HBSE Class 10 Mathematics Question Paper 2020
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HBSE Class 10 Mathematics Question Paper 2020 – Text
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Page 1
CLASS : 10th (Secondary) Code No. 4803
Series : Sec. M/2020
Roll No. SET : A
xf.kr
MATHEMATICS
(Academic/Open)
[ fgUnh ,oa vaxzsth ek/;e ]
[ Hindi and English Medium ]
(Only for Fresh/Re-appear Candidates)
le; % 3 ?k.Vs ] [ iw.kkZad % 80
Time allowed : 3 hours ] [ Maximum Marks : 80
• Ñi;k tk¡p dj ysa fd bl iz'u-i= esa eqfnzr i`"B 16 rFkk
iz'u 32 gSaA
Please make sure that the printed pages in this
question paper are 16 in number and it contains
32 questions.
• iz'u-i= esa nkfgus gkFk dh vksj fn;s x;s dksM uEcj rFkk lsV dks
Nk= mÙkj-iqfLrdk ds eq[;-i`"B ij fy[ksaA
The Code No. and Set on the right side of the
question paper should be written by the candidate
on the front page of the answer-book.
• Ñi;k iz'u dk mÙkj fy[kuk 'kq: djus ls igys] iz'u dk Øekad
vo'; fy[ksaA
Before beginning to answer a question, its Serial
Number must be written.
4803/(Set : A) P. T. O.
Series : Sec. M/2020
Roll No. SET : A
xf.kr
MATHEMATICS
(Academic/Open)
[ fgUnh ,oa vaxzsth ek/;e ]
[ Hindi and English Medium ]
(Only for Fresh/Re-appear Candidates)
le; % 3 ?k.Vs ] [ iw.kkZad % 80
Time allowed : 3 hours ] [ Maximum Marks : 80
• Ñi;k tk¡p dj ysa fd bl iz'u-i= esa eqfnzr i`"B 16 rFkk
iz'u 32 gSaA
Please make sure that the printed pages in this
question paper are 16 in number and it contains
32 questions.
• iz'u-i= esa nkfgus gkFk dh vksj fn;s x;s dksM uEcj rFkk lsV dks
Nk= mÙkj-iqfLrdk ds eq[;-i`"B ij fy[ksaA
The Code No. and Set on the right side of the
question paper should be written by the candidate
on the front page of the answer-book.
• Ñi;k iz'u dk mÙkj fy[kuk 'kq: djus ls igys] iz'u dk Øekad
vo'; fy[ksaA
Before beginning to answer a question, its Serial
Number must be written.
4803/(Set : A) P. T. O.
Page 2
(2) 4803/(Set : A)
• mÙkj-iqfLrdk ds chp esa [kkyh iUuk / iUus u NksMsa+A
Don’t leave blank page/pages in your answer-book.
• mÙkj-iqfLrdk ds vfrfjDr dksbZ vU; 'khV ugha feysxhA vr%
vko';drkuqlkj gh fy[ksa vkSj fy[kk mÙkj u dkVsaA
Except answer-book, no extra sheet will be given.
Write to the point and do not strike the written
answer.
• ijh{kkFkhZ viuk jksy ua0 iz'u&i= ij vo'; fy[ksaA
Candidates must write their Roll Number on the
question paper.
• d`i;k iz'uksa dk mÙkj nsus lss iwoZ ;g lqfuf'pr dj ysa fd iz'u-i=
iw.kZ o lgh gS] ijh{kk ds mijkUr bl lEcU/k esa dksbZ Hkh nkok
Lohdkj ugha fd;k tk;sxkA
Before answering the questions, ensure that you
have been supplied the correct and complete
question paper, no claim in this regard, will be
entertained after examination.
lkekU; funsZ'k %
General Instruction :
(i) lHkh iz'u vfuok;Z gSaA
All questions are compulsory.
(ii) bl iz'u-i= esa dqy 32 iz'u gSa tks fd pkj [k.Mksa v]
c] l vkSj n esa ck¡Vs x;s gSa %
This question paper consists of 32 questions
in all which are divided into four Sections :
A, B, C and D :
4803/(Set : A)
• mÙkj-iqfLrdk ds chp esa [kkyh iUuk / iUus u NksMsa+A
Don’t leave blank page/pages in your answer-book.
• mÙkj-iqfLrdk ds vfrfjDr dksbZ vU; 'khV ugha feysxhA vr%
vko';drkuqlkj gh fy[ksa vkSj fy[kk mÙkj u dkVsaA
Except answer-book, no extra sheet will be given.
Write to the point and do not strike the written
answer.
• ijh{kkFkhZ viuk jksy ua0 iz'u&i= ij vo'; fy[ksaA
Candidates must write their Roll Number on the
question paper.
• d`i;k iz'uksa dk mÙkj nsus lss iwoZ ;g lqfuf'pr dj ysa fd iz'u-i=
iw.kZ o lgh gS] ijh{kk ds mijkUr bl lEcU/k esa dksbZ Hkh nkok
Lohdkj ugha fd;k tk;sxkA
Before answering the questions, ensure that you
have been supplied the correct and complete
question paper, no claim in this regard, will be
entertained after examination.
lkekU; funsZ'k %
General Instruction :
(i) lHkh iz'u vfuok;Z gSaA
All questions are compulsory.
(ii) bl iz'u-i= esa dqy 32 iz'u gSa tks fd pkj [k.Mksa v]
c] l vkSj n esa ck¡Vs x;s gSa %
This question paper consists of 32 questions
in all which are divided into four Sections :
A, B, C and D :
4803/(Set : A)
Page 3
(3) 4803/(Set : A)
[k.M v % bl [k.M esa 1 ls 16 rd dqy 16 iz'u gSa]
izR;sd iz'u 1 vad dk gSA
Section A : There are 16 questions from 1
to 16, each of 1 mark.
[k.M c % bl [k.M esa 17 ls 21 rd dqy 5 iz'u gSa]
izR;sd iz'u 3 vad dk gSA
Section B : There are 5 questions from 17
to 21, each of 3 marks.
[k.M l % bl [k.M esa 22 ls 27 rd dqy 6 iz'u gSa]
izR;sd iz'u 4 vad dk gSA
Section C : There are 6 questions from 22
to 27, each of 4 marks.
[k.M n % bl [k.M esa 28 ls 32 rd dqy 5 iz'u gSa]
izR;sd iz'u 5 vad dk gSA
Section D : There are 5 questions from 28
to 32, each of 5 marks.
(iii) [k.M n esa nks iz'uksa esa vkUrfjd fodYi fn;s x;s gSaA
mlesa ls ,d iz'u dks pquuk gSA
Section D contains two questions where
internal choice have been provided. You
have to choose one of them.
4803/(Set : A) P. T. O.
[k.M v % bl [k.M esa 1 ls 16 rd dqy 16 iz'u gSa]
izR;sd iz'u 1 vad dk gSA
Section A : There are 16 questions from 1
to 16, each of 1 mark.
[k.M c % bl [k.M esa 17 ls 21 rd dqy 5 iz'u gSa]
izR;sd iz'u 3 vad dk gSA
Section B : There are 5 questions from 17
to 21, each of 3 marks.
[k.M l % bl [k.M esa 22 ls 27 rd dqy 6 iz'u gSa]
izR;sd iz'u 4 vad dk gSA
Section C : There are 6 questions from 22
to 27, each of 4 marks.
[k.M n % bl [k.M esa 28 ls 32 rd dqy 5 iz'u gSa]
izR;sd iz'u 5 vad dk gSA
Section D : There are 5 questions from 28
to 32, each of 5 marks.
(iii) [k.M n esa nks iz'uksa esa vkUrfjd fodYi fn;s x;s gSaA
mlesa ls ,d iz'u dks pquuk gSA
Section D contains two questions where
internal choice have been provided. You
have to choose one of them.
4803/(Set : A) P. T. O.
Page 4
(4) 4803/(Set : A)
[k.M & v
SECTION – A
p
1. 0.375 dks ds :i eas O;Dr dhft,A 1
q
p
Express 0.375 in the form .
q
2. 6x 2 − 7x − 3 ds 'kwU;d gSa % 1
1 3
(A) − ,
3 2
7 3
(B) − , −
3 6
7 3
(C) , −
6 6
(D) buesa ls dksbZ ugha
The zeroes of 6x 2 − 7x − 3 are :
1 3
(A) − ,
3 2
7 3
(B) − , −
3 6
7 3
(C) , −
6 6
(D) None of these
4803/(Set : A)
[k.M & v
SECTION – A
p
1. 0.375 dks ds :i eas O;Dr dhft,A 1
q
p
Express 0.375 in the form .
q
2. 6x 2 − 7x − 3 ds 'kwU;d gSa % 1
1 3
(A) − ,
3 2
7 3
(B) − , −
3 6
7 3
(C) , −
6 6
(D) buesa ls dksbZ ugha
The zeroes of 6x 2 − 7x − 3 are :
1 3
(A) − ,
3 2
7 3
(B) − , −
3 6
7 3
(C) , −
6 6
(D) None of these
4803/(Set : A)
Page 5
(5) 4803/(Set : A)
3. x + y = 14, x − y = 4 dks gy dhft,A 1
Solve :
x + y = 14, x − y = 4
4. dkSu&lh ,d Js.kh A. P. gS \ 1
(A) 2, 4, 8, 12, …….
(B) 0.2, 0.22, 0.222, ……
(C) –10, –6, –2, 2, ……
(D) 1, 3, 9, 27, …...
Which one is an A. P. series ?
(A) 2, 4, 8, 12, …….
(B) 0.2, 0.22, 0.222, ……
(C) –10, –6, –2, 2, ……
(D) 1, 3, 9, 27, …...
5. 2, 7, 12, …… . A. P. dk 10ok¡ in Kkr dhft,A 1
Find the 10th term of A. P. 2, 7, 12, …… .
