Class 10 Mathematics: Question Paper for 2015 | Mathematics (Maths) Class 10 PDF Download

 Page 1


30/2 1 P.T.O. 
narjmWu H$moS >H$mo CÎma-nwpñVH$m Ho$ _wI-n¥ð 
>na Adí` {bIo§ & 
Candidates must write the Code on the 
title page of the answer-book. 
 Series RLH  
H$moS> Z§.   
30/2
 
  Code No. 
amob Z§. 
Roll No. 
 
 
 
 
 
 
 
 
 
 
 
g§H${bV narjm – II 
SUMMATIVE ASSESSMENT – II 
J{UV 
MATHEMATICS 
{ZYm©[aV g_` : 3 KÊQ>o   A{YH$V_ A§H$ : 90 
Time allowed : 3 hours Maximum Marks : 90 
 
? H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _o§ _w{ÐV n¥ð> 11 h¢ & 
? àíZ-nÌ _| Xm{hZo hmW H$s Amoa {XE JE H$moS >Zå~a H$mo N>mÌ CÎma-nwpñVH$m Ho$ _wI-n¥ð> na 
{bI| & 
? H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _| >31 àíZ h¢ & 
? H¥$n`m àíZ H$m CÎma {bIZm ewê$ H$aZo go nhbo, àíZ H$m H«$_m§H$ Adí` {bI| & 
? 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 & 
? Please check that this question paper contains 11 printed pages. 
? Code number given on the right hand side of the question paper should be 
written on the title page of the answer-book by the candidate. 
? Please check that this question paper contains 31 questions. 
? Please write down the Serial Number of the question before 
attempting it. 
? 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. 
SET-2 
Page 2


30/2 1 P.T.O. 
narjmWu H$moS >H$mo CÎma-nwpñVH$m Ho$ _wI-n¥ð 
>na Adí` {bIo§ & 
Candidates must write the Code on the 
title page of the answer-book. 
 Series RLH  
H$moS> Z§.   
30/2
 
  Code No. 
amob Z§. 
Roll No. 
 
 
 
 
 
 
 
 
 
 
 
g§H${bV narjm – II 
SUMMATIVE ASSESSMENT – II 
J{UV 
MATHEMATICS 
{ZYm©[aV g_` : 3 KÊQ>o   A{YH$V_ A§H$ : 90 
Time allowed : 3 hours Maximum Marks : 90 
 
? H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _o§ _w{ÐV n¥ð> 11 h¢ & 
? àíZ-nÌ _| Xm{hZo hmW H$s Amoa {XE JE H$moS >Zå~a H$mo N>mÌ CÎma-nwpñVH$m Ho$ _wI-n¥ð> na 
{bI| & 
? H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _| >31 àíZ h¢ & 
? H¥$n`m àíZ H$m CÎma {bIZm ewê$ H$aZo go nhbo, àíZ H$m H«$_m§H$ Adí` {bI| & 
? 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 & 
? Please check that this question paper contains 11 printed pages. 
? Code number given on the right hand side of the question paper should be 
written on the title page of the answer-book by the candidate. 
? Please check that this question paper contains 31 questions. 
? Please write down the Serial Number of the question before 
attempting it. 
? 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. 
SET-2 
30/2 2 
gm_mÝ` {ZX}e : 
(i) g^r àíZ A{Zdm`© h¢ & 
(ii) Bg àíZ-nÌ _| 31 àíZ h¢ Omo Mma IÊS>m| ? A, ~, g Am¡a X _| {d^m{OV h¢ & 
(iii) IÊS> A _| EH$-EH$ A§H$ dmbo 4 àíZ h¢ & IÊS> ~ _| 6 àíZ h¢ {OZ_| go àË`oH$ 2 A§H$ 
H$m h¡ & IÊS> g _| 10 àíZ VrZ-VrZ A§H$m| Ho$ h¢ & IÊS> X _| 11 àíZ h¢ {OZ_| go àË`oH$ 
4 A§H$ H$m h¡ &   
(iv) H¡$bHw$boQ>a H$m à`moJ d{O©V h¡ &  
General Instructions : 
(i) All questions are compulsory. 
(ii) The question paper consists of 31 questions divided into four sections ? A, 
B, C and D. 
(iii) Section A contains 4 questions of 1 mark each. Section B contains  
6 questions of 2 marks each, Section C contains 10 questions of 3 marks 
each and Section D contains 11 questions of 4 marks each. 
(iv) Use of calculators is not permitted. 
 
