 15 h¢Ÿ& 
Please check that this question paper contains 15 printed pages. 
(ii) àíZ-nÌ _| Xm{hZo hmW H$s Amoa {XE JE àíZ-nÌ H$moS> H$mo N>mÌ CÎma-nwpñVH$m Ho$ _wI-n¥ð> na 
{bI|& 
Q.P. Code given on the right hand side of the question paper should be written on 
the title page of the answer-book by the candidate.  
(iii) H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _| 38 àíZ h¢& 
Please check that this question paper contains 38 questions. 
(iv) H¥$n`m àíZ H$m CÎma {bIZm ewê$ H$aZo go nhbo, CÎma-nwpñVH$m _| àíZ H$m H«$_m§H$ Adí` 
{bI|& 
Please write down the Serial Number of the question in the answer-book before 
attempting it. 
(v) Bg àíZ-nÌ H$mo n‹T>Zo Ho$ {bE 15 {_ZQ> H$m g_` {X`m J`m h¡& àíZ-nÌ H$m {dVaU nydm©• _| 
10.15 ~Oo {H$`m OmEJm& 10.15 ~Oo go 10.30 ~Oo VH$ N>mÌ Ho$db àíZ-nÌ H$mo n‹T>|Jo Am¡a 
Bg Ad{Y Ho$ Xm¡amZ do CÎma-nwpñVH$m na H$moB© CÎma Zht {bI|Jo& 
15 minute time has been allotted to read this question paper. The question paper 
will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will 
read the question paper only and will not write any answer on the answer-book 
during this period. 
 
30/4/2 
àíZ-nÌ H$moS> 
Q.P. Code 
 
narjmWu àíZ-nÌ H$moS> H$mo CÎma-nwpñVH$m Ho$ 
_wI-n¥ð> na Adí` {bI|Ÿ& 
Candidates must write the Q.P. Code 
on the title page of the answer-book. 
SET ~ 2 
Series WX1YZ/4 
 
amob Z§. 
Roll No. 
 
 
# 
  
30/4/2  2
gm_mÝ` {ZX}e … 
{ZåZ{b{IV {ZX}em| H$mo ~hþV gmdYmZr go n{‹T>E Am¡a CZH$m nmbZ H$s{OE … 
(i) Bg àíZ-nÌ _| 38 àíZ h¢Ÿ& g^r àíZ A{Zdm`© h¢Ÿ& 
(ii) àíZ-nÌ nm§M IÊS>m| _| {d^m{OV h¡ - IÊS> H$, I, J, K VWm ‹S>Ÿ& 
(iii) IÊS> H$ _| àíZ g§»`m 1 go 18 VH$ ~hþ{dH$ënr` VWm àíZ g§»`m 19 Ed§ 20 A{^H$WZ Ed§ 
H$maU AmYm[aV EH$-EH$ A§H$ Ho$ àíZ h¢Ÿ& 
(iv) IÊS> I _| àíZ g§»`m 21 go 25 VH$ A{V bKw-CÎmar` (VSA) àH$ma Ho$ Xmo-Xmo A§H$m| Ho$ àíZ h¢Ÿ& 
 (v) IÊS> J _| àíZ g§»`m 26 go 31 VH$ bKw-CÎmar` (SA) àH$ma Ho$ VrZ-VrZ A§H$m| Ho$  
àíZ h¢Ÿ& 
(vi) IÊS> K _| àíZ g§»`m 32 go 35 VH$ XrK©-CÎmar` (LA) àH$ma Ho$ nm§M-nm§M A§H$m| Ho$ àíZ h¢Ÿ& 
(vii) IÊS> ‹S> _| àíZ g§»`m 36 go 38 VH$ òmoV / àH$aU BH$mB© AmYm[aV Mma-Mma A§H$m| Ho$ àíZ h¢Ÿ& 
Am§V[aH$ {dH$ën Xmo-Xmo A§H$m| Ho$ àíZ _| {X`m J`m h¡Ÿ& 
(viii) àíZ-nÌ _| g_J« {dH$ën Zht {X`m J`m h¡Ÿ& `Ú{n, IÊS> I Ho$ 2 àíZm| _|, IÊS> J Ho$ 2 àíZm| _|, 
IÊS> K Ho$ 2 àíZm| _| VWm IÊS> ‹S> Ho$ 3 àíZm| _| Am§V[aH$ {dH$ën H$m àmdYmZ {X`m J`m h¡Ÿ& 
(ix) Ohm§ Amdí`H$ hmo, ñdÀN> AmH¥${V`m§ ~ZmE§Ÿ& `{X Amdí`H$ hmo Vmo p=22/7 b|Ÿ& 
(x) H¡$bHw$boQ>a H$m Cn`moJ d{O©V h¡Ÿ& 
IÊS> - H$ 
IÊS> - H$ _| ~hþ{dH$ënr` àH$ma Ho$ àíZ h¢Ÿ& àË`oH$ àíZ 1 A§H$ H$m h¡Ÿ& 
1. ? (0
o
 = ? = 90
o
) Ho$ g^r _mZm| Ho$ {bE {ZåZ _| go H$m¡Z ghr h¡ ? 1 
(a) cos
2
 ? – sin
2
 ? = 1 (b) cosec
2
 ? – sec
2
 ? = 1 
(c) sec
2
 ? – tan
2
 ? = 1 (d) cot
2
 ? – tan
2
 ? = 1 
2. `{X k + 2, 4k – 6 Am¡a 3k – 2 {H$gr EH$ A.P. Ho$ VrZ H«$_mJV nX h¢, Vmo k H$m 
_mZ hmoJm … 1 
(a) 3 (b) – 3 (c) 4 (d) – 4 
3. {XE JE ? ABC _| PQ || BC h¡Ÿ& `{X PB = 6 go_r., AP = 4 go_r. Am¡a AQ = 8 
go_r. h¡, Vmo AC H$s bå~mB© hmoJr … 1 
(a) 12 go_r. 
(b) 20 go_r. 
(c) 6 go_r. 
(d) 14 go_r. 
4. g~go N>moQ>r g§`wº$ g§»`m Am¡a g~go N>moQ>r A^mÁ` g§»`m Ho$ HCF H$m AZwnmV CZHo$ 
LCM go h¡ … 1 
(a) 1:2 (b) 2:1 (c) 1:1 (d) 1:3 
5. 52 nÎmm| H$s AÀN>r àH$ma go \|$Q>r JB© EH$ JÈ>r go EH$ nÎmm `mÑÀN>`m {ZH$mbm OmVm h¡Ÿ& 
{ZH$mbm J`m nÎmm EH$ BŠH$m Zht hmoZo H$s àm{`H$Vm h¡ … 1 
(a) 
1
13
 (b) 
9
13
 (c) 
4
13
 (d) 
12
13
 