6. dks"Bd esa fn, 'kCnksa esa ls lgh 'kCnksa dk iz;ksx djrs gq,] fjDr
LFkku dks Hkfj, % 1
lHkh o`Ùk ---------- gksrs gSaA ¼lokZaxle] le:i½
4803/(Set : A) P. T. O.
3. x + y = 14, x − y = 4 dks gy dhft,A 1
Solve :
x + y = 14, x − y = 4
4. dkSu&lh ,d Js.kh A. P. gS \ 1
(A) 2, 4, 8, 12, …….
(B) 0.2, 0.22, 0.222, ……
(C) –10, –6, –2, 2, ……
(D) 1, 3, 9, 27, …...
Which one is an A. P. series ?
(A) 2, 4, 8, 12, …….
(B) 0.2, 0.22, 0.222, ……
(C) –10, –6, –2, 2, ……
(D) 1, 3, 9, 27, …...
5. 2, 7, 12, …… . A. P. dk 10ok¡ in Kkr dhft,A 1
Find the 10th term of A. P. 2, 7, 12, …… .
6. dks"Bd esa fn, 'kCnksa esa ls lgh 'kCnksa dk iz;ksx djrs gq,] fjDr
LFkku dks Hkfj, % 1
lHkh o`Ùk ---------- gksrs gSaA ¼lokZaxle] le:i½
4803/(Set : A) P. T. O.
Page 6
(6) 4803/(Set : A)
Fill in the blank using correct word given in
bracket :
All circles are ………… . (congruent, similar)
7. nks le:i f=Hkqtksa dh Hkqtkvksa dk vuqikr 4 : 9 gS] rks muds
{ks=Qyksa dk vuqikr gS % 1
(A) 16 : 81 (B) 8 : 18
(C) 81 : 16 (D) 12 : 27
Sides of two similar triangles are in the ratio 4 : 9.
Areas of their triangles are in the ratio :
(A) 16 : 81 (B) 8 : 18
(C) 81 : 16 (D) 12 : 27
8. ;fn nks le:i f=Hkqtksa dk {ks=Qy Øe'k% 36 eh2 vkSj
121 eh2 gS] rks mudh laxr Hkqtkvksa dk vuqikr gS % 1
(A) 11 : 6
(B) 6 : 11
(C) 9 : 11
(D) buesa ls dksbZ ugha
4803/(Set : A)
Fill in the blank using correct word given in
bracket :
All circles are ………… . (congruent, similar)
7. nks le:i f=Hkqtksa dh Hkqtkvksa dk vuqikr 4 : 9 gS] rks muds
{ks=Qyksa dk vuqikr gS % 1
(A) 16 : 81 (B) 8 : 18
(C) 81 : 16 (D) 12 : 27
Sides of two similar triangles are in the ratio 4 : 9.
Areas of their triangles are in the ratio :
(A) 16 : 81 (B) 8 : 18
(C) 81 : 16 (D) 12 : 27
8. ;fn nks le:i f=Hkqtksa dk {ks=Qy Øe'k% 36 eh2 vkSj
121 eh2 gS] rks mudh laxr Hkqtkvksa dk vuqikr gS % 1
(A) 11 : 6
(B) 6 : 11
(C) 9 : 11
(D) buesa ls dksbZ ugha
4803/(Set : A)
Page 7
(7) 4803/(Set : A)
If the areas of two similar triangles are 36 m2
and 121 m2 respectively, the ratio of there
corresponding sides is :
(A) 11 : 6 (B) 6 : 11
(C) 9 : 11 (D) None of these
9. ,d fcUnq Q ls ,d o`Ùk ij Li'kZ js[kk dh yEckbZ 24 lseh rFkk
Q dh dsUæ ls nwjh 25 lseh gSA o`Ùk dh f=T;k Kkr dhft,A 1
From a point Q, the length of tangent to a circle
is 24 cm and distance of Q from centre is 25
cm. Find the radius of circle.
10. (2, 3) vkSj (4, 1) fcUnqvksa ds chp dh nwjh Kkr dhft,A 1
Find the distance between the points (2, 3) and
(4, 1).
11. ;fn js[kk[k.M dk e/; fcUnq (3, 4) gS ftldk ,d fljk
(7, –2) gS] rks nwljs fljs dk funsZ'kkad fcUnq Kkr dhft,A 1
If (3, 4) is mid point of the line segment whose
one end is (7, –2), then find the coordinates of
the other end point.
4803/(Set : A) P. T. O.
If the areas of two similar triangles are 36 m2
and 121 m2 respectively, the ratio of there
corresponding sides is :
(A) 11 : 6 (B) 6 : 11
(C) 9 : 11 (D) None of these
9. ,d fcUnq Q ls ,d o`Ùk ij Li'kZ js[kk dh yEckbZ 24 lseh rFkk
Q dh dsUæ ls nwjh 25 lseh gSA o`Ùk dh f=T;k Kkr dhft,A 1
From a point Q, the length of tangent to a circle
is 24 cm and distance of Q from centre is 25
cm. Find the radius of circle.
10. (2, 3) vkSj (4, 1) fcUnqvksa ds chp dh nwjh Kkr dhft,A 1
Find the distance between the points (2, 3) and
(4, 1).
11. ;fn js[kk[k.M dk e/; fcUnq (3, 4) gS ftldk ,d fljk
(7, –2) gS] rks nwljs fljs dk funsZ'kkad fcUnq Kkr dhft,A 1
If (3, 4) is mid point of the line segment whose
one end is (7, –2), then find the coordinates of
the other end point.
4803/(Set : A) P. T. O.
Page 8
(8) 4803/(Set : A)
tan 65 o
12. dk eku Kkr dhft,A 1
cot 25 o
tan 65 o
Find the value of .
cot 25 o
13. ;fn sin A = 3 , rks cos A gS % 1
4
4 7
(A) (B)
7 4
3
(C) (D) buesa ls dksbZ ugha
7
3
If sin A = , then cos A is :
4
4 7
(A) (B)
7 4
3
(C) (D) None of these
7
14. f=T;k 4 lseh okys ,d o`Ùk ds f=T;k[kaM dk {ks=Qy Kkr
dhft,] ftldk dks.k 30° gSA ¼π = 3.14 dk ç;ksx dhft,½ 1
Find the area of a sector of a circle with radius
4 cm, if angle of the sector is 30°. (Use π = 3.14)
4803/(Set : A)
tan 65 o
12. dk eku Kkr dhft,A 1
cot 25 o
tan 65 o
Find the value of .
cot 25 o
13. ;fn sin A = 3 , rks cos A gS % 1
4
4 7
(A) (B)
7 4
3
(C) (D) buesa ls dksbZ ugha
7
3
If sin A = , then cos A is :
4
4 7
(A) (B)
7 4
3
(C) (D) None of these
7
14. f=T;k 4 lseh okys ,d o`Ùk ds f=T;k[kaM dk {ks=Qy Kkr
dhft,] ftldk dks.k 30° gSA ¼π = 3.14 dk ç;ksx dhft,½ 1
Find the area of a sector of a circle with radius
4 cm, if angle of the sector is 30°. (Use π = 3.14)
4803/(Set : A)
Page 9
(9) 4803/(Set : A)
15. yEco`Ùkh; csyu ds vk/kkj dk O;kl 2r gS rFkk mldh Å¡pkbZ h
gSA oØ i`"Bh; {ks=Qy gS % 1
(A) πr 2h
(B) 2πrh
(C) 2πr (r + h)
(D) buesa ls dksbZ ugha
The diameter of the base of right circular
cylinder is 2r and its height is h. The curved
surface area is :
(A) πr 2h
(B) 2πrh
(C) 2πr (r + h)
(D) None of these
16. ,d FkSys esa 3 uhyh xsan] 2 lQsn xsan vkSj 4 yky xsan gSaA ;fn
,d xsan FkSys ls ;kn`fPNd fudkyh tkrh gS] rks blds lQsn gksus
dh çkf;drk D;k gksxh \ 1
A bag contains 3 blue balls, 2 white balls and 4
red balls. If one ball is taken out at random from
the bag. What is the probability that it will be
White ?
4803/(Set : A) P. T. O.
15. yEco`Ùkh; csyu ds vk/kkj dk O;kl 2r gS rFkk mldh Å¡pkbZ h
gSA oØ i`"Bh; {ks=Qy gS % 1
(A) πr 2h
(B) 2πrh
(C) 2πr (r + h)
(D) buesa ls dksbZ ugha
The diameter of the base of right circular
cylinder is 2r and its height is h. The curved
surface area is :
(A) πr 2h
(B) 2πrh
(C) 2πr (r + h)
(D) None of these
16. ,d FkSys esa 3 uhyh xsan] 2 lQsn xsan vkSj 4 yky xsan gSaA ;fn
,d xsan FkSys ls ;kn`fPNd fudkyh tkrh gS] rks blds lQsn gksus
dh çkf;drk D;k gksxh \ 1
A bag contains 3 blue balls, 2 white balls and 4
red balls. If one ball is taken out at random from
the bag. What is the probability that it will be
White ?
4803/(Set : A) P. T. O.
Page 10
( 10 ) 4803/(Set : A)
[k.M & c
SECTION – B
17. fl) dhft, fd 2 ,d vifjes; la[;k gSA 3
Prove that 2 is an irrational number.
18. cgqin p(x ) = 3x 3 + x 2 + 2x + 5 dks cgqin
2
q (x ) = x + 2x + 1 ds }kjk Hkkx dhft,A HkkxQy vkSj
'ks"kQy Kkr dhft,A 3
Divide the polynomial p(x ) = 3x 3 + x 2 + 2x + 5
by the polynomial q (x ) = x 2 + 2x + 1 . Find the
quotient and remainder.