IÊS> A 
SECTION A 
àíZ g§»`m 1 go 4 VH$ àË`oH$ àíZ 1 A§H$ H$m h¡ &  
Question numbers 1 to 4 carry 1 mark each. 
1. AmH¥${V 1 _|, O H|$Ð dmbo d¥Îm H$s PQ EH$ Ordm h¡ VWm PT EH$ ñne© aoIm h¡ & `{X 
? QPT = 60 ? h¡, Vmo ? PRQ kmV H$s{OE & 
 
AmH¥${V 1 
Page 3


30/2 1 P.T.O. 
narjmWu H$moS >H$mo CÎma-nwpñVH$m Ho$ _wI-n¥ð 
>na Adí` {bIo§ & 
Candidates must write the Code on the 
title page of the answer-book. 
 Series RLH  
H$moS> Z§.   
30/2
 
  Code No. 
amob Z§. 
Roll No. 
 
 
 
 
 
 
 
 
 
 
 
g§H${bV narjm – II 
SUMMATIVE ASSESSMENT – II 
J{UV 
MATHEMATICS 
{ZYm©[aV g_` : 3 KÊQ>o   A{YH$V_ A§H$ : 90 
Time allowed : 3 hours Maximum Marks : 90 
 
? H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _o§ _w{ÐV n¥ð> 11 h¢ & 
? àíZ-nÌ _| Xm{hZo hmW H$s Amoa {XE JE H$moS >Zå~a H$mo N>mÌ CÎma-nwpñVH$m Ho$ _wI-n¥ð> na 
{bI| & 
? H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _| >31 àíZ h¢ & 
? H¥$n`m àíZ H$m CÎma {bIZm ewê$ H$aZo go nhbo, àíZ H$m H«$_m§H$ Adí` {bI| & 
? 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 & 
? Please check that this question paper contains 11 printed pages. 
? Code number given on the right hand side of the question paper should be 
written on the title page of the answer-book by the candidate. 
? Please check that this question paper contains 31 questions. 
? Please write down the Serial Number of the question before 
attempting it. 
? 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. 
SET-2 
30/2 2 
gm_mÝ` {ZX}e : 
(i) g^r àíZ A{Zdm`© h¢ & 
(ii) Bg àíZ-nÌ _| 31 àíZ h¢ Omo Mma IÊS>m| ? A, ~, g Am¡a X _| {d^m{OV h¢ & 
(iii) IÊS> A _| EH$-EH$ A§H$ dmbo 4 àíZ h¢ & IÊS> ~ _| 6 àíZ h¢ {OZ_| go àË`oH$ 2 A§H$ 
H$m h¡ & IÊS> g _| 10 àíZ VrZ-VrZ A§H$m| Ho$ h¢ & IÊS> X _| 11 àíZ h¢ {OZ_| go àË`oH$ 
4 A§H$ H$m h¡ &   
(iv) H¡$bHw$boQ>a H$m à`moJ d{O©V h¡ &  
General Instructions : 
(i) All questions are compulsory. 
(ii) The question paper consists of 31 questions divided into four sections ? A, 
B, C and D. 
(iii) Section A contains 4 questions of 1 mark each. Section B contains  
6 questions of 2 marks each, Section C contains 10 questions of 3 marks 
each and Section D contains 11 questions of 4 marks each. 
(iv) Use of calculators is not permitted. 
 