Page 3


30/4/2 1 [P.T.O. 
 
 
 
 
 
 
 
 
 
 
 
J{UV (_mZH$) - g¡ÕmpÝVH$ 
MATHEMATICS (STANDARD) - Theory 
{ZYm©[aV g_` … 3 KÊQ>o 
Time allowed : 3 hours 
A{YH$V_ A§H$ … 80 
Maximum Marks : 80 
ZmoQ> / NOTE :    
(i) H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _| _w{ÐV n¥ð> 15 h¢Ÿ& 
Please check that this question paper contains 15 printed pages. 
(ii) àíZ-nÌ _| Xm{hZo hmW H$s Amoa {XE JE àíZ-nÌ H$moS> H$mo N>mÌ CÎma-nwpñVH$m Ho$ _wI-n¥ð> na 
{bI|& 
Q.P. Code given on the right hand side of the question paper should be written on 
the title page of the answer-book by the candidate.  
(iii) H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _| 38 àíZ h¢& 
Please check that this question paper contains 38 questions. 
(iv) H¥$n`m àíZ H$m CÎma {bIZm ewê$ H$aZo go nhbo, CÎma-nwpñVH$m _| àíZ H$m H«$_m§H$ Adí` 
{bI|& 
Please write down the Serial Number of the question in the answer-book before 
attempting it. 
(v) Bg àíZ-nÌ H$mo n‹T>Zo Ho$ {bE 15 {_ZQ> H$m g_` {X`m J`m h¡& àíZ-nÌ H$m {dVaU nydm©• _| 
10.15 ~Oo {H$`m OmEJm& 10.15 ~Oo go 10.30 ~Oo VH$ N>mÌ Ho$db àíZ-nÌ H$mo n‹T>|Jo Am¡a 
Bg Ad{Y Ho$ Xm¡amZ do CÎma-nwpñVH$m na H$moB© CÎma Zht {bI|Jo& 
15 minute time has been allotted to read this question paper. The question paper 
will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will 
read the question paper only and will not write any answer on the answer-book 
during this period. 
 
30/4/2 
àíZ-nÌ H$moS> 
Q.P. Code 
 
narjmWu àíZ-nÌ H$moS> H$mo CÎma-nwpñVH$m Ho$ 
_wI-n¥ð> na Adí` {bI|Ÿ& 
Candidates must write the Q.P. Code 
on the title page of the answer-book. 
SET ~ 2 
Series WX1YZ/4 
 
amob Z§. 
Roll No. 
 