19. 90 lseh dh yEckbZ okyh ,d yM+dh cYc yxs ,d [kaHks ds
vk/kkj ls ijs 1.2 eh/ls- dh pky ls py jgh gSA ;fn cYc
Hkwfe ls 3.6 eh dh Å¡pkbZ ij gS] rks 4 lsd.M ckn ml yM+dh
dh Nk;k dh yEckbZ Kkr dhft,A 3
A girl of height 90 cm is walking away from the
base of a lamp-post at a speed of 1.2 m/s. If the
lamp is 3.6 m above the ground, find the length
of her shadow after 4 seconds.
20. fl) dhft, % 3
sec A (1 − sin A) (sec A + tan A) = 1
4803/(Set : A)
[k.M & c
SECTION – B
17. fl) dhft, fd 2 ,d vifjes; la[;k gSA 3
Prove that 2 is an irrational number.
18. cgqin p(x ) = 3x 3 + x 2 + 2x + 5 dks cgqin
2
q (x ) = x + 2x + 1 ds }kjk Hkkx dhft,A HkkxQy vkSj
'ks"kQy Kkr dhft,A 3
Divide the polynomial p(x ) = 3x 3 + x 2 + 2x + 5
by the polynomial q (x ) = x 2 + 2x + 1 . Find the
quotient and remainder.
19. 90 lseh dh yEckbZ okyh ,d yM+dh cYc yxs ,d [kaHks ds
vk/kkj ls ijs 1.2 eh/ls- dh pky ls py jgh gSA ;fn cYc
Hkwfe ls 3.6 eh dh Å¡pkbZ ij gS] rks 4 lsd.M ckn ml yM+dh
dh Nk;k dh yEckbZ Kkr dhft,A 3
A girl of height 90 cm is walking away from the
base of a lamp-post at a speed of 1.2 m/s. If the
lamp is 3.6 m above the ground, find the length
of her shadow after 4 seconds.
20. fl) dhft, % 3
sec A (1 − sin A) (sec A + tan A) = 1
4803/(Set : A)
Page 11
( 11 ) 4803/(Set : A)
Prove that :
sec A (1 − sin A) (sec A + tan A) = 1
21. o`Ùk dh ifjf/k Kkr dhft, ftldk {ks=Qy 6.16 lseh2 gSA 3
Find the circumference of a circle whose area is
6.16 cm2 .
[k.M & l
SECTION – C
22. gy dhft, % 4
5 1 6 3
+ = 2 vkSj − =1
x −1 y − 2 x −1 y − 2
Solve :
5 1 6 3
+ = 2 and − =1
x −1 y − 2 x −1 y − 2
23. ,d eksVj&cksV] ftldh fLFkj ty esa pky 18 fdeh@?k.Vk gS]
24 fdeh /kkjk ds çfrdwy tkus esa] ogh nwjh /kkjk ds vuqdwy
tkus dh vis{kk 1 ?kaVk vf/kd ysrh gSA /kkjk dh pky Kkr
dhft,A 4
4803/(Set : A) P. T. O.
Prove that :
sec A (1 − sin A) (sec A + tan A) = 1
21. o`Ùk dh ifjf/k Kkr dhft, ftldk {ks=Qy 6.16 lseh2 gSA 3
Find the circumference of a circle whose area is
6.16 cm2 .
[k.M & l
SECTION – C
22. gy dhft, % 4
5 1 6 3
+ = 2 vkSj − =1
x −1 y − 2 x −1 y − 2
Solve :
5 1 6 3
+ = 2 and − =1
x −1 y − 2 x −1 y − 2
23. ,d eksVj&cksV] ftldh fLFkj ty esa pky 18 fdeh@?k.Vk gS]
24 fdeh /kkjk ds çfrdwy tkus esa] ogh nwjh /kkjk ds vuqdwy
tkus dh vis{kk 1 ?kaVk vf/kd ysrh gSA /kkjk dh pky Kkr
dhft,A 4
4803/(Set : A) P. T. O.
Page 12
( 12 ) 4803/(Set : A)
The speed of motor-boat is 18 km/h in still
water. It takes one hour more to 24 km
upstream than to return downstream the same
distance. Find the speed of the stream.
24. A. P. : 24, 21, 18, …… ds fdrus in fy, tk,¡] rkfd
mudk ;ksx 78 gks \ 4
How many terms of A. P. : 24, 21, 18, ……
should be taken so that their sum is 78 ?
25. fdlh cká fcUnq ls o`Ùk ij [khaph xbZ Li'kZ js[kkvksa dh yEckb;k¡
cjkcj gksrh gSa] fl) dhft,A 4
Prove that the length of tangents drawn from an
external point to a circle are equal.
26. fcUnq (−4, 6)] fcUnqvksa A(−6, 10) vkSj B(3, −8) dks tksM+us
okys js[kk[k.M dks fdl vuqikr esa foHkkftr djrk gSA 4
In what ratio does the point (−4, 6) divides the
line segment joining the points A(−6, 10) and
B(3, −8).
27. vPNh çdkj ls QsaVh xbZ 52 iÙkksa dh ,d xM~Mh esa ls ,d iÙkk
fudkyk tkrk gSA çkf;drk Kkr dhft, fd ;g iÙkk (i) ,d
bDdk gksxk] (ii) ,d bDdk ugha gksxkA 4
4803/(Set : A)
The speed of motor-boat is 18 km/h in still
water. It takes one hour more to 24 km
upstream than to return downstream the same
distance. Find the speed of the stream.
24. A. P. : 24, 21, 18, …… ds fdrus in fy, tk,¡] rkfd
mudk ;ksx 78 gks \ 4
How many terms of A. P. : 24, 21, 18, ……
should be taken so that their sum is 78 ?
25. fdlh cká fcUnq ls o`Ùk ij [khaph xbZ Li'kZ js[kkvksa dh yEckb;k¡
cjkcj gksrh gSa] fl) dhft,A 4
Prove that the length of tangents drawn from an
external point to a circle are equal.
26. fcUnq (−4, 6)] fcUnqvksa A(−6, 10) vkSj B(3, −8) dks tksM+us
okys js[kk[k.M dks fdl vuqikr esa foHkkftr djrk gSA 4
In what ratio does the point (−4, 6) divides the
line segment joining the points A(−6, 10) and
B(3, −8).
27. vPNh çdkj ls QsaVh xbZ 52 iÙkksa dh ,d xM~Mh esa ls ,d iÙkk
fudkyk tkrk gSA çkf;drk Kkr dhft, fd ;g iÙkk (i) ,d
bDdk gksxk] (ii) ,d bDdk ugha gksxkA 4
4803/(Set : A)
Page 13
( 13 ) 4803/(Set : A)
One card is drawn from a well-shuffled deck of
52 cards. Calculate the probability that the card
will (i) be an ace, (ii) not be an ace.
[k.M & n
SECTION – D
28. iw.kZ oxZ cukus dh fof/k ls lehdj.k 2x 2 − 5x + 3 = 0 dks
gy dhft,A 5
Solve the equation 2x 2 − 5x + 3 = 0 by
completing the square method.
29. 4 lseh, 5 lseh vkSj 6 lseh Hkqtkvksa okys ,d f=Hkqt dh jpuk
dhft, vkSj fQj blds le:i ,d vU; f=Hkqt dh jpuk
dhft,] ftldh Hkqtk,¡ fn, gq, f=Hkqt dh laxr Hkqtkvksa dh 2
3
xquh gksaA 5
Construct a triangle whose sides are 4 cm, 5 cm
and 6 cm and construct a similar triangle whose
2
sides are th of the corresponding sides of
3
given triangle.
30. fl) dhft, % 5
sin θ + cos θ − 1 1
=
sin θ − cos θ + 1 sec θ + tan θ
4803/(Set : A) P. T. O.
One card is drawn from a well-shuffled deck of
52 cards. Calculate the probability that the card
will (i) be an ace, (ii) not be an ace.
[k.M & n
SECTION – D
28. iw.kZ oxZ cukus dh fof/k ls lehdj.k 2x 2 − 5x + 3 = 0 dks
gy dhft,A 5
Solve the equation 2x 2 − 5x + 3 = 0 by
completing the square method.
29. 4 lseh, 5 lseh vkSj 6 lseh Hkqtkvksa okys ,d f=Hkqt dh jpuk
dhft, vkSj fQj blds le:i ,d vU; f=Hkqt dh jpuk
dhft,] ftldh Hkqtk,¡ fn, gq, f=Hkqt dh laxr Hkqtkvksa dh 2
3
xquh gksaA 5
Construct a triangle whose sides are 4 cm, 5 cm
and 6 cm and construct a similar triangle whose
2
sides are th of the corresponding sides of
3
given triangle.
30. fl) dhft, % 5
sin θ + cos θ − 1 1
=
sin θ − cos θ + 1 sec θ + tan θ
4803/(Set : A) P. T. O.
Page 14
( 14 ) 4803/(Set : A)
Prove that :
sin θ + cos θ − 1 1
=
sin θ − cos θ + 1 sec θ + tan θ
vFkok
OR
1.2 eh yach ,d yM+dh Hkwfe ls 88.2 eh dh Å¡pkbZ ij ,d
{kSfrt js[kk esa gok esa mM+ jgs xqCckjs dks ns[krh gSA fdlh Hkh
{k.k yM+dh dh vk¡[k ls xqCckjs dk mUu;u dks.k 60° dk gSA
dqN le; ckn mUu;u dks.k ?kVdj 30° gks tkrk gSA bl
vUrjky ds nkSjku xqCckjs }kjk r; dh xbZ nwjh Kkr dhft,A
A 1.2 m tall girl spots a balloon moving with the
wind in a horizontal line at a height of 88.2 m
from the ground. The angle of elevation of the
balloon from the eyes of the girl at any instant is
60°. After some time, the angle of elevation
reduces to 30°. Find the distance travelled by
the balloon during the interval.