IÊS> A 
SECTION A 
àíZ g§»`m 1 go 4 VH$ àË`oH$ àíZ 1 A§H$ H$m h¡ &  
Question numbers 1 to 4 carry 1 mark each. 
1. AmH¥${V 1 _|, O H|$Ð dmbo d¥Îm H$s PQ EH$ Ordm h¡ VWm PT EH$ ñne© aoIm h¡ & `{X 
? QPT = 60 ? h¡, Vmo ? PRQ kmV H$s{OE & 
 
AmH¥${V 1 
30/2 3 P.T.O. 
In Figure 1, PQ is a chord of a circle with centre O and PT is a tangent. If 
? QPT = 60 ?, find ? PRQ. 
 
Figure 1 
2. `{X {ÛKmV g_rH$aU  px
2
 – 2 5 px + 15 = 0  Ho$ Xmo g_mZ _yb hm|, Vmo p H$m _mZ kmV 
H$s{OE & 
If the quadratic equation  px
2
 – 2 5 px + 15 = 0  has two equal roots, 
then find the value of p. 
 
3. AmH¥${V 2 _|, EH$ _rZma AB H$s D±$MmB© 20 _rQ>a h¡ Am¡a BgH$s ^y{_ na naN>mB© BC H$s 
bå~mB© 20 3 _rQ>a h¡ & gy`© H$m CÞVm§e kmV H$s{OE & 
 
AmH¥${V 2 
 
In Figure 2, a tower AB is 20 m high and BC, its shadow on the ground, 
is 20 3 m long. Find the Sun’s altitude. 
 
Figure 2 
Page 4


30/2 1 P.T.O. 
narjmWu H$moS >H$mo CÎma-nwpñVH$m Ho$ _wI-n¥ð 
>na Adí` {bIo§ & 
Candidates must write the Code on the 
title page of the answer-book. 
 Series RLH  
H$moS> Z§.   
30/2
 
  Code No. 
amob Z§. 
Roll No. 
 
 
 
 
 
 
 
 
 
 
 
g§H${bV narjm – II 
SUMMATIVE ASSESSMENT – II 
J{UV 
MATHEMATICS 
{ZYm©[aV g_` : 3 KÊQ>o   A{YH$V_ A§H$ : 90 
Time allowed : 3 hours Maximum Marks : 90 
 
? H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _o§ _w{ÐV n¥ð> 11 h¢ & 
? àíZ-nÌ _| Xm{hZo hmW H$s Amoa {XE JE H$moS >Zå~a H$mo N>mÌ CÎma-nwpñVH$m Ho$ _wI-n¥ð> na 
{bI| & 
? H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _| >31 àíZ h¢ & 
? H¥$n`m àíZ H$m CÎma {bIZm ewê$ H$aZo go nhbo, àíZ H$m H«$_m§H$ Adí` {bI| & 
? 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 & 
? Please check that this question paper contains 11 printed pages. 
? Code number given on the right hand side of the question paper should be 
written on the title page of the answer-book by the candidate. 
? Please check that this question paper contains 31 questions. 
? Please write down the Serial Number of the question before 
attempting it. 
? 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. 
SET-2 
30/2 2 
gm_mÝ` {ZX}e : 
(i) g^r àíZ A{Zdm`© h¢ & 
(ii) Bg àíZ-nÌ _| 31 àíZ h¢ Omo Mma IÊS>m| ? A, ~, g Am¡a X _| {d^m{OV h¢ & 
(iii) IÊS> A _| EH$-EH$ A§H$ dmbo 4 àíZ h¢ & IÊS> ~ _| 6 àíZ h¢ {OZ_| go àË`oH$ 2 A§H$ 
H$m h¡ & IÊS> g _| 10 àíZ VrZ-VrZ A§H$m| Ho$ h¢ & IÊS> X _| 11 àíZ h¢ {OZ_| go àË`oH$ 
4 A§H$ H$m h¡ &   
(iv) H¡$bHw$boQ>a H$m à`moJ d{O©V h¡ &  
General Instructions : 
(i) All questions are compulsory. 
(ii) The question paper consists of 31 questions divided into four sections ? A, 
B, C and D. 
(iii) Section A contains 4 questions of 1 mark each. Section B contains  
6 questions of 2 marks each, Section C contains 10 questions of 3 marks 
each and Section D contains 11 questions of 4 marks each. 
(iv) Use of calculators is not permitted. 
 