 
# 
  
30/4/2  2
gm_mÝ` {ZX}e … 
{ZåZ{b{IV {ZX}em| H$mo ~hþV gmdYmZr go n{‹T>E Am¡a CZH$m nmbZ H$s{OE … 
(i) Bg àíZ-nÌ _| 38 àíZ h¢Ÿ& g^r àíZ A{Zdm`© h¢Ÿ& 
(ii) àíZ-nÌ nm§M IÊS>m| _| {d^m{OV h¡ - IÊS> H$, I, J, K VWm ‹S>Ÿ& 
(iii) IÊS> H$ _| àíZ g§»`m 1 go 18 VH$ ~hþ{dH$ënr` VWm àíZ g§»`m 19 Ed§ 20 A{^H$WZ Ed§ 
H$maU AmYm[aV EH$-EH$ A§H$ Ho$ àíZ h¢Ÿ& 
(iv) IÊS> I _| àíZ g§»`m 21 go 25 VH$ A{V bKw-CÎmar` (VSA) àH$ma Ho$ Xmo-Xmo A§H$m| Ho$ àíZ h¢Ÿ& 
 (v) IÊS> J _| àíZ g§»`m 26 go 31 VH$ bKw-CÎmar` (SA) àH$ma Ho$ VrZ-VrZ A§H$m| Ho$  
àíZ h¢Ÿ& 
(vi) IÊS> K _| àíZ g§»`m 32 go 35 VH$ XrK©-CÎmar` (LA) àH$ma Ho$ nm§M-nm§M A§H$m| Ho$ àíZ h¢Ÿ& 
(vii) IÊS> ‹S> _| àíZ g§»`m 36 go 38 VH$ òmoV / àH$aU BH$mB© AmYm[aV Mma-Mma A§H$m| Ho$ àíZ h¢Ÿ& 
Am§V[aH$ {dH$ën Xmo-Xmo A§H$m| Ho$ àíZ _| {X`m J`m h¡Ÿ& 
(viii) àíZ-nÌ _| g_J« {dH$ën Zht {X`m J`m h¡Ÿ& `Ú{n, IÊS> I Ho$ 2 àíZm| _|, IÊS> J Ho$ 2 àíZm| _|, 
IÊS> K Ho$ 2 àíZm| _| VWm IÊS> ‹S> Ho$ 3 àíZm| _| Am§V[aH$ {dH$ën H$m àmdYmZ {X`m J`m h¡Ÿ& 
(ix) Ohm§ Amdí`H$ hmo, ñdÀN> AmH¥${V`m§ ~ZmE§Ÿ& `{X Amdí`H$ hmo Vmo p=22/7 b|Ÿ& 
(x) H¡$bHw$boQ>a H$m Cn`moJ d{O©V h¡Ÿ& 
IÊS> - H$ 
IÊS> - H$ _| ~hþ{dH$ënr` àH$ma Ho$ àíZ h¢Ÿ& àË`oH$ àíZ 1 A§H$ H$m h¡Ÿ& 
1. ? (0
o
 = ? = 90
o
) Ho$ g^r _mZm| Ho$ {bE {ZåZ _| go H$m¡Z ghr h¡ ? 1 
(a) cos
2
 ? – sin
2
 ? = 1 (b) cosec
2
 ? – sec
2
 ? = 1 
(c) sec
2
 ? – tan
2
 ? = 1 (d) cot
2
 ? – tan
2
 ? = 1 
2. `{X k + 2, 4k – 6 Am¡a 3k – 2 {H$gr EH$ A.P. Ho$ VrZ H«$_mJV nX h¢, Vmo k H$m 
_mZ hmoJm … 1 
(a) 3 (b) – 3 (c) 4 (d) – 4 
3. {XE JE ? ABC _| PQ || BC h¡Ÿ& `{X PB = 6 go_r., AP = 4 go_r. Am¡a AQ = 8 
go_r. h¡, Vmo AC H$s bå~mB© hmoJr … 1 
(a) 12 go_r. 
(b) 20 go_r. 
(c) 6 go_r. 
(d) 14 go_r. 
4. g~go N>moQ>r g§`wº$ g§»`m Am¡a g~go N>moQ>r A^mÁ` g§»`m Ho$ HCF H$m AZwnmV CZHo$ 
LCM go h¡ … 1 
(a) 1:2 (b) 2:1 (c) 1:1 (d) 1:3 
5. 52 nÎmm| H$s AÀN>r àH$ma go \|$Q>r JB© EH$ JÈ>r go EH$ nÎmm `mÑÀN>`m {ZH$mbm OmVm h¡Ÿ& 
{ZH$mbm J`m nÎmm EH$ BŠH$m Zht hmoZo H$s àm{`H$Vm h¡ … 1 
(a) 
1
13
 (b) 
9
13
 (c) 
4
13
 (d) 
12
13
 
 
30/4/2  [P.T.O. 3
GENERAL INSTRUCTIONS : 
Read the following instructions carefully and follow them : 
(i) This question paper contains 38 questions. All questions are compulsory. 
(ii) Question paper is divided into FIVE sections – Section A, B, C, D and E. 
(iii) In section A – question number 1 to 18 are multiple choice questions (MCQs) and 
question number 19 and 20 are Assertion-Reason based questions of 1 mark each. 
(iv) In section B – question number 21 to 25 are Very Short Answer (VSA) type questions 
of 2 marks each. 
(v) In section C – question number 26 to 31 are Short Answer (SA) type questions 
carrying 3 marks each. 
(vi) In section D – question number 32 to 35 are Long Answer (LA) type questions 
carrying 5 marks each. 
(vii) In section E – question number 36 to 38 are case based integrated units of 
assessment questions carrying 4 marks each. Internal choice is provided in 2 marks 
question in each case-study. 
(viii) There is no overall choice. However, an internal choice has been provided in 2 
questions in Section B, 2 questions in Section C, 2 questions in Section D and 3 
questions in Section E. 
(ix) Draw neat figures wherever required. Take p = 22/7 wherever required if not stated. 
(x) Use of calculators is NOT allowed. 
SECTION - A 
Section - A consists of Multiple Choice type questions of 1 mark each. 
1. Which of the following is true for all values of ? (0
o
 = ? = 90
o
) ? 1 
(a) cos
2
 ? – sin
2
 ? = 1 (b) cosec
2
 ? – sec
2
 ? = 1 
(c) sec
2
 ? – tan
2
 ? = 1 (d) cot
2
 ? – tan
2
 ? = 1 
2. If k + 2, 4k – 6 and 3k – 2 are three consecutive terms of an A.P., 
then the value of k is : 1 
(a) 3 (b) – 3 (c) 4 (d) – 4 
3. In ? ABC, PQ || BC. If PB = 6 cm, AP = 4 cm, AQ = 8 cm, find the 
length of AC. 1 
(a) 12 cm 
(b) 20 cm 
(c) 6 cm 
(d) 14 cm 
4. The ratio of HCF to LCM of the least composite number and the least 
prime number is : 1 
(a) 1:2 (b) 2:1 (c) 1:1 (d) 1:3 
5. A card is drawn at random from a well-shuffled pack of 52 cards. The 
probability that the card drawn is not an ace is : 1 
(a) 
1
13
 (b) 
9
13
 (c) 
4
13
 (d) 
12
13
 
Page 4


30/4/2 1 [P.T.O. 
 
