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 Page 1


.30/3/3 1 P.T.O. 
narjmWu àíZ-nÌ H$moS> >H$mo CÎma-nwpñVH$m Ho$ 
_wI-n¥ð >na Adí` {bIo§ & 
Candidates must write the Q.P. Code 
on the title page of the answer-book. 
 Series PPQQB/3  SET ~3 
  àíZ-nÌ H$moS>  
   
 
 
Q.P. Code 
amob Z§. 
Roll No. 
 
 
 
 NOTE 
(I) 
11
(I) Please check that this question paper 
contains 11 printed pages. 
(II) (II) 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) 
14 
(III) Please check that this question paper 
contains 14 questions. 
(IV) (IV) Please write down the serial 
number of the question in the 
answer-book before attempting it. 
(V) 
15 
10.15
10.15 10.30 
(V) 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. 
 J{UV (_mZH$)  
MATHEMATICS (STANDARD)  
: 2 : 40 
Time allowed : 2 hours Maximum Marks : 40 
 
30/3/3
Page 2


.30/3/3 1 P.T.O. 
narjmWu àíZ-nÌ H$moS> >H$mo CÎma-nwpñVH$m Ho$ 
_wI-n¥ð >na Adí` {bIo§ & 
Candidates must write the Q.P. Code 
on the title page of the answer-book. 
 Series PPQQB/3  SET ~3 
  àíZ-nÌ H$moS>  
   
 
 
Q.P. Code 
amob Z§. 
Roll No. 
 
 
 
 NOTE 
(I) 
11
(I) Please check that this question paper 
contains 11 printed pages. 
(II) (II) 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) 
14 
(III) Please check that this question paper 
contains 14 questions. 
(IV) (IV) Please write down the serial 
number of the question in the 
answer-book before attempting it. 
(V) 
15 
10.15
10.15 10.30 
(V) 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. 
 J{UV (_mZH$)  
MATHEMATICS (STANDARD)  
: 2 : 40 
Time allowed : 2 hours Maximum Marks : 40 
 
30/3/3
.30/3/3 2 
: 
: 
(i) 14
(ii) 
(iii) 6 1 6 2
(iv) 4 7 10 3
(v) 4 11 14 4
(vi) 
IÊS> H$ 
1 6 2 
1. AmH¥${V 1 _|, H|$Ð O dmbo d¥Îm na PQ VWm PR ñne©-aoImE± ItMr JB© h¢ & `{X  
 OPR = 45 h¡, Vmo {gÕ H$s{OE {H$ ORPQ EH$ dJ© h¡ &  2 
 
1
2. {XE JE ~ma§~maVm ~§Q>Z H$m ~hþbH$ kmV H$s{OE : 2 
   
15  25 6 
25  35 11 
35  45 22 
45  55 23 
55  65 14 
65  75 5 
3. 10 VWm àW_ 14 nXm| H$m `moJ\$b 1505 
gmd© AÝVa kmV H$s{OE & 2 
4. 9, 7, 5, ..... Am¡a 15, 12, 9, ..... Ho$ nd| nX 
g_mZ hm|Jo ? 2 
Page 3


.30/3/3 1 P.T.O. 
narjmWu àíZ-nÌ H$moS> >H$mo CÎma-nwpñVH$m Ho$ 
_wI-n¥ð >na Adí` {bIo§ & 
Candidates must write the Q.P. Code 
on the title page of the answer-book. 
 Series PPQQB/3  SET ~3 
  àíZ-nÌ H$moS>  
   
 
 
Q.P. Code 
amob Z§. 
Roll No. 
 
 
 
 NOTE 
(I) 
11
(I) Please check that this question paper 
contains 11 printed pages. 
(II) (II) 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) 
14 
(III) Please check that this question paper 
contains 14 questions. 
(IV) (IV) Please write down the serial 
number of the question in the 
answer-book before attempting it. 
(V) 
15 
10.15
10.15 10.30 
(V) 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. 
 J{UV (_mZH$)  
MATHEMATICS (STANDARD)  
: 2 : 40 
Time allowed : 2 hours Maximum Marks : 40 
 
30/3/3
.30/3/3 2 
: 
: 
(i) 14
(ii) 
(iii) 6 1 6 2
(iv) 4 7 10 3
(v) 4 11 14 4
(vi) 
IÊS> H$ 
1 6 2 
1. AmH¥${V 1 _|, H|$Ð O dmbo d¥Îm na PQ VWm PR ñne©-aoImE± ItMr JB© h¢ & `{X  
 OPR = 45 h¡, Vmo {gÕ H$s{OE {H$ ORPQ EH$ dJ© h¡ &  2 
 