IÊS> A 
SECTION A 
àíZ g§»`m 1 go 4 VH$ àË`oH$ àíZ 1 A§H$ H$m h¡ &  
Question numbers 1 to 4 carry 1 mark each. 
1. AmH¥${V 1 _|, O H|$Ð dmbo d¥Îm H$s PQ EH$ Ordm h¡ VWm PT EH$ ñne© aoIm h¡ & `{X 
? QPT = 60 ? h¡, Vmo ? PRQ kmV H$s{OE & 
 
AmH¥${V 1 
30/2 3 P.T.O. 
In Figure 1, PQ is a chord of a circle with centre O and PT is a tangent. If 
? QPT = 60 ?, find ? PRQ. 
 
Figure 1 
2. `{X {ÛKmV g_rH$aU  px
2
 – 2 5 px + 15 = 0  Ho$ Xmo g_mZ _yb hm|, Vmo p H$m _mZ kmV 
H$s{OE & 
If the quadratic equation  px
2
 – 2 5 px + 15 = 0  has two equal roots, 
then find the value of p. 
 
3. AmH¥${V 2 _|, EH$ _rZma AB H$s D±$MmB© 20 _rQ>a h¡ Am¡a BgH$s ^y{_ na naN>mB© BC H$s 
bå~mB© 20 3 _rQ>a h¡ & gy`© H$m CÞVm§e kmV H$s{OE & 
 
AmH¥${V 2 
 
In Figure 2, a tower AB is 20 m high and BC, its shadow on the ground, 
is 20 3 m long. Find the Sun’s altitude. 
 
Figure 2 
30/2 4 
4. Xmo {^Þ nmgm| H$mo EH $gmW CN>mbm J`m & XmoZm| nmgm| Ho$ D$nar Vbm| na AmB© g§»`mAm| H$m 
JwUZ\$b 6 AmZo H$s àm{`H$Vm kmV H$s{OE & 
Two different dice are tossed together. Find the probability that the 
product of the two numbers on the top of the dice is 6. 
 
 
IÊS> ~ 
SECTION B 
 
àíZ g§»`m 5 go 10 VH$ àË`oH$ àíZ 2 A§H H$m h¡ & 
Question numbers 5 to 10 carry 2 marks each. 
 
5. `{X {~ÝXþ A(x, y), B(– 5, 7) VWm C(– 4, 5) ñ§maoIr` hm|, Vmo x VWm y _| gå~ÝY kmV 
H$s{OE & 
Find the relation between x and y if the points A(x, y), B(– 5, 7) and  
C(– 4, 5) are collinear. 
 
6. EH$ g_m§Va lo‹T>r Ho$ àW_ n nXm| Ho$ `moJ\$b H$mo S
n
 Ûmam Xem©`m OmVm h¡ & Bg lo‹T>r _| `{X  
S
5
 + S
7
 = 167 VWm S
10
 = 235 h¡, Vmo g_m§Va lo‹T>r kmV H$s{OE & 
In an AP, if S
5
 + S
7
 = 167 and S
10
 = 235, then find the AP, where S
n
 
denotes the sum of its first n terms. 
 