 
 
 
 
 
 
 
 
 
 
J{UV (_mZH$) - g¡ÕmpÝVH$ 
MATHEMATICS (STANDARD) - Theory 
{ZYm©[aV g_` … 3 KÊQ>o 
Time allowed : 3 hours 
A{YH$V_ A§H$ … 80 
Maximum Marks : 80 
ZmoQ> / NOTE :    
(i) H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _| _w{ÐV n¥ð> 15 h¢Ÿ& 
Please check that this question paper contains 15 printed pages. 
(ii) àíZ-nÌ _| Xm{hZo hmW H$s Amoa {XE JE àíZ-nÌ H$moS> H$mo N>mÌ CÎma-nwpñVH$m Ho$ _wI-n¥ð> na 
{bI|& 
Q.P. Code given on the right hand side of the question paper should be written on 
the title page of the answer-book by the candidate.  
(iii) H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _| 38 àíZ h¢& 
Please check that this question paper contains 38 questions. 
(iv) H¥$n`m àíZ H$m CÎma {bIZm ewê$ H$aZo go nhbo, CÎma-nwpñVH$m _| àíZ H$m H«$_m§H$ Adí` 
{bI|& 
Please write down the Serial Number of the question in the answer-book before 
attempting it. 
(v) Bg àíZ-nÌ H$mo n‹T>Zo Ho$ {bE 15 {_ZQ> H$m g_` {X`m J`m h¡& àíZ-nÌ H$m {dVaU nydm©• _| 
10.15 ~Oo {H$`m OmEJm& 10.15 ~Oo go 10.30 ~Oo VH$ N>mÌ Ho$db àíZ-nÌ H$mo n‹T>|Jo Am¡a 
Bg Ad{Y Ho$ Xm¡amZ do CÎma-nwpñVH$m na H$moB© CÎma Zht {bI|Jo& 
15 minute time has been allotted to read this question paper. The question paper 
will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will 
read the question paper only and will not write any answer on the answer-book 
during this period. 
 
30/4/2 
àíZ-nÌ H$moS> 
Q.P. Code 
 
narjmWu àíZ-nÌ H$moS> H$mo CÎma-nwpñVH$m Ho$ 
_wI-n¥ð> na Adí` {bI|Ÿ& 
Candidates must write the Q.P. Code 
on the title page of the answer-book. 
SET ~ 2 
Series WX1YZ/4 
 
amob Z§. 
Roll No. 
 
 
# 
  
30/4/2  2
gm_mÝ` {ZX}e … 
{ZåZ{b{IV {ZX}em| H$mo ~hþV gmdYmZr go n{‹T>E Am¡a CZH$m nmbZ H$s{OE … 
(i) Bg àíZ-nÌ _| 38 àíZ h¢Ÿ& g^r àíZ A{Zdm`© h¢Ÿ& 
(ii) àíZ-nÌ nm§M IÊS>m| _| {d^m{OV h¡ - IÊS> H$, I, J, K VWm ‹S>Ÿ& 
(iii) IÊS> H$ _| àíZ g§»`m 1 go 18 VH$ ~hþ{dH$ënr` VWm àíZ g§»`m 19 Ed§ 20 A{^H$WZ Ed§ 
H$maU AmYm[aV EH$-EH$ A§H$ Ho$ àíZ h¢Ÿ& 
(iv) IÊS> I _| àíZ g§»`m 21 go 25 VH$ A{V bKw-CÎmar` (VSA) àH$ma Ho$ Xmo-Xmo A§H$m| Ho$ àíZ h¢Ÿ& 
 (v) IÊS> J _| àíZ g§»`m 26 go 31 VH$ bKw-CÎmar` (SA) àH$ma Ho$ VrZ-VrZ A§H$m| Ho$  
àíZ h¢Ÿ& 
(vi) IÊS> K _| àíZ g§»`m 32 go 35 VH$ XrK©-CÎmar` (LA) àH$ma Ho$ nm§M-nm§M A§H$m| Ho$ àíZ h¢Ÿ& 
(vii) IÊS> ‹S> _| àíZ g§»`m 36 go 38 VH$ òmoV / àH$aU BH$mB© AmYm[aV Mma-Mma A§H$m| Ho$ àíZ h¢Ÿ& 
Am§V[aH$ {dH$ën Xmo-Xmo A§H$m| Ho$ àíZ _| {X`m J`m h¡Ÿ& 
(viii) àíZ-nÌ _| g_J« {dH$ën Zht {X`m J`m h¡Ÿ& `Ú{n, IÊS> I Ho$ 2 àíZm| _|, IÊS> J Ho$ 2 àíZm| _|, 
IÊS> K Ho$ 2 àíZm| _| VWm IÊS> ‹S> Ho$ 3 àíZm| _| Am§V[aH$ {dH$ën H$m àmdYmZ {X`m J`m h¡Ÿ& 
(ix) Ohm§ Amdí`H$ hmo, ñdÀN> AmH¥${V`m§ ~ZmE§Ÿ& `{X Amdí`H$ hmo Vmo p=22/7 b|Ÿ& 
(x) H¡$bHw$boQ>a H$m Cn`moJ d{O©V h¡Ÿ& 
IÊS> - H$ 
IÊS> - H$ _| ~hþ{dH$ënr` àH$ma Ho$ àíZ h¢Ÿ& àË`oH$ àíZ 1 A§H$ H$m h¡Ÿ& 
1. ? (0
o
 = ? = 90
o
) Ho$ g^r _mZm| Ho$ {bE {ZåZ _| go H$m¡Z ghr h¡ ? 1 
(a) cos
2
 ? – sin
2
 ? = 1 (b) cosec
2
 ? – sec
2
 ? = 1 
(c) sec
2
 ? – tan
2
 ? = 1 (d) cot
2
 ? – tan
2
 ? = 1 
2. `{X k + 2, 4k – 6 Am¡a 3k – 2 {H$gr EH$ A.P. Ho$ VrZ H«$_mJV nX h¢, Vmo k H$m 
_mZ hmoJm … 1 
(a) 3 (b) – 3 (c) 4 (d) – 4 
3. {XE JE ? ABC _| PQ || BC h¡Ÿ& `{X PB = 6 go_r., AP = 4 go_r. Am¡a AQ = 8 
go_r. h¡, Vmo AC H$s bå~mB© hmoJr … 1 
(a) 12 go_r. 
(b) 20 go_r. 
(c) 6 go_r. 
(d) 14 go_r. 
4. g~go N>moQ>r g§`wº$ g§»`m Am¡a g~go N>moQ>r A^mÁ` g§»`m Ho$ HCF H$m AZwnmV CZHo$ 
LCM go h¡ … 1 
(a) 1:2 (b) 2:1 (c) 1:1 (d) 1:3 
5. 52 nÎmm| H$s AÀN>r àH$ma go \|$Q>r JB© EH$ JÈ>r go EH$ nÎmm `mÑÀN>`m {ZH$mbm OmVm h¡Ÿ& 
{ZH$mbm J`m nÎmm EH$ BŠH$m Zht hmoZo H$s àm{`H$Vm h¡ … 1 
(a) 
1
13
 (b) 
9
13
 (c) 
4
13
 (d) 
12
13
 