31. nks ?kuksa] ftuesa ls çR;sd dk vk;ru 64 lseh3 gS] ds layXu
Qydksa dks feykdj ,d Bksl cuk;k tkrk gSA blls çkIr ?kukHk
dk i`"Bh; {ks=Qy Kkr dhft,A 5
4803/(Set : A)
Prove that :
sin θ + cos θ − 1 1
=
sin θ − cos θ + 1 sec θ + tan θ
vFkok
OR
1.2 eh yach ,d yM+dh Hkwfe ls 88.2 eh dh Å¡pkbZ ij ,d
{kSfrt js[kk esa gok esa mM+ jgs xqCckjs dks ns[krh gSA fdlh Hkh
{k.k yM+dh dh vk¡[k ls xqCckjs dk mUu;u dks.k 60° dk gSA
dqN le; ckn mUu;u dks.k ?kVdj 30° gks tkrk gSA bl
vUrjky ds nkSjku xqCckjs }kjk r; dh xbZ nwjh Kkr dhft,A
A 1.2 m tall girl spots a balloon moving with the
wind in a horizontal line at a height of 88.2 m
from the ground. The angle of elevation of the
balloon from the eyes of the girl at any instant is
60°. After some time, the angle of elevation
reduces to 30°. Find the distance travelled by
the balloon during the interval.
31. nks ?kuksa] ftuesa ls çR;sd dk vk;ru 64 lseh3 gS] ds layXu
Qydksa dks feykdj ,d Bksl cuk;k tkrk gSA blls çkIr ?kukHk
dk i`"Bh; {ks=Qy Kkr dhft,A 5
4803/(Set : A)
Page 15
( 15 ) 4803/(Set : A)
Two cubes each of volume 64 cm3 are joined
end to end. Find the surface area of the resulting
cuboid.
32. uhps fn;k gqvk caVu ,d d{kk ds 30 fo|kfFkZ;ksa dk Hkkj n'kkZ
jgk gSA fo|kfFkZ;ksa dk ek/;d Hkkj Kkr dhft, % 5
Hkkj ¼fd0xzk0 esa½ 40-45 45-50 50-55 55-60 60-65 65-70 70-75
fo|kfFkZ;ksa dh 2 3 8 6 6 3 2
la[;k
The distribution below gives the weight of 30
students of a class. Find the median weight of
the students :
Weight (in kg) 40-45 45-50 50-55 55-60 60-65 65-70 70-75
Number of 2 3 8 6 6 3 2
Students
vFkok
OR
fdlh eksgYys ds 25 ifjokjksa dk Hkkstu ij O;; fuEufyf[kr gSA
Hkkstu ij gqvk ek/; O;; Kkr dhft, %
[kpZ ¼#0 esa½ 100-150 150-200 200-250 250-300 300-350
ifjokjksa dh la[;k 4 5 12 2 2
4803/(Set : A) P. T. O.
Two cubes each of volume 64 cm3 are joined
end to end. Find the surface area of the resulting
cuboid.
32. uhps fn;k gqvk caVu ,d d{kk ds 30 fo|kfFkZ;ksa dk Hkkj n'kkZ
jgk gSA fo|kfFkZ;ksa dk ek/;d Hkkj Kkr dhft, % 5
Hkkj ¼fd0xzk0 esa½ 40-45 45-50 50-55 55-60 60-65 65-70 70-75
fo|kfFkZ;ksa dh 2 3 8 6 6 3 2
la[;k
The distribution below gives the weight of 30
students of a class. Find the median weight of
the students :
Weight (in kg) 40-45 45-50 50-55 55-60 60-65 65-70 70-75
Number of 2 3 8 6 6 3 2
Students
vFkok
OR
fdlh eksgYys ds 25 ifjokjksa dk Hkkstu ij O;; fuEufyf[kr gSA
Hkkstu ij gqvk ek/; O;; Kkr dhft, %
[kpZ ¼#0 esa½ 100-150 150-200 200-250 250-300 300-350
ifjokjksa dh la[;k 4 5 12 2 2
4803/(Set : A) P. T. O.
Page 16
( 16 ) 4803/(Set : A)
The table below shows daily expenditure on food
of 25 households in a locality. Find the mean
daily expenditure :
Expenditure (in Rs.) 100-150 150-200 200-250 250-300 300-350
No. of households 4 5 12 2 2
4803/(Set : A)
The table below shows daily expenditure on food
of 25 households in a locality. Find the mean
daily expenditure :
Expenditure (in Rs.) 100-150 150-200 200-250 250-300 300-350
No. of households 4 5 12 2 2
4803/(Set : A)
Page 17
CLASS : 10th (Secondary) Code No. 4803
Series : Sec. M/2020
Roll No. SET : B
xf.kr
MATHEMATICS
(Academic/Open)
[ fgUnh ,oa vaxzsth ek/;e ]
[ Hindi and English Medium ]
(Only for Fresh/Re-appear Candidates)
le; % 3 ?k.Vs ] [ iw.kkZad % 80
Time allowed : 3 hours ] [ Maximum Marks : 80
• Ñi;k tk¡p dj ysa fd bl iz'u-i= esa eqfnzr i`"B 16 rFkk
iz'u 32 gSaA
Please make sure that the printed pages in this
question paper are 16 in number and it contains
32 questions.
• iz'u-i= esa nkfgus gkFk dh vksj fn;s x;s dksM uEcj rFkk lsV dks
Nk= mÙkj-iqfLrdk ds eq[;-i`"B ij fy[ksaA
The Code No. and Set on the right side of the
question paper should be written by the candidate
on the front page of the answer-book.
• Ñi;k iz'u dk mÙkj fy[kuk 'kq: djus ls igys] iz'u dk Øekad
vo'; fy[ksaA
Before beginning to answer a question, its Serial
Number must be written.
4803/(Set : B) P. T. O.
Series : Sec. M/2020
Roll No. SET : B
xf.kr
MATHEMATICS
(Academic/Open)
[ fgUnh ,oa vaxzsth ek/;e ]
[ Hindi and English Medium ]
(Only for Fresh/Re-appear Candidates)
le; % 3 ?k.Vs ] [ iw.kkZad % 80
Time allowed : 3 hours ] [ Maximum Marks : 80
• Ñi;k tk¡p dj ysa fd bl iz'u-i= esa eqfnzr i`"B 16 rFkk
iz'u 32 gSaA
Please make sure that the printed pages in this
question paper are 16 in number and it contains
32 questions.
• iz'u-i= esa nkfgus gkFk dh vksj fn;s x;s dksM uEcj rFkk lsV dks
Nk= mÙkj-iqfLrdk ds eq[;-i`"B ij fy[ksaA
The Code No. and Set on the right side of the
question paper should be written by the candidate
on the front page of the answer-book.
• Ñi;k iz'u dk mÙkj fy[kuk 'kq: djus ls igys] iz'u dk Øekad
vo'; fy[ksaA
Before beginning to answer a question, its Serial
Number must be written.
4803/(Set : B) P. T. O.
Page 18
(2) 4803/(Set : B)
• mÙkj-iqfLrdk ds chp esa [kkyh iUuk / iUus u NksMsa+A
Don’t leave blank page/pages in your answer-book.
• mÙkj-iqfLrdk ds vfrfjDr dksbZ vU; 'khV ugha feysxhA vr%
vko';drkuqlkj gh fy[ksa vkSj fy[kk mÙkj u dkVsaA
Except answer-book, no extra sheet will be given.
Write to the point and do not strike the written
answer.
• ijh{kkFkhZ viuk jksy ua0 iz'u&i= ij vo'; fy[ksaA
Candidates must write their Roll Number on the
question paper.
• d`i;k iz'uksa dk mÙkj nsus lss iwoZ ;g lqfuf'pr dj ysa fd iz'u-i=
iw.kZ o lgh gS] ijh{kk ds mijkUr bl lEcU/k esa dksbZ Hkh nkok
Lohdkj ugha fd;k tk;sxkA
Before answering the questions, ensure that you
have been supplied the correct and complete
question paper, no claim in this regard, will be
entertained after examination.
lkekU; funsZ'k %
General Instruction :
(i) lHkh iz'u vfuok;Z gSaA
All questions are compulsory.
(ii) bl iz'u-i= esa dqy 32 iz'u gSa tks fd pkj [k.Mksa v]
c] l vkSj n esa ck¡Vs x;s gSa %
This question paper consists of 32 questions
in all which are divided into four Sections :
A, B, C and D :
4803/(Set : B)
• mÙkj-iqfLrdk ds chp esa [kkyh iUuk / iUus u NksMsa+A
Don’t leave blank page/pages in your answer-book.
• mÙkj-iqfLrdk ds vfrfjDr dksbZ vU; 'khV ugha feysxhA vr%
vko';drkuqlkj gh fy[ksa vkSj fy[kk mÙkj u dkVsaA
Except answer-book, no extra sheet will be given.
Write to the point and do not strike the written
answer.
• ijh{kkFkhZ viuk jksy ua0 iz'u&i= ij vo'; fy[ksaA
Candidates must write their Roll Number on the
question paper.
• d`i;k iz'uksa dk mÙkj nsus lss iwoZ ;g lqfuf'pr dj ysa fd iz'u-i=
iw.kZ o lgh gS] ijh{kk ds mijkUr bl lEcU/k esa dksbZ Hkh nkok
Lohdkj ugha fd;k tk;sxkA
Before answering the questions, ensure that you
have been supplied the correct and complete
question paper, no claim in this regard, will be
entertained after examination.
lkekU; funsZ'k %
General Instruction :
(i) lHkh iz'u vfuok;Z gSaA
All questions are compulsory.
(ii) bl iz'u-i= esa dqy 32 iz'u gSa tks fd pkj [k.Mksa v]
c] l vkSj n esa ck¡Vs x;s gSa %
This question paper consists of 32 questions
in all which are divided into four Sections :
A, B, C and D :
4803/(Set : B)
Page 19
(3) 4803/(Set : B)
[k.M v % bl [k.M esa 1 ls 16 rd dqy 16 iz'u gSa]
izR;sd iz'u 1 vad dk gSA
Section A : There are 16 questions from 1
to 16, each of 1 mark.