7. AmH¥${V 3 _|, Xmo ñne© aoImE± RQ VWm RP d¥Îm Ho$ ~mø {~ÝXþ R go ItMr JB© h¢ & d¥Îm H$m 
Ho$ÝÐ O h¡ & `{X ? PRQ = 120 ? h¡, Vmo {gÕ H$s{OE {H$ OR = PR + RQ. 
 
AmH¥${V 3 
Page 5


30/2 1 P.T.O. 
narjmWu H$moS >H$mo CÎma-nwpñVH$m Ho$ _wI-n¥ð 
>na Adí` {bIo§ & 
Candidates must write the Code on the 
title page of the answer-book. 
 Series RLH  
H$moS> Z§.   
30/2
 
  Code No. 
amob Z§. 
Roll No. 
 
 
 
 
 
 
 
 
 
 
 
g§H${bV narjm – II 
SUMMATIVE ASSESSMENT – II 
J{UV 
MATHEMATICS 
{ZYm©[aV g_` : 3 KÊQ>o   A{YH$V_ A§H$ : 90 
Time allowed : 3 hours Maximum Marks : 90 
 
? H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _o§ _w{ÐV n¥ð> 11 h¢ & 
? àíZ-nÌ _| Xm{hZo hmW H$s Amoa {XE JE H$moS >Zå~a H$mo N>mÌ CÎma-nwpñVH$m Ho$ _wI-n¥ð> na 
{bI| & 
? H¥$n`m Om±M H$a b| {H$ Bg àíZ-nÌ _| >31 àíZ h¢ & 
? H¥$n`m àíZ H$m CÎma {bIZm ewê$ H$aZo go nhbo, àíZ H$m H«$_m§H$ Adí` {bI| & 
? 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 & 
? Please check that this question paper contains 11 printed pages. 
? Code number given on the right hand side of the question paper should be 
written on the title page of the answer-book by the candidate. 
? Please check that this question paper contains 31 questions. 
? Please write down the Serial Number of the question before 
attempting it. 
? 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. 
SET-2 
30/2 2 
gm_mÝ` {ZX}e : 
(i) g^r àíZ A{Zdm`© h¢ & 
(ii) Bg àíZ-nÌ _| 31 àíZ h¢ Omo Mma IÊS>m| ? A, ~, g Am¡a X _| {d^m{OV h¢ & 
(iii) IÊS> A _| EH$-EH$ A§H$ dmbo 4 àíZ h¢ & IÊS> ~ _| 6 àíZ h¢ {OZ_| go àË`oH$ 2 A§H$ 
H$m h¡ & IÊS> g _| 10 àíZ VrZ-VrZ A§H$m| Ho$ h¢ & IÊS> X _| 11 àíZ h¢ {OZ_| go àË`oH$ 
4 A§H$ H$m h¡ &   
(iv) H¡$bHw$boQ>a H$m à`moJ d{O©V h¡ &  
General Instructions : 
(i) All questions are compulsory. 
(ii) The question paper consists of 31 questions divided into four sections ? A, 
B, C and D. 
(iii) Section A contains 4 questions of 1 mark each. Section B contains  
6 questions of 2 marks each, Section C contains 10 questions of 3 marks 
each and Section D contains 11 questions of 4 marks each. 
(iv) Use of calculators is not permitted. 
 
IÊS> A 
SECTION A 
àíZ g§»`m 1 go 4 VH$ àË`oH$ àíZ 1 A§H$ H$m h¡ &  
Question numbers 1 to 4 carry 1 mark each. 
1. AmH¥${V 1 _|, O H|$Ð dmbo d¥Îm H$s PQ EH$ Ordm h¡ VWm PT EH$ ñne© aoIm h¡ & `{X 
? QPT = 60 ? h¡, Vmo ? PRQ kmV H$s{OE & 
 
AmH¥${V 1 
30/2 3 P.T.O. 
In Figure 1, PQ is a chord of a circle with centre O and PT is a tangent. If 
? QPT = 60 ?, find ? PRQ. 
 