 
30/4/2  [P.T.O. 3
GENERAL INSTRUCTIONS : 
Read the following instructions carefully and follow them : 
(i) This question paper contains 38 questions. All questions are compulsory. 
(ii) Question paper is divided into FIVE sections – Section A, B, C, D and E. 
(iii) In section A – question number 1 to 18 are multiple choice questions (MCQs) and 
question number 19 and 20 are Assertion-Reason based questions of 1 mark each. 
(iv) In section B – question number 21 to 25 are Very Short Answer (VSA) type questions 
of 2 marks each. 
(v) In section C – question number 26 to 31 are Short Answer (SA) type questions 
carrying 3 marks each. 
(vi) In section D – question number 32 to 35 are Long Answer (LA) type questions 
carrying 5 marks each. 
(vii) In section E – question number 36 to 38 are case based integrated units of 
assessment questions carrying 4 marks each. Internal choice is provided in 2 marks 
question in each case-study. 
(viii) There is no overall choice. However, an internal choice has been provided in 2 
questions in Section B, 2 questions in Section C, 2 questions in Section D and 3 
questions in Section E. 
(ix) Draw neat figures wherever required. Take p = 22/7 wherever required if not stated. 
(x) Use of calculators is NOT allowed. 
SECTION - A 
Section - A consists of Multiple Choice type questions of 1 mark each. 
1. Which of the following is true for all values of ? (0
o
 = ? = 90
o
) ? 1 
(a) cos
2
 ? – sin
2
 ? = 1 (b) cosec
2
 ? – sec
2
 ? = 1 
(c) sec
2
 ? – tan
2
 ? = 1 (d) cot
2
 ? – tan
2
 ? = 1 
2. If k + 2, 4k – 6 and 3k – 2 are three consecutive terms of an A.P., 
then the value of k is : 1 
(a) 3 (b) – 3 (c) 4 (d) – 4 
3. In ? ABC, PQ || BC. If PB = 6 cm, AP = 4 cm, AQ = 8 cm, find the 
length of AC. 1 
(a) 12 cm 
(b) 20 cm 
(c) 6 cm 
(d) 14 cm 
4. The ratio of HCF to LCM of the least composite number and the least 
prime number is : 1 
(a) 1:2 (b) 2:1 (c) 1:1 (d) 1:3 
5. A card is drawn at random from a well-shuffled pack of 52 cards. The 
probability that the card drawn is not an ace is : 1 
(a) 
1
13
 (b) 
9
13
 (c) 
4
13
 (d) 
12
13
 
  
30/4/2  4
6.  
 