[k.M c % bl [k.M esa 17 ls 21 rd dqy 5 iz'u gSa]
izR;sd iz'u 3 vad dk gSA
Section B : There are 5 questions from 17
to 21, each of 3 marks.
[k.M l % bl [k.M esa 22 ls 27 rd dqy 6 iz'u gSa]
izR;sd iz'u 4 vad dk gSA
Section C : There are 6 questions from 22
to 27, each of 4 marks.
[k.M n % bl [k.M esa 28 ls 32 rd dqy 5 iz'u gSa]
izR;sd iz'u 5 vad dk gSA
Section D : There are 5 questions from 28
to 32, each of 5 marks.
(iii) [k.M n esa nks iz'uksa esa vkUrfjd fodYi fn;s x;s gSaA
mlesa ls ,d iz'u dks pquuk gSA
Section D contains two questions where
internal choice have been provided. You
have to choose one of them.
4803/(Set : B) P. T. O.
[k.M v % bl [k.M esa 1 ls 16 rd dqy 16 iz'u gSa]
izR;sd iz'u 1 vad dk gSA
Section A : There are 16 questions from 1
to 16, each of 1 mark.
[k.M c % bl [k.M esa 17 ls 21 rd dqy 5 iz'u gSa]
izR;sd iz'u 3 vad dk gSA
Section B : There are 5 questions from 17
to 21, each of 3 marks.
[k.M l % bl [k.M esa 22 ls 27 rd dqy 6 iz'u gSa]
izR;sd iz'u 4 vad dk gSA
Section C : There are 6 questions from 22
to 27, each of 4 marks.
[k.M n % bl [k.M esa 28 ls 32 rd dqy 5 iz'u gSa]
izR;sd iz'u 5 vad dk gSA
Section D : There are 5 questions from 28
to 32, each of 5 marks.
(iii) [k.M n esa nks iz'uksa esa vkUrfjd fodYi fn;s x;s gSaA
mlesa ls ,d iz'u dks pquuk gSA
Section D contains two questions where
internal choice have been provided. You
have to choose one of them.
4803/(Set : B) P. T. O.
Page 20
(4) 4803/(Set : B)
[k.M & v
SECTION – A
p
1. 0.104 dks ds :i eas O;Dr dhft,A 1
q
p
Express 0.104 in the form .
q
2. 4x 2 − 4x + 1 ds 'kwU;d gSa % 1
1 1
(A) − ,−
2 2
1 1
(B) ,
2 2
1
(C) 1,
4
1
(D) − , 1
4
The zeroes of 4x 2 − 4x + 1 are :
1 1
(A) − ,−
2 2
1 1
(B) ,
2 2
1
(C) 1,
4
1
(D) − , 1
4
4803/(Set : B)
[k.M & v
SECTION – A
p
1. 0.104 dks ds :i eas O;Dr dhft,A 1
q
p
Express 0.104 in the form .
q
2. 4x 2 − 4x + 1 ds 'kwU;d gSa % 1
1 1
(A) − ,−
2 2
1 1
(B) ,
2 2
1
(C) 1,
4
1
(D) − , 1
4
The zeroes of 4x 2 − 4x + 1 are :
1 1
(A) − ,−
2 2
1 1
(B) ,
2 2
1
(C) 1,
4
1
(D) − , 1
4
4803/(Set : B)
Page 21
(5) 4803/(Set : B)
x y
3. x − y = 3, + = 6 dks gy dhft,A 1
3 2
Solve :
x y
x − y = 3, + =6
3 2
4. dkSu&lh ,d Js.kh A. P. gS \ 1
(A) 1, 2, 4, 8, …….
(B) 5, 8, 12, 15, ……
(C) 3, 6, 9, 12, ……
(D) buesa ls dksbZ ugha
Which one is an A. P. series ?
(A) 1, 2, 4, 8, …….
(B) 5, 8, 12, 15, ……
(C) 3, 6, 9, 12, ……
(D) None of these
5. 7, 10, 13, 16, …… A. P. dk 12ok¡ in Kkr dhft,A 1
Find the 12th term of A. P. 7, 10, 13, 16, …… .
6. dks"Bd esa fn, 'kCnksa esa ls lgh 'kCnksa dk iz;ksx djrs gq,] fjDr
LFkku dks Hkfj, % 1
lHkh oxZ ---------- gksrs gSaA ¼le:i] lokZaxle½
4803/(Set : B) P. T. O.
x y
3. x − y = 3, + = 6 dks gy dhft,A 1
3 2
Solve :
x y
x − y = 3, + =6
3 2
4. dkSu&lh ,d Js.kh A. P. gS \ 1
(A) 1, 2, 4, 8, …….
(B) 5, 8, 12, 15, ……
(C) 3, 6, 9, 12, ……
(D) buesa ls dksbZ ugha
Which one is an A. P. series ?
(A) 1, 2, 4, 8, …….
(B) 5, 8, 12, 15, ……
(C) 3, 6, 9, 12, ……
(D) None of these
5. 7, 10, 13, 16, …… A. P. dk 12ok¡ in Kkr dhft,A 1
Find the 12th term of A. P. 7, 10, 13, 16, …… .
6. dks"Bd esa fn, 'kCnksa esa ls lgh 'kCnksa dk iz;ksx djrs gq,] fjDr
LFkku dks Hkfj, % 1
lHkh oxZ ---------- gksrs gSaA ¼le:i] lokZaxle½
4803/(Set : B) P. T. O.
Page 22
(6) 4803/(Set : B)
Fill in the blank using the correct word given in
bracket :
All squares are ………… . (similar, congruent)
7. nks le:i f=Hkqtksa dh Hkqtkvksa dk vuqikr 3 : 5 gS] rks muds
{ks=Qyksa dk vuqikr gS % 1
(A) 5:3 (B) 9 : 25
(C) 3 : 5 (D) buesa ls dksbZ ugha
Sides of two similar triangles are in the ratio 3 : 5
areas of their triangles are in the ratio :
(A) 5:3 (B) 9 : 25
(C) 3 : 5 (D) None of these
8. ;fn DE || BC vkSj AD : BD = 2 : 3, rks {ks=Qy (ΔADE) %
{ks=Qy (ΔABC) gS % 1
(A) 2:5
(B) 3:5
(C) 4 : 25
(D) 2 : 3
4803/(Set : B)
Fill in the blank using the correct word given in
bracket :
All squares are ………… . (similar, congruent)
7. nks le:i f=Hkqtksa dh Hkqtkvksa dk vuqikr 3 : 5 gS] rks muds
{ks=Qyksa dk vuqikr gS % 1
(A) 5:3 (B) 9 : 25
(C) 3 : 5 (D) buesa ls dksbZ ugha
Sides of two similar triangles are in the ratio 3 : 5
areas of their triangles are in the ratio :
(A) 5:3 (B) 9 : 25
(C) 3 : 5 (D) None of these
8. ;fn DE || BC vkSj AD : BD = 2 : 3, rks {ks=Qy (ΔADE) %
{ks=Qy (ΔABC) gS % 1
(A) 2:5
(B) 3:5
(C) 4 : 25
(D) 2 : 3
4803/(Set : B)
Page 23
(7) 4803/(Set : B)
If DE || BC and AD : BD = 2 : 3, then area (ΔADE)
% area (ΔABC) is :
(A) 2:5
(B) 3:5
(C) 4 : 25
(D) 2 : 3
9. ,d fcUnq ls ,d o`Ùk ij Li'kZ js[kk dh yEckbZ 4 lseh vkSj
fcUnq dh o`Ùk ds dsUæ ls nwjh 5 lseh gSA o`Ùk dh f=T;k Kkr
dhft,A 1
The length of tangent from a point which is at a
distance of 5 cm from the centre of circle is
4 cm. Find the radius of circle.
10. (−5, 7) vkSj (−1, 3) fcUnqvksa ds chp dh nwjh Kkr dhft,A 1
Find the distance between the points (−5, 7) and
(−1, 3).
11. ;fn ,d js[kk[k.M dk ,d fljk ewy fcUnq gS ftldk e/; fcUnq
(1, 0) gS] nwljs fljs dk funsZ'kkad Kkr dhft,A 1
If origin is at one end of a line segment whose
mid point is (1, 0), find the coordinates of other
end of segment.
4803/(Set : B) P. T. O.
If DE || BC and AD : BD = 2 : 3, then area (ΔADE)
% area (ΔABC) is :
(A) 2:5
(B) 3:5
(C) 4 : 25
(D) 2 : 3
9. ,d fcUnq ls ,d o`Ùk ij Li'kZ js[kk dh yEckbZ 4 lseh vkSj
fcUnq dh o`Ùk ds dsUæ ls nwjh 5 lseh gSA o`Ùk dh f=T;k Kkr
dhft,A 1
The length of tangent from a point which is at a
distance of 5 cm from the centre of circle is
4 cm. Find the radius of circle.
10. (−5, 7) vkSj (−1, 3) fcUnqvksa ds chp dh nwjh Kkr dhft,A 1
Find the distance between the points (−5, 7) and
(−1, 3).
11. ;fn ,d js[kk[k.M dk ,d fljk ewy fcUnq gS ftldk e/; fcUnq
(1, 0) gS] nwljs fljs dk funsZ'kkad Kkr dhft,A 1
If origin is at one end of a line segment whose
mid point is (1, 0), find the coordinates of other
end of segment.
4803/(Set : B) P. T. O.