1
2. {XE JE ~ma§~maVm ~§Q>Z H$m ~hþbH$ kmV H$s{OE : 2 
   
15  25 6 
25  35 11 
35  45 22 
45  55 23 
55  65 14 
65  75 5 
3. 10 VWm àW_ 14 nXm| H$m `moJ\$b 1505 
gmd© AÝVa kmV H$s{OE & 2 
4. 9, 7, 5, ..... Am¡a 15, 12, 9, ..... Ho$ nd| nX 
g_mZ hm|Jo ? 2 
.30/3/3 3 P.T.O. 
General Instructions : 
Read the following instructions very carefully and strictly follow them :  
(i) This question paper contains 14 questions. All questions are compulsory.  
(ii) This question paper is divided into three sections  Sections A, B and C.  
(iii) Section A comprises of 6 questions (Q.no. 1 to 6) of 2 marks each. Internal 
choice has been provided in two questions.   
(iv) Section B comprises of 4 questions (Q.no. 7 to 10) of 3 marks each. Internal 
choice has been provided in one question.   
(v) Section C comprises of 4 questions (Q.no. 11 to 14) of 4 marks each. Internal 
choice has been provided in one question. It also contains two case study based 
questions.  
(vi) Use of calculator is not permitted. 
SECTION A 
Question numbers 1 to 6 carry 2 marks each.  
1. In Figure 1, PQ and PR are tangents to the circle centred at O. If  
 OPR = 45 , then prove that ORPQ is a square.   2 
 
Figure 1 
2. Find the mode of the given frequency distribution :  2 
Class  Frequency  
15  25 6 
25  35 11 
35  45 22 
45  55 23 
55  65 14 
65  75 5 
3. 
sum of the first 14 terms is 1505.   2 
4. 
th
 terms of the APs : 9, 7, 5, ..... and  
15, 12, 9, ..... the same ?  2 
Page 4


.30/3/3 1 P.T.O. 
narjmWu àíZ-nÌ H$moS> >H$mo CÎma-nwpñVH$m Ho$ 
_wI-n¥ð >na Adí` {bIo§ & 
Candidates must write the Q.P. Code 
on the title page of the answer-book. 
 Series PPQQB/3  SET ~3 
  àíZ-nÌ H$moS>  
   
 
 
Q.P. Code 
amob Z§. 
Roll No. 
 
 
 
 NOTE 
(I) 
11
(I) Please check that this question paper 
contains 11 printed pages. 
(II) (II) 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) 
14 
(III) Please check that this question paper 
contains 14 questions. 
(IV) (IV) Please write down the serial 
number of the question in the 
answer-book before attempting it. 
(V) 
15 
10.15
10.15 10.30 
(V) 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. 
 J{UV (_mZH$)  
MATHEMATICS (STANDARD)  
: 2 : 40 
Time allowed : 2 hours Maximum Marks : 40 
 
30/3/3
.30/3/3 2 
: 
: 
(i) 14
(ii) 
(iii) 6 1 6 2
(iv) 4 7 10 3
(v) 4 11 14 4
(vi) 
IÊS> H$ 
1 6 2 
1. AmH¥${V 1 _|, H|$Ð O dmbo d¥Îm na PQ VWm PR ñne©-aoImE± ItMr JB© h¢ & `{X  
 OPR = 45 h¡, Vmo {gÕ H$s{OE {H$ ORPQ EH$ dJ© h¡ &  2 
 