 
 
 
 Xr JB© AmH¥${V _|, ?ABC~?QPRŸ& `{X AC = 6 go_r., BC = 5 go_r.,  
QR = 3 go_r. Am¡a PR = x h¡, Vmo x H$m _mZ hmoJm … 1 
(a) 3.6 go_r. (b) 2.5 go_r. (c) 10 go_r. (d) 3.2 go_r. 
7. g_rH$aU x
2 
+ 3x – 10 = 0 Ho$ _yb h¢ … 1 
(a) 2, –5 (b) –2, 5 (c) 2, 5 (d) –2, –5 
8. `{X 6 _r. D±$Mo EH$ I§^o H$s N>m`m, ^y{_ na 2 3 _r. b§~r h¡, Vmo gy`© H$m CÞVm§e  
hmoJm … 1 
(a) 60
o
 (b) 45
 o 
(c) 30
 o
 (d) 90
 o
 
9. _yb {~ÝXw go {~ÝXw (– 6, 8) H$s Xyar h¡ … 1 
(a) 6 (b) – 6 (c) 8 (d) 10 
10. ‘d’ ì`mg Ho$ AY©d¥Îm H$m joÌ\$b Š`m h¡ ? 1 
(a) 
2
1
pd
16
 (b) 
2
1
pd
4
 (c) 
2
1
pd
8
 (d) 
2
1
pd
2
 
11. {ZåZ ~§Q>Z Ho$ {bE _mÜ`H$ Am¡a ~hþbH$ dJm] H$s {ZMbr gr_mAm| H$m `moJ h¡ … 1 
dJ© A§Vamb 0-5 5-10 10-15 15-20 20-25 
~ma§~maVm 10 15 12 20 9 
(a) 15 (b) 25 (c) 30 (d) 35 
12. 9 go_r. {ÌÁ`m Ho$ EH$ d¥Îm Ho$ Ho$ÝÐ go 41 go_r. Xya pñWV EH$ q~Xw go d¥Îm na ItMr JB© 
ñne© aoIm H$s b§~mB© h¡ … 1 
(a) 40 go_r. (b) 9 go_r. (c) 41 go_r. (d) 50 go_r. 
13. Xr JB© AmH¥${V _|, O d¥Îm H$m Ho$ÝÐ Am¡a PQ d¥Îm H$s Ordm h¡Ÿ& `{X P na ñne© aoIm 
PR, Ordm PQ go 50
o
 H$m H$moU ~ZmVr h¡, Vmo ?POQ H$s _mn h¡ … 1 
(a) 50
 o 
(b) 40
o
 
(c) 100
 o 
(d) 130
 o
 
Page 5


30/4/2 1 [P.T.O. 
 
 
 
 
 
 
 
 
 
 
 
J{UV (_mZH$) - g¡ÕmpÝVH$ 
MATHEMATICS (STANDARD) - Theory 
{ZYm©[aV g_` … 3 KÊQ>o 
Time allowed : 3 hours 
A{YH$V_ A§H$ … 80 
Maximum Marks : 80 
ZmoQ> / NOTE :    
(i) H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _| _w{ÐV n¥ð> 15 h¢Ÿ& 
Please check that this question paper contains 15 printed pages. 
(ii) àíZ-nÌ _| Xm{hZo hmW H$s Amoa {XE JE àíZ-nÌ H$moS> H$mo N>mÌ CÎma-nwpñVH$m Ho$ _wI-n¥ð> na 
{bI|& 
Q.P. Code given on the right hand side of the question paper should be written on 
the title page of the answer-book by the candidate.  
(iii) H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _| 38 àíZ h¢& 
Please check that this question paper contains 38 questions. 
(iv) H¥$n`m àíZ H$m CÎma {bIZm ewê$ H$aZo go nhbo, CÎma-nwpñVH$m _| àíZ H$m H«$_m§H$ Adí` 
{bI|& 
Please write down the Serial Number of the question in the answer-book before 
attempting it. 
(v) Bg àíZ-nÌ H$mo n‹T>Zo Ho$ {bE 15 {_ZQ> H$m g_` {X`m J`m h¡& àíZ-nÌ H$m {dVaU nydm©• _| 
10.15 ~Oo {H$`m OmEJm& 10.15 ~Oo go 10.30 ~Oo VH$ N>mÌ Ho$db àíZ-nÌ H$mo n‹T>|Jo Am¡a 
Bg Ad{Y Ho$ Xm¡amZ do CÎma-nwpñVH$m na H$moB© CÎma Zht {bI|Jo& 
15 minute time has been allotted to read this question paper. The question paper 
will be distributed at 10.15 a.m. From 10.15 a.m. to 10.30 a.m., the students will 
read the question paper only and will not write any answer on the answer-book 
during this period. 
 
30/4/2 
àíZ-nÌ H$moS> 
Q.P. Code 
 
narjmWu àíZ-nÌ H$moS> H$mo CÎma-nwpñVH$m Ho$ 
_wI-n¥ð> na Adí` {bI|Ÿ& 
Candidates must write the Q.P. Code 
on the title page of the answer-book. 
SET ~ 2 
Series WX1YZ/4 
 
amob Z§. 
Roll No. 
 