Figure 1 
2. `{X {ÛKmV g_rH$aU  px
2
 – 2 5 px + 15 = 0  Ho$ Xmo g_mZ _yb hm|, Vmo p H$m _mZ kmV 
H$s{OE & 
If the quadratic equation  px
2
 – 2 5 px + 15 = 0  has two equal roots, 
then find the value of p. 
 
3. AmH¥${V 2 _|, EH$ _rZma AB H$s D±$MmB© 20 _rQ>a h¡ Am¡a BgH$s ^y{_ na naN>mB© BC H$s 
bå~mB© 20 3 _rQ>a h¡ & gy`© H$m CÞVm§e kmV H$s{OE & 
 
AmH¥${V 2 
 
In Figure 2, a tower AB is 20 m high and BC, its shadow on the ground, 
is 20 3 m long. Find the Sun’s altitude. 
 
Figure 2 
30/2 4 
4. Xmo {^Þ nmgm| H$mo EH $gmW CN>mbm J`m & XmoZm| nmgm| Ho$ D$nar Vbm| na AmB© g§»`mAm| H$m 
JwUZ\$b 6 AmZo H$s àm{`H$Vm kmV H$s{OE & 
Two different dice are tossed together. Find the probability that the 
product of the two numbers on the top of the dice is 6. 
 
 
IÊS> ~ 
SECTION B 
 
àíZ g§»`m 5 go 10 VH$ àË`oH$ àíZ 2 A§H H$m h¡ & 
Question numbers 5 to 10 carry 2 marks each. 
 
5. `{X {~ÝXþ A(x, y), B(– 5, 7) VWm C(– 4, 5) ñ§maoIr` hm|, Vmo x VWm y _| gå~ÝY kmV 
H$s{OE & 
Find the relation between x and y if the points A(x, y), B(– 5, 7) and  
C(– 4, 5) are collinear. 
 
6. EH$ g_m§Va lo‹T>r Ho$ àW_ n nXm| Ho$ `moJ\$b H$mo S
n
 Ûmam Xem©`m OmVm h¡ & Bg lo‹T>r _| `{X  
S
5
 + S
7
 = 167 VWm S
10
 = 235 h¡, Vmo g_m§Va lo‹T>r kmV H$s{OE & 
In an AP, if S
5
 + S
7
 = 167 and S
10
 = 235, then find the AP, where S
n
 
denotes the sum of its first n terms. 
 
7. AmH¥${V 3 _|, Xmo ñne© aoImE± RQ VWm RP d¥Îm Ho$ ~mø {~ÝXþ R go ItMr JB© h¢ & d¥Îm H$m 
Ho$ÝÐ O h¡ & `{X ? PRQ = 120 ? h¡, Vmo {gÕ H$s{OE {H$ OR = PR + RQ. 
 
AmH¥${V 3 
30/2 5 P.T.O. 
In Figure 3, two tangents RQ and RP are drawn from an external point R 
to the circle with centre O. If ?  PRQ  =  120 ?, then prove that  
OR = PR + RQ. 
 
Figure 3 
 
8. AmH¥${V 4 _|, 3 go_r {ÌÁ`m dmbo EH$ d¥Îm Ho$ n[aJV EH$ {Ì^wO ABC Bg àH$ma ItMm J`m 
h¡ {H$ aoImIÊS> BD VWm DC H$s b§~mB`m± H«$_e… 6 go_r VWm 9 go_r h¡§ & `{X  
? ABC H$m joÌ\$b 54 dJ© go_r h¡, Vmo ^wOmAm| AB VWm AC H$s bå~mB`m± kmV H$s{OE & 
 
AmH¥${V 4 
 
In Figure 4, a triangle ABC is drawn to circumscribe a circle of radius  
3 cm, such that the segments BD and DC are respectively of lengths 6 cm 
and 9 cm. If the area of ? ABC is 54 cm
2
, then find the lengths of sides 
AB and AC. 
 
Figure 4