1
2. {XE JE ~ma§~maVm ~§Q>Z H$m ~hþbH$ kmV H$s{OE : 2 
   
15  25 6 
25  35 11 
35  45 22 
45  55 23 
55  65 14 
65  75 5 
3. 10 VWm àW_ 14 nXm| H$m `moJ\$b 1505 
gmd© AÝVa kmV H$s{OE & 2 
4. 9, 7, 5, ..... Am¡a 15, 12, 9, ..... Ho$ nd| nX 
g_mZ hm|Jo ? 2 
.30/3/3 3 P.T.O. 
General Instructions : 
Read the following instructions very carefully and strictly follow them :  
(i) This question paper contains 14 questions. All questions are compulsory.  
(ii) This question paper is divided into three sections  Sections A, B and C.  
(iii) Section A comprises of 6 questions (Q.no. 1 to 6) of 2 marks each. Internal 
choice has been provided in two questions.   
(iv) Section B comprises of 4 questions (Q.no. 7 to 10) of 3 marks each. Internal 
choice has been provided in one question.   
(v) Section C comprises of 4 questions (Q.no. 11 to 14) of 4 marks each. Internal 
choice has been provided in one question. It also contains two case study based 
questions.  
(vi) Use of calculator is not permitted. 
SECTION A 
Question numbers 1 to 6 carry 2 marks each.  
1. In Figure 1, PQ and PR are tangents to the circle centred at O. If  
 OPR = 45 , then prove that ORPQ is a square.   2 
 
Figure 1 
2. Find the mode of the given frequency distribution :  2 
Class  Frequency  
15  25 6 
25  35 11 
35  45 22 
45  55 23 
55  65 14 
65  75 5 
3. 
sum of the first 14 terms is 1505.   2 
4. 
th
 terms of the APs : 9, 7, 5, ..... and  
15, 12, 9, ..... the same ?  2 
.30/3/3 4 
5. (H$) x Ho$ {bE {ÛKmV g_rH$aU   
  x
2
  2ax  (4b
2
  a
2
) = 0 
  H$mo hb H$s{OE & 2 
   AWdm 
(I) `{X {ÛKmV g_rH$aU  
  (1 + a
2
) x
2
 + 2abx + (b
2
  c
2
) = 0 
  Ho$ _yb ~am~a Ed§ dmñV{dH$ h¢, Vmo {gÕ H$s{OE {H$ : 
  b
2
 = c
2
 (1 + a
2
) 2 
6. (H$) 7 go_r ì`mg Ho$ ~obZmH$ma ~V©Z, {Og_| Hw$N> nmZr ^am h¡, _| 1·4 go_r ì`mg Ho$  
150 o nmZr _| 
Sy>~ OmE± & ~obZmH$ma ~V©Z _| Ob ñVa H$s d¥{Õ kmV H$s{OE & 2 
AWdm 
(I) AmH¥${V 2 _|, 6 go_r 
àH$ma ~Zo KZm^ H$m Hw$b n¥ð>r` joÌ\$b kmV H$s{OE &  2 
 
2 
IÊS> I 
7 10 3 
7. g_wÐ _| Xmo Zmd Omo EH$-Xÿgao go 80 _r. H$s Xÿar na h¢ Am¡a AB H$s Va\$ 
30 VWm 
45 h¢, O¡go {H$ AmH¥${V 3 s D±$MmB© kmV H$s{OE &  3 
 
3 
Page 5


.30/3/3 1 P.T.O. 
narjmWu àíZ-nÌ H$moS> >H$mo CÎma-nwpñVH$m Ho$ 
_wI-n¥ð >na Adí` {bIo§ & 
Candidates must write the Q.P. Code 
on the title page of the answer-book. 
 Series PPQQB/3  SET ~3 
  àíZ-nÌ H$moS>  
   
 
 
Q.P. Code 
amob Z§. 
Roll No. 
 
 
 
 NOTE 
(I) 
11
(I) Please check that this question paper 
contains 11 printed pages. 
(II) (II) 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) 
14 
(III) Please check that this question paper 
contains 14 questions. 
(IV) (IV) Please write down the serial 
number of the question in the 
answer-book before attempting it. 
(V) 
15 
10.15
10.15 10.30 
(V) 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. 
 J{UV (_mZH$)  
MATHEMATICS (STANDARD)  
: 2 : 40 
Time allowed : 2 hours Maximum Marks : 40 
 
30/3/3
.30/3/3 2 
: 
: 
(i) 14
(ii) 
(iii) 6 1 6 2
(iv) 4 7 10 3
(v) 4 11 14 4
(vi) 
IÊS> H$ 
1 6 2 
1. AmH¥${V 1 _|, H|$Ð O dmbo d¥Îm na PQ VWm PR ñne©-aoImE± ItMr JB© h¢ & `{X  
 OPR = 45 h¡, Vmo {gÕ H$s{OE {H$ ORPQ EH$ dJ© h¡ &  2 
 