 
# 
  
30/4/2  2
gm_mÝ` {ZX}e … 
{ZåZ{b{IV {ZX}em| H$mo ~hþV gmdYmZr go n{‹T>E Am¡a CZH$m nmbZ H$s{OE … 
(i) Bg àíZ-nÌ _| 38 àíZ h¢Ÿ& g^r àíZ A{Zdm`© h¢Ÿ& 
(ii) àíZ-nÌ nm§M IÊS>m| _| {d^m{OV h¡ - IÊS> H$, I, J, K VWm ‹S>Ÿ& 
(iii) IÊS> H$ _| àíZ g§»`m 1 go 18 VH$ ~hþ{dH$ënr` VWm àíZ g§»`m 19 Ed§ 20 A{^H$WZ Ed§ 
H$maU AmYm[aV EH$-EH$ A§H$ Ho$ àíZ h¢Ÿ& 
(iv) IÊS> I _| àíZ g§»`m 21 go 25 VH$ A{V bKw-CÎmar` (VSA) àH$ma Ho$ Xmo-Xmo A§H$m| Ho$ àíZ h¢Ÿ& 
 (v) IÊS> J _| àíZ g§»`m 26 go 31 VH$ bKw-CÎmar` (SA) àH$ma Ho$ VrZ-VrZ A§H$m| Ho$  
àíZ h¢Ÿ& 
(vi) IÊS> K _| àíZ g§»`m 32 go 35 VH$ XrK©-CÎmar` (LA) àH$ma Ho$ nm§M-nm§M A§H$m| Ho$ àíZ h¢Ÿ& 
(vii) IÊS> ‹S> _| àíZ g§»`m 36 go 38 VH$ òmoV / àH$aU BH$mB© AmYm[aV Mma-Mma A§H$m| Ho$ àíZ h¢Ÿ& 
Am§V[aH$ {dH$ën Xmo-Xmo A§H$m| Ho$ àíZ _| {X`m J`m h¡Ÿ& 
(viii) àíZ-nÌ _| g_J« {dH$ën Zht {X`m J`m h¡Ÿ& `Ú{n, IÊS> I Ho$ 2 àíZm| _|, IÊS> J Ho$ 2 àíZm| _|, 
IÊS> K Ho$ 2 àíZm| _| VWm IÊS> ‹S> Ho$ 3 àíZm| _| Am§V[aH$ {dH$ën H$m àmdYmZ {X`m J`m h¡Ÿ& 
(ix) Ohm§ Amdí`H$ hmo, ñdÀN> AmH¥${V`m§ ~ZmE§Ÿ& `{X Amdí`H$ hmo Vmo p=22/7 b|Ÿ& 
(x) H¡$bHw$boQ>a H$m Cn`moJ d{O©V h¡Ÿ& 
IÊS> - H$ 
IÊS> - H$ _| ~hþ{dH$ënr` àH$ma Ho$ àíZ h¢Ÿ& àË`oH$ àíZ 1 A§H$ H$m h¡Ÿ& 
1. ? (0
o
 = ? = 90
o
) Ho$ g^r _mZm| Ho$ {bE {ZåZ _| go H$m¡Z ghr h¡ ? 1 
(a) cos
2
 ? – sin
2
 ? = 1 (b) cosec
2
 ? – sec
2
 ? = 1 
(c) sec
2
 ? – tan
2
 ? = 1 (d) cot
2
 ? – tan
2
 ? = 1 
2. `{X k + 2, 4k – 6 Am¡a 3k – 2 {H$gr EH$ A.P. Ho$ VrZ H«$_mJV nX h¢, Vmo k H$m 
_mZ hmoJm … 1 
(a) 3 (b) – 3 (c) 4 (d) – 4 
3. {XE JE ? ABC _| PQ || BC h¡Ÿ& `{X PB = 6 go_r., AP = 4 go_r. Am¡a AQ = 8 
go_r. h¡, Vmo AC H$s bå~mB© hmoJr … 1 
(a) 12 go_r. 
(b) 20 go_r. 
(c) 6 go_r. 
(d) 14 go_r. 
4. g~go N>moQ>r g§`wº$ g§»`m Am¡a g~go N>moQ>r A^mÁ` g§»`m Ho$ HCF H$m AZwnmV CZHo$ 
LCM go h¡ … 1 
(a) 1:2 (b) 2:1 (c) 1:1 (d) 1:3 
5. 52 nÎmm| H$s AÀN>r àH$ma go \|$Q>r JB© EH$ JÈ>r go EH$ nÎmm `mÑÀN>`m {ZH$mbm OmVm h¡Ÿ& 
{ZH$mbm J`m nÎmm EH$ BŠH$m Zht hmoZo H$s àm{`H$Vm h¡ … 1 
(a) 
1
13
 (b) 
9
13
 (c) 
4
13
 (d) 
12
13
 
 
30/4/2  [P.T.O. 3
GENERAL INSTRUCTIONS : 
Read the following instructions carefully and follow them : 
(i) This question paper contains 38 questions. All questions are compulsory. 
(ii) Question paper is divided into FIVE sections – Section A, B, C, D and E. 
(iii) In section A – question number 1 to 18 are multiple choice questions (MCQs) and 
question number 19 and 20 are Assertion-Reason based questions of 1 mark each. 
(iv) In section B – question number 21 to 25 are Very Short Answer (VSA) type questions 
of 2 marks each. 
(v) In section C – question number 26 to 31 are Short Answer (SA) type questions 
carrying 3 marks each. 
(vi) In section D – question number 32 to 35 are Long Answer (LA) type questions 
carrying 5 marks each. 
(vii) In section E – question number 36 to 38 are case based integrated units of 
assessment questions carrying 4 marks each. Internal choice is provided in 2 marks 
question in each case-study. 
(viii) There is no overall choice. However, an internal choice has been provided in 2 
questions in Section B, 2 questions in Section C, 2 questions in Section D and 3 
questions in Section E. 
(ix) Draw neat figures wherever required. Take p = 22/7 wherever required if not stated. 
(x) Use of calculators is NOT allowed. 
SECTION - A 
Section - A consists of Multiple Choice type questions of 1 mark each. 
1. Which of the following is true for all values of ? (0
o
 = ? = 90
o
) ? 1 
(a) cos
2
 ? – sin
2
 ? = 1 (b) cosec
2
 ? – sec
2
 ? = 1 
(c) sec
2
 ? – tan
2
 ? = 1 (d) cot
2
 ? – tan
2
 ? = 1 
2. If k + 2, 4k – 6 and 3k – 2 are three consecutive terms of an A.P., 
then the value of k is : 1 
(a) 3 (b) – 3 (c) 4 (d) – 4 
3. In ? ABC, PQ || BC. If PB = 6 cm, AP = 4 cm, AQ = 8 cm, find the 
length of AC. 1 
(a) 12 cm 
(b) 20 cm 
(c) 6 cm 
(d) 14 cm 
4. The ratio of HCF to LCM of the least composite number and the least 
prime number is : 1 
(a) 1:2 (b) 2:1 (c) 1:1 (d) 1:3 
5. A card is drawn at random from a well-shuffled pack of 52 cards. The 
probability that the card drawn is not an ace is : 1 
(a) 
1
13
 (b) 
9
13
 (c) 
4
13
 (d) 
12
13
 