Page 24
(8) 4803/(Set : B)
tan 26 o
12. dk eku Kkr dhft,A 1
cot 64 o
tan 26 o
Find the value of .
cot 64 o
13. ;fn sin A = 3 , rks tan A gS % 1
4
4 3
(A) (B)
3 7
4
(C) (D) buesa ls dksbZ ugha
7
3
If sin A = , then tan A is :
4
4 3
(A) (B)
3 7
4
(C) (D) None of these
7
14. 6 lseh f=T;k okys ,d o`Ùk ds f=T;k[k.M dk {ks=Qy Kkr
dhft, ftldk dks.k 60° gSA 1
Find the area of a sector of a circle with radius
6 cm, if angle of the sector is 60°.
4803/(Set : B)
tan 26 o
12. dk eku Kkr dhft,A 1
cot 64 o
tan 26 o
Find the value of .
cot 64 o
13. ;fn sin A = 3 , rks tan A gS % 1
4
4 3
(A) (B)
3 7
4
(C) (D) buesa ls dksbZ ugha
7
3
If sin A = , then tan A is :
4
4 3
(A) (B)
3 7
4
(C) (D) None of these
7
14. 6 lseh f=T;k okys ,d o`Ùk ds f=T;k[k.M dk {ks=Qy Kkr
dhft, ftldk dks.k 60° gSA 1
Find the area of a sector of a circle with radius
6 cm, if angle of the sector is 60°.
4803/(Set : B)
Page 25
(9) 4803/(Set : B)
15. yEco`Ùkh; csyu ds vk/kkj dk O;kl 2r gS rFkk mldh Å¡pkbZ h
gS] lEiw.kZ i`"Bh; {ks=Qy gS % 1
(A) 2πrh
(B) 2πr (r + h)
(C) πr 2h
(D) buesa ls dksbZ ugha
The diameter of the base of right circular
cylinder is 2r and its height is h. The total
surface area is :
(A) 2πrh
(B) 2πr (r + h)
(C) πr 2h
(D) None of these
16. ,d FkSys esa 3 uhyh xsan] 2 lQsn xsan vkSj 4 yky xsan gSaA ;fn
,d xsan FkSys ls ;kn`fPNd fudkyh tkrh gSa] rks blds uhys gksus
dh çkf;drk D;k gksxh \ 1
A bag contains 3 blue balls, 2 white balls and 4
red balls. If one ball is taken out at random from
the bag. What is the probability that it will be
Blue ?
4803/(Set : B) P. T. O.
15. yEco`Ùkh; csyu ds vk/kkj dk O;kl 2r gS rFkk mldh Å¡pkbZ h
gS] lEiw.kZ i`"Bh; {ks=Qy gS % 1
(A) 2πrh
(B) 2πr (r + h)
(C) πr 2h
(D) buesa ls dksbZ ugha
The diameter of the base of right circular
cylinder is 2r and its height is h. The total
surface area is :
(A) 2πrh
(B) 2πr (r + h)
(C) πr 2h
(D) None of these
16. ,d FkSys esa 3 uhyh xsan] 2 lQsn xsan vkSj 4 yky xsan gSaA ;fn
,d xsan FkSys ls ;kn`fPNd fudkyh tkrh gSa] rks blds uhys gksus
dh çkf;drk D;k gksxh \ 1
A bag contains 3 blue balls, 2 white balls and 4
red balls. If one ball is taken out at random from
the bag. What is the probability that it will be
Blue ?
4803/(Set : B) P. T. O.
Page 26
( 10 ) 4803/(Set : B)
[k.M & c
SECTION – B
17. fl) dhft, fd 3 ,d vifjes; la[;k gSA 3
Prove that 3 is an irrational number.
18. cgqin p ( x ) = 3x 2 − x 3 − 3x + 5 dks cgqin
2
q (x ) = x − 1 − x ds }kjk Hkkx dhft,A HkkxQy vkSj 'ks"kQy
Kkr dhft,A 3
Divide the polynomial p ( x ) = 3x 2 − x 3 − 3x + 5
by the polynomial q (x ) = x − 1 − x 2 . Find the
quotient and remainder.
19. CM vkSj RN Øe'k% ΔABC vkSj ΔPQR dh ekf/;dk,¡ gSa ;fn
ΔABC ~ ΔPQR gSa] rks fl) dhft, fd % 3
ΔAMC ~ ΔPNR
CM and RN are respectively the medians of
ΔABC and ΔPQR. If ΔABC ~ ΔPQR, prove that :
ΔAMC ~ ΔPNR
20. fl) dhft, % 3
cot A − cos A cosec A − 1
=
cot A + cos A cosec A + 1
4803/(Set : B)
[k.M & c
SECTION – B
17. fl) dhft, fd 3 ,d vifjes; la[;k gSA 3
Prove that 3 is an irrational number.
18. cgqin p ( x ) = 3x 2 − x 3 − 3x + 5 dks cgqin
2
q (x ) = x − 1 − x ds }kjk Hkkx dhft,A HkkxQy vkSj 'ks"kQy
Kkr dhft,A 3
Divide the polynomial p ( x ) = 3x 2 − x 3 − 3x + 5
by the polynomial q (x ) = x − 1 − x 2 . Find the
quotient and remainder.
19. CM vkSj RN Øe'k% ΔABC vkSj ΔPQR dh ekf/;dk,¡ gSa ;fn
ΔABC ~ ΔPQR gSa] rks fl) dhft, fd % 3
ΔAMC ~ ΔPNR
CM and RN are respectively the medians of
ΔABC and ΔPQR. If ΔABC ~ ΔPQR, prove that :
ΔAMC ~ ΔPNR
20. fl) dhft, % 3
cot A − cos A cosec A − 1
=
cot A + cos A cosec A + 1
4803/(Set : B)
Page 27
( 11 ) 4803/(Set : B)
Prove that :
cot A − cos A cosec A − 1
=
cot A + cos A cosec A + 1
21. o`Ùk dk {ks=Qy D;k gS] ftldh ifjf/k 11 lseh Hkqtk okys oxZ ds
ifjeki ds cjkcj gS \ 3
What is the area of the circle, the circumference
of which is equal to the perimeter of a square of
side 11 cm ?
[k.M & l
SECTION – C
2 3 5 4
22. + = 13 vkSj − = −2 dks gy dhft,A 4
x y x y
Solve :
2 3 5 4
+ = 13 and − = −2
x y x y
23. ,d jsyxkM+h ,d leku pky ls 360 fdeh dh nwjh r; djrh
gSA ;fn ;g pky 5 fdeh/?k.Vk vf/kd gksrh] rks og mlh ;k=k
esa 1 ?kaVk de le; ysrhA jsyxkM+h dh pky Kkr dhft,A 4
4803/(Set : B) P. T. O.
Prove that :
cot A − cos A cosec A − 1
=
cot A + cos A cosec A + 1
21. o`Ùk dk {ks=Qy D;k gS] ftldh ifjf/k 11 lseh Hkqtk okys oxZ ds
ifjeki ds cjkcj gS \ 3
What is the area of the circle, the circumference
of which is equal to the perimeter of a square of
side 11 cm ?
[k.M & l
SECTION – C
2 3 5 4
22. + = 13 vkSj − = −2 dks gy dhft,A 4
x y x y
Solve :
2 3 5 4
+ = 13 and − = −2
x y x y
23. ,d jsyxkM+h ,d leku pky ls 360 fdeh dh nwjh r; djrh
gSA ;fn ;g pky 5 fdeh/?k.Vk vf/kd gksrh] rks og mlh ;k=k
esa 1 ?kaVk de le; ysrhA jsyxkM+h dh pky Kkr dhft,A 4
4803/(Set : B) P. T. O.
Page 28
( 12 ) 4803/(Set : B)
A train travels 360 km at a uniform speed. If the
speed had been 5 km/h more, it would have
taken 1 hour less for the same journey. Find the
speed of the train.
24. A. P. : 9, 17, 25, …… ds fdrus in fy, tk,¡] rkfd mudk
;ksx 636 gks \ 4
How many terms of A. P. : 9, 17, 25, …… should
be taken so that their sum is 636 ?
25. fdlh cká fcUnq ls o`Ùk ij [khaph xbZ Li'kZ js[kkvksa dh yEckb;k¡
cjkcj gksrh gSa] fl) dhft,A 4
Prove that the length of tangents drawn from an
external point to a circle are equal.
26. ml fcUnq ds funsZ'kkad Kkr dhft, tks fcUnqvksa (4, −3) vkSj
(8, 5) dks tksM+us okys js[kk[k.M dks vkarfjd :i ls 3 : 1 ds
vuqikr esa foHkkftr djrk gSA 4
Find the coordinates of the point which divide
the line segment joining the points (4, −3) and
(8, 5) in a ratio 3 : 1 internally.
4803/(Set : B)
A train travels 360 km at a uniform speed. If the
speed had been 5 km/h more, it would have
taken 1 hour less for the same journey. Find the
speed of the train.
24. A. P. : 9, 17, 25, …… ds fdrus in fy, tk,¡] rkfd mudk
;ksx 636 gks \ 4
How many terms of A. P. : 9, 17, 25, …… should
be taken so that their sum is 636 ?
25. fdlh cká fcUnq ls o`Ùk ij [khaph xbZ Li'kZ js[kkvksa dh yEckb;k¡
cjkcj gksrh gSa] fl) dhft,A 4
Prove that the length of tangents drawn from an
external point to a circle are equal.
26. ml fcUnq ds funsZ'kkad Kkr dhft, tks fcUnqvksa (4, −3) vkSj
(8, 5) dks tksM+us okys js[kk[k.M dks vkarfjd :i ls 3 : 1 ds
vuqikr esa foHkkftr djrk gSA 4
Find the coordinates of the point which divide
the line segment joining the points (4, −3) and
(8, 5) in a ratio 3 : 1 internally.
4803/(Set : B)
Page 29
( 13 ) 4803/(Set : B)
27. ,d cDls esa 4 uhys] 3 lQsn vkSj 2 yky daps (marbles)
gSaA ;fn bl cDls esa ls ,d dapk ;kn`PN;k fudkyk tkrk gS] rks
bldh D;k çkf;drk gS fd ;g dapk (i) lQsn gS (ii) uhyk gS
(iii) yky gSA 4
A box contains 4 blue, 3 white and 2 red
marbles. If a marble is drawn at random from
the box, what is the probability that it will be
(i) White (ii) Blue (iii) Red.
[k.M & n
SECTION – D
28. iw.kZ oxZ cukus dh fof/k ls lehdj.k 5x 2 − 6x − 2 = 0 dks
gy dhft,A 5
Solve the equation 5 x 2 − 6x − 2 = 0 by
completing the square method.
29. 5 lseh, 6 lseh vkSj 7 lseh Hkqtkvksa okys ,d f=Hkqt dh jpuk
dhft, vkSj blds le:i ,d vU; f=Hkqt dh jpuk dhft,
ftldh Hkqtk,¡ fn, gq, f=Hkqt dh laxr Hkqtkvksa dh 7 xquh gksaA
5
5
Construct a triangle whose sides are 5 cm, 6 cm
and 7 cm and construct a similar triangle whose
7
sides are th of the corresponding sides of
5
given triangle.
4803/(Set : B) P. T. O.
27. ,d cDls esa 4 uhys] 3 lQsn vkSj 2 yky daps (marbles)
gSaA ;fn bl cDls esa ls ,d dapk ;kn`PN;k fudkyk tkrk gS] rks
bldh D;k çkf;drk gS fd ;g dapk (i) lQsn gS (ii) uhyk gS
(iii) yky gSA 4
A box contains 4 blue, 3 white and 2 red
marbles. If a marble is drawn at random from
the box, what is the probability that it will be
(i) White (ii) Blue (iii) Red.
[k.M & n
SECTION – D
28. iw.kZ oxZ cukus dh fof/k ls lehdj.k 5x 2 − 6x − 2 = 0 dks
gy dhft,A 5
Solve the equation 5 x 2 − 6x − 2 = 0 by
completing the square method.
29. 5 lseh, 6 lseh vkSj 7 lseh Hkqtkvksa okys ,d f=Hkqt dh jpuk
dhft, vkSj blds le:i ,d vU; f=Hkqt dh jpuk dhft,
ftldh Hkqtk,¡ fn, gq, f=Hkqt dh laxr Hkqtkvksa dh 7 xquh gksaA
5
5
Construct a triangle whose sides are 5 cm, 6 cm
and 7 cm and construct a similar triangle whose
7
sides are th of the corresponding sides of
5
given triangle.
4803/(Set : B) P. T. O.
Page 30
( 14 ) 4803/(Set : B)
30. fl) dhft, % 5
cos A − sin A + 1
= cos ec A + cot A
cos A + sin A − 1
Prove that :
cos A − sin A + 1
= cos ec A + cot A
cos A + sin A − 1
vFkok
OR
,d unh ds iqy ds ,d fcUnq ls unh ds lEeq[k fdukjksa ds
voueu dks.k Øe'k% 30° vkSj 45° gSA ;fn iqy fdukjksa ls 3
ehVj dh Å¡pkbZ ij gks] rks unh dh pkSM+kbZ Kkr dhft,A
From a point on a bridge across a river, the
angle of depression of the banks on opposite
sides of the river are 30° and 45° respectively. If
the bridge is at a height of 3 m from the banks,
find the width of the river.
31. dksbZ crZu ,d [kks[kys v/kZxksys ds vkdkj dk gS ftlds Åij
,d [kks[kyk csyu v/;kjksfir gSA v/kZxksys dk O;kl 14 lseh gS
vkSj bl crZu dh dqy Å¡pkbZ 13 lseh gSA bl crZu dk
vkUrfjd i`"Bh; {ks=Qy Kkr dhft,A 5
4803/(Set : B)
30. fl) dhft, % 5
cos A − sin A + 1
= cos ec A + cot A
cos A + sin A − 1
Prove that :
cos A − sin A + 1
= cos ec A + cot A
cos A + sin A − 1
vFkok
OR
,d unh ds iqy ds ,d fcUnq ls unh ds lEeq[k fdukjksa ds
voueu dks.k Øe'k% 30° vkSj 45° gSA ;fn iqy fdukjksa ls 3
ehVj dh Å¡pkbZ ij gks] rks unh dh pkSM+kbZ Kkr dhft,A
From a point on a bridge across a river, the
angle of depression of the banks on opposite
sides of the river are 30° and 45° respectively. If
the bridge is at a height of 3 m from the banks,
find the width of the river.
31. dksbZ crZu ,d [kks[kys v/kZxksys ds vkdkj dk gS ftlds Åij
,d [kks[kyk csyu v/;kjksfir gSA v/kZxksys dk O;kl 14 lseh gS
vkSj bl crZu dh dqy Å¡pkbZ 13 lseh gSA bl crZu dk
vkUrfjd i`"Bh; {ks=Qy Kkr dhft,A 5
4803/(Set : B)
Page 31
( 15 ) 4803/(Set : B)
A vessel is in the form of a hollow hemisphere
mounted by a hollow cylinder. The diameter of
the hemisphere is 14 cm and total height of the
vessel is 13 cm. Find the inner surface area of
the vessel.
32. fuEufyf[kr lkj.kh esa xzkeh.k {ks= ds fo|ky;ksa esa efgyk f'k{kdksa
ds çfr'kr caVu dks n'kkZrh gSA efgyk f'k{kdksa dk ek/; çfr'kr
Kkr dhft, % 5
efgyk f'k{kdksa dk 15-25 25-35 35-45 45-55 55-65 65-75 75-85
çfr'kr
{ks=ksas dh la[;k 6 11 7 4 4 2 1
The table below gives the percentage distribution
of female teachers in the schools of rural areas.
Find the mean percentage of female teachers :
Percentage of 15-25 25-35 35-45 45-55 55-65 65-75 75-85
female teachers
Number of 6 11 7 4 4 2 1
areas
4803/(Set : B) P. T. O.
A vessel is in the form of a hollow hemisphere
mounted by a hollow cylinder. The diameter of
the hemisphere is 14 cm and total height of the
vessel is 13 cm. Find the inner surface area of
the vessel.
32. fuEufyf[kr lkj.kh esa xzkeh.k {ks= ds fo|ky;ksa esa efgyk f'k{kdksa
ds çfr'kr caVu dks n'kkZrh gSA efgyk f'k{kdksa dk ek/; çfr'kr
Kkr dhft, % 5
efgyk f'k{kdksa dk 15-25 25-35 35-45 45-55 55-65 65-75 75-85
çfr'kr
{ks=ksas dh la[;k 6 11 7 4 4 2 1
The table below gives the percentage distribution
of female teachers in the schools of rural areas.
Find the mean percentage of female teachers :
Percentage of 15-25 25-35 35-45 45-55 55-65 65-75 75-85
female teachers
Number of 6 11 7 4 4 2 1
areas
4803/(Set : B) P. T. O.
Page 32
( 16 ) 4803/(Set : B)
vFkok
OR
fuEufyf[kr ckjackjrk caVu fdlh eksgYys ds fctyh dh ekfld
[kir n'kkZrk gSA bl caVu dk ek/;d Kkr dhft, %
ekfld [kir 65-85 85-105 105-125 125-145 145-165 165-185
¼bdkb;ksa esa½
miHkksDrkvksa 4 5 13 20 14 4
dh la[;k
The following distribution gives the monthly
consumption of consumers of a locality. Find the
median of the distribution :
Monthly 65-85 85-105 105-125 125-145 145-165 165-185
Consumption
(in Units)
Number of 4 5 13 20 14 4
Consumers
4803/(Set : B)
vFkok
OR
fuEufyf[kr ckjackjrk caVu fdlh eksgYys ds fctyh dh ekfld
[kir n'kkZrk gSA bl caVu dk ek/;d Kkr dhft, %
ekfld [kir 65-85 85-105 105-125 125-145 145-165 165-185
¼bdkb;ksa esa½
miHkksDrkvksa 4 5 13 20 14 4
dh la[;k
The following distribution gives the monthly
consumption of consumers of a locality. Find the
median of the distribution :
Monthly 65-85 85-105 105-125 125-145 145-165 165-185
Consumption
(in Units)
Number of 4 5 13 20 14 4
Consumers
4803/(Set : B)
Page 33
CLASS : 10th (Secondary) Code No. 4803
Series : Sec. M/2020
Roll No. SET : C
xf.kr
MATHEMATICS
(Academic/Open)
[ fgUnh ,oa vaxzsth ek/;e ]
[ Hindi and English Medium ]
(Only for Fresh/Re-appear Candidates)
le; % 3 ?k.Vs ] [ iw.kkZad % 80
Time allowed : 3 hours ] [ Maximum Marks : 80
• Ñi;k tk¡p dj ysa fd bl iz'u-i= esa eqfnzr i`"B 16 rFkk
iz'u 32 gSaA
Please make sure that the printed pages in this
question paper are 16 in number and it contains
32 questions.
• iz'u-i= esa nkfgus gkFk dh vksj fn;s x;s dksM uEcj rFkk lsV dks
Nk= mÙkj-iqfLrdk ds eq[;-i`"B ij fy[ksaA
The Code No. and Set on the right side of the
question paper should be written by the candidate
on the front page of the answer-book.
• Ñi;k iz'u dk mÙkj fy[kuk 'kq: djus ls igys] iz'u dk Øekad
vo'; fy[ksaA
Before beginning to answer a question, its Serial
Number must be written.
4803/(Set : C) P. T. O.
Series : Sec. M/2020
Roll No. SET : C
xf.kr
MATHEMATICS
(Academic/Open)
[ fgUnh ,oa vaxzsth ek/;e ]
[ Hindi and English Medium ]
(Only for Fresh/Re-appear Candidates)
le; % 3 ?k.Vs ] [ iw.kkZad % 80
Time allowed : 3 hours ] [ Maximum Marks : 80
• Ñi;k tk¡p dj ysa fd bl iz'u-i= esa eqfnzr i`"B 16 rFkk
iz'u 32 gSaA
Please make sure that the printed pages in this
question paper are 16 in number and it contains
32 questions.
• iz'u-i= esa nkfgus gkFk dh vksj fn;s x;s dksM uEcj rFkk lsV dks
Nk= mÙkj-iqfLrdk ds eq[;-i`"B ij fy[ksaA
The Code No. and Set on the right side of the
question paper should be written by the candidate
on the front page of the answer-book.
• Ñi;k iz'u dk mÙkj fy[kuk 'kq: djus ls igys] iz'u dk Øekad
vo'; fy[ksaA
Before beginning to answer a question, its Serial
Number must be written.
4803/(Set : C) P. T. O.
Page 34
(2) 4803/(Set : C)
• mÙkj-iqfLrdk ds chp esa [kkyh iUuk / iUus u NksMsa+A
Don’t leave blank page/pages in your answer-book.
• mÙkj-iqfLrdk ds vfrfjDr dksbZ vU; 'khV ugha feysxhA vr%
vko';drkuqlkj gh fy[ksa vkSj fy[kk mÙkj u dkVsaA
Except answer-book, no extra sheet will be given.
Write to the point and do not strike the written
answer.
• ijh{kkFkhZ viuk jksy ua0 iz'u&i= ij vo'; fy[ksaA
Candidates must write their Roll Number on the
question paper.
• d`i;k iz'uksa dk mÙkj nsus lss iwoZ ;g lqfuf'pr dj ysa fd iz'u-i=
iw.kZ o lgh gS] ijh{kk ds mijkUr bl lEcU/k esa dksbZ Hkh nkok
Lohdkj ugha fd;k tk;sxkA
Before answering the questions, ensure that you
have been supplied the correct and complete
question paper, no claim in this regard, will be
entertained after examination.
lkekU; funsZ'k %
General Instruction :
(i) lHkh iz'u vfuok;Z gSaA
All questions are compulsory.
(ii) bl iz'u-i= esa dqy 32 iz'u gSa tks fd pkj [k.Mksa v]
c] l vkSj n esa ck¡Vs x;s gSa %
This question paper consists of 32 questions
in all which are divided into four Sections :
A, B, C and D :
4803/(Set : C)
• mÙkj-iqfLrdk ds chp esa [kkyh iUuk / iUus u NksMsa+A
Don’t leave blank page/pages in your answer-book.
• mÙkj-iqfLrdk ds vfrfjDr dksbZ vU; 'khV ugha feysxhA vr%
vko';drkuqlkj gh fy[ksa vkSj fy[kk mÙkj u dkVsaA
Except answer-book, no extra sheet will be given.
Write to the point and do not strike the written
answer.
• ijh{kkFkhZ viuk jksy ua0 iz'u&i= ij vo'; fy[ksaA
Candidates must write their Roll Number on the
question paper.
• d`i;k iz'uksa dk mÙkj nsus lss iwoZ ;g lqfuf'pr dj ysa fd iz'u-i=
iw.kZ o lgh gS] ijh{kk ds mijkUr bl lEcU/k esa dksbZ Hkh nkok
Lohdkj ugha fd;k tk;sxkA
Before answering the questions, ensure that you
have been supplied the correct and complete
question paper, no claim in this regard, will be
entertained after examination.
lkekU; funsZ'k %
General Instruction :
(i) lHkh iz'u vfuok;Z gSaA
All questions are compulsory.
(ii) bl iz'u-i= esa dqy 32 iz'u gSa tks fd pkj [k.Mksa v]
c] l vkSj n esa ck¡Vs x;s gSa %
This question paper consists of 32 questions
in all which are divided into four Sections :
A, B, C and D :
4803/(Set : C)
Page 35
(3) 4803/(Set : C)
[k.M v % bl [k.M esa 1 ls 16 rd dqy 16 iz'u gSa]
izR;sd iz'u 1 vad dk gSA
Section A : There are 16 questions from 1
to 16, each of 1 mark.
[k.M c % bl [k.M esa 17 ls 21 rd dqy 5 iz'u gSa]
izR;sd iz'u 3 vad dk gSA
Section B : There are 5 questions from 17
to 21, each of 3 marks.
[k.M l % bl [k.M esa 22 ls 27 rd dqy 6 iz'u gSa]
izR;sd iz'u 4 vad dk gSA
Section C : There are 6 questions from 22
to 27, each of 4 marks.
[k.M n % bl [k.M esa 28 ls 32 rd dqy 5 iz'u gSa]
izR;sd iz'u 5 vad dk gSA
Section D : There are 5 questions from 28
to 32, each of 5 marks.
(iii) [k.M n esa nks iz'uksa esa vkUrfjd fodYi fn;s x;s gSaA
mlesa ls ,d iz'u dks pquuk gSA
Section D contains two questions where
internal choice have been provided. You
have to choose one of them.
4803/(Set : C) P. T. O.
[k.M v % bl [k.M esa 1 ls 16 rd dqy 16 iz'u gSa]
izR;sd iz'u 1 vad dk gSA
Section A : There are 16 questions from 1
to 16, each of 1 mark.
[k.M c % bl [k.M esa 17 ls 21 rd dqy 5 iz'u gSa]
izR;sd iz'u 3 vad dk gSA
Section B : There are 5 questions from 17
to 21, each of 3 marks.
[k.M l % bl [k.M esa 22 ls 27 rd dqy 6 iz'u gSa]
izR;sd iz'u 4 vad dk gSA
Section C : There are 6 questions from 22
to 27, each of 4 marks.
[k.M n % bl [k.M esa 28 ls 32 rd dqy 5 iz'u gSa]
izR;sd iz'u 5 vad dk gSA
Section D : There are 5 questions from 28
to 32, each of 5 marks.
(iii) [k.M n esa nks iz'uksa esa vkUrfjd fodYi fn;s x;s gSaA
mlesa ls ,d iz'u dks pquuk gSA
Section D contains two questions where
internal choice have been provided. You
have to choose one of them.
4803/(Set : C) P. T. O.
Page 36
(4) 4803/(Set : C)
[k.M & v
SECTION – A
p
1. 0.0875 dks ds :i eas O;Dr dhft,A 1
q
p
Express 0.0875 in the form .
q
2. 3x 2 − x − 4 ds 'kwU;d gSa % 1
4
(A) − 1, −
3
4
(B) 1, −
3
4
(C) − 1,
3
4
(D) 1,
3
The zeroes of 3x 2 − x − 4 are :
4
(A) − 1, −
3
4
(B) 1, −
3
4
(C) − 1,
3
4
(D) 1,
3
4803/(Set : C)
[k.M & v
SECTION – A
p
1. 0.0875 dks ds :i eas O;Dr dhft,A 1
q
p
Express 0.0875 in the form .
q
2. 3x 2 − x − 4 ds 'kwU;d gSa % 1
4
(A) − 1, −
3
4
(B) 1, −
3
4
(C) − 1,
3
4
(D) 1,
3
The zeroes of 3x 2 − x − 4 are :
4
(A) − 1, −
3
4
(B) 1, −
3
4
(C) − 1,
3
4
(D) 1,
3
4803/(Set : C)
Page 37
(5) 4803/(Set : C)
3. x + y = 5 vkSj 2x − 3y = 4 dks gy dhft,A 1
Solve :
x + y = 5 and 2x − 3y = 4
4. dkSu&lh ,d Js.kh A. P. gS \ 1
(A) 1, 3, 9, 27, …….
(B) a, 2a, 3a, 4a, ……
(C) a, a 2 , a 3 , a 4 , ……
(D) 12 , 22 , 32 , 42 , …...
Which one is an A. P. series ?
(A) 1, 3, 9, 27, …….
(B) a, 2a, 3a, 4a, ……
(C) a, a 2 , a 3 , a 4 , ……
(D) 12 , 22 , 32 , 42 , …...
5. 10, 7, 4, …… A. P. dk 30ok¡ in Kkr dhft,A 1
Find the 30th term of A. P. 10, 7, 4, …… .
6. dks"Bd esa fn, 'kCnksa esa ls lgh 'kCnksa dk iz;ksx djrs gq,] fjDr
LFkku dks Hkfj, % 1
lHkh ---------- f=Hkqt le:i gksrs gSaA ¼lef}ckgq] leckgq½
4803/(Set : C) P. T. O.
3. x + y = 5 vkSj 2x − 3y = 4 dks gy dhft,A 1
Solve :
x + y = 5 and 2x − 3y = 4
4. dkSu&lh ,d Js.kh A. P. gS \ 1
(A) 1, 3, 9, 27, …….
(B) a, 2a, 3a, 4a, ……
(C) a, a 2 , a 3 , a 4 , ……
(D) 12 , 22 , 32 , 42 , …...
Which one is an A. P. series ?
(A) 1, 3, 9, 27, …….
(B) a, 2a, 3a, 4a, ……
(C) a, a 2 , a 3 , a 4 , ……
(D) 12 , 22 , 32 , 42 , …...
5. 10, 7, 4, …… A. P. dk 30ok¡ in Kkr dhft,A 1
Find the 30th term of A. P. 10, 7, 4, …… .
6. dks"Bd esa fn, 'kCnksa esa ls lgh 'kCnksa dk iz;ksx djrs gq,] fjDr
LFkku dks Hkfj, % 1
lHkh ---------- f=Hkqt le:i gksrs gSaA ¼lef}ckgq] leckgq½
4803/(Set : C) P. T. O.
Page 38
(6) 4803/(Set : C)
Fill in the blank using the correct word given in
bracket :
All ………… triangles are similar.
(isosceles, equilateral)
7. nks le:i f=Hkqtksa ds {ks=Qyksa dk vuqikr 4 : 5 gS] rks mudh
laxr Hkqtkvksa dk vuqikr gS % 1
(A) 16 