1
2. {XE JE ~ma§~maVm ~§Q>Z H$m ~hþbH$ kmV H$s{OE : 2 
   
15  25 6 
25  35 11 
35  45 22 
45  55 23 
55  65 14 
65  75 5 
3. 10 VWm àW_ 14 nXm| H$m `moJ\$b 1505 
gmd© AÝVa kmV H$s{OE & 2 
4. 9, 7, 5, ..... Am¡a 15, 12, 9, ..... Ho$ nd| nX 
g_mZ hm|Jo ? 2 
.30/3/3 3 P.T.O. 
General Instructions : 
Read the following instructions very carefully and strictly follow them :  
(i) This question paper contains 14 questions. All questions are compulsory.  
(ii) This question paper is divided into three sections  Sections A, B and C.  
(iii) Section A comprises of 6 questions (Q.no. 1 to 6) of 2 marks each. Internal 
choice has been provided in two questions.   
(iv) Section B comprises of 4 questions (Q.no. 7 to 10) of 3 marks each. Internal 
choice has been provided in one question.   
(v) Section C comprises of 4 questions (Q.no. 11 to 14) of 4 marks each. Internal 
choice has been provided in one question. It also contains two case study based 
questions.  
(vi) Use of calculator is not permitted. 
SECTION A 
Question numbers 1 to 6 carry 2 marks each.  
1. In Figure 1, PQ and PR are tangents to the circle centred at O. If  
 OPR = 45 , then prove that ORPQ is a square.   2 
 
Figure 1 
2. Find the mode of the given frequency distribution :  2 
Class  Frequency  
15  25 6 
25  35 11 
35  45 22 
45  55 23 
55  65 14 
65  75 5 
3. 
sum of the first 14 terms is 1505.   2 
4. 
th
 terms of the APs : 9, 7, 5, ..... and  
15, 12, 9, ..... the same ?  2 
.30/3/3 4 
5. (H$) x Ho$ {bE {ÛKmV g_rH$aU   
  x
2
  2ax  (4b
2
  a
2
) = 0 
  H$mo hb H$s{OE & 2 
   AWdm 
(I) `{X {ÛKmV g_rH$aU  
  (1 + a
2
) x
2
 + 2abx + (b
2
  c
2
) = 0 
  Ho$ _yb ~am~a Ed§ dmñV{dH$ h¢, Vmo {gÕ H$s{OE {H$ : 
  b
2
 = c
2
 (1 + a
2
) 2 
6. (H$) 7 go_r ì`mg Ho$ ~obZmH$ma ~V©Z, {Og_| Hw$N> nmZr ^am h¡, _| 1·4 go_r ì`mg Ho$  
150 o nmZr _| 
Sy>~ OmE± & ~obZmH$ma ~V©Z _| Ob ñVa H$s d¥{Õ kmV H$s{OE & 2 
AWdm 
(I) AmH¥${V 2 _|, 6 go_r 
àH$ma ~Zo KZm^ H$m Hw$b n¥ð>r` joÌ\$b kmV H$s{OE &  2 
 
2 
IÊS> I 
7 10 3 
7. g_wÐ _| Xmo Zmd Omo EH$-Xÿgao go 80 _r. H$s Xÿar na h¢ Am¡a AB H$s Va\$ 
30 VWm 
45 h¢, O¡go {H$ AmH¥${V 3 s D±$MmB© kmV H$s{OE &  3 
 
3 
.30/3/3 5 P.T.O. 
5. (a) Solve the quadratic equation for x :    
  x
2
  2ax  (4b
2
  a
2
) = 0 2 
   OR 
(b) If the quadratic equation  
  (1 + a
2
) x
2
 + 2abx + (b
2
  c
2
) = 0 
 has equal and real roots, then prove that : 
  b
2
 = c
2
 (1 + a
2
) 2 
6. (a) 150 spherical marbles, each of diameter 1·4 cm, are dropped in a 
cylindrical vessel of diameter 7 cm containing some water, and are 
completely immersed in water. Find the rise in the level of water 
in the cylindrical vessel.   2 
OR 
(b) Three cubes of side 6 cm each, are joined as shown in Figure 2.  
Find the total surface area of the resulting cuboid.  2 
 
Figure 2 
 
SECTION B 
Question numbers  7 to 10 carry 3 marks each.  
7. Two boats are sailing in the sea 80 m apart from each other towards a cliff 
AB. The angles of depression of the boats from the top of the cliff are 30 
and 45 respectively, as shown in Figure 3. Find the height of the cliff.    3 
 
Figure 3

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