  
30/4/2  4
6.  
 
 
 
 
 Xr JB© AmH¥${V _|, ?ABC~?QPRŸ& `{X AC = 6 go_r., BC = 5 go_r.,  
QR = 3 go_r. Am¡a PR = x h¡, Vmo x H$m _mZ hmoJm … 1 
(a) 3.6 go_r. (b) 2.5 go_r. (c) 10 go_r. (d) 3.2 go_r. 
7. g_rH$aU x
2 
+ 3x – 10 = 0 Ho$ _yb h¢ … 1 
(a) 2, –5 (b) –2, 5 (c) 2, 5 (d) –2, –5 
8. `{X 6 _r. D±$Mo EH$ I§^o H$s N>m`m, ^y{_ na 2 3 _r. b§~r h¡, Vmo gy`© H$m CÞVm§e  
hmoJm … 1 
(a) 60
o
 (b) 45
 o 
(c) 30
 o
 (d) 90
 o
 
9. _yb {~ÝXw go {~ÝXw (– 6, 8) H$s Xyar h¡ … 1 
(a) 6 (b) – 6 (c) 8 (d) 10 
10. ‘d’ ì`mg Ho$ AY©d¥Îm H$m joÌ\$b Š`m h¡ ? 1 
(a) 
2
1
pd
16
 (b) 
2
1
pd
4
 (c) 
2
1
pd
8
 (d) 
2
1
pd
2
 
11. {ZåZ ~§Q>Z Ho$ {bE _mÜ`H$ Am¡a ~hþbH$ dJm] H$s {ZMbr gr_mAm| H$m `moJ h¡ … 1 
dJ© A§Vamb 0-5 5-10 10-15 15-20 20-25 
~ma§~maVm 10 15 12 20 9 
(a) 15 (b) 25 (c) 30 (d) 35 
12. 9 go_r. {ÌÁ`m Ho$ EH$ d¥Îm Ho$ Ho$ÝÐ go 41 go_r. Xya pñWV EH$ q~Xw go d¥Îm na ItMr JB© 
ñne© aoIm H$s b§~mB© h¡ … 1 
(a) 40 go_r. (b) 9 go_r. (c) 41 go_r. (d) 50 go_r. 
13. Xr JB© AmH¥${V _|, O d¥Îm H$m Ho$ÝÐ Am¡a PQ d¥Îm H$s Ordm h¡Ÿ& `{X P na ñne© aoIm 
PR, Ordm PQ go 50
o
 H$m H$moU ~ZmVr h¡, Vmo ?POQ H$s _mn h¡ … 1 
(a) 50
 o 
(b) 40
o
 
(c) 100
 o 
(d) 130
 o
 
 
30/4/2  [P.T.O. 5
6.  
 
 
 
 
 In the given figure, ?ABC~?QPR. If AC = 6 cm, BC = 5 cm,  
QR = 3 cm and PR = x; then the value of x is : 1 
(a) 3.6 cm (b) 2.5 cm (c) 10 cm (d) 3.2 cm 
7. The roots of the equation x
2 
+ 3x – 10 = 0 are : 1 
(a) 2, –5 (b) –2, 5 (c) 2, 5 (d) –2, –5 
8. If a pole 6 m high casts a shadow 2 3 m long on the ground, then 
sun’s elevation is : 1 
(a) 60
o
 (b) 45
 o 
(c) 30
 o
 (d) 90
 o
 
9. The distance of the point (– 6, 8) from origin is : 1 
(a) 6 (b) – 6 (c) 8 (d) 10 
10. What is the area of a semi-circle of diameter ‘d’ ? 1 
(a) 
2
1
pd
16
 (b) 
2
1
pd
4
 (c) 
2
1
pd
8
 (d) 
2
1
pd
2
 
11. For the following distribution : 1 
Class 0-5 5-10 10-15 15-20 20-25 
Frequency 10 15 12 20 9 
 The sum of lower limits of median class and modal class is : 
(a) 15 (b) 25 (c) 30 (d) 35 
12. The length of tangent drawn to a circle of radius 9 cm from a point  
41 cm from the centre is : 1 
(a) 40 cm (b) 9 cm (c) 41 cm (d) 50 cm 
13. In the given figure, O is the centre of the circle and PQ is the chord. 
If the tangent PR at P makes an angle of 50
o
 with PQ, then the 
measure of ?POQ is : 1 
(a) 50
 o 
(b) 40
o
 
(c) 100
 o 
(d) 130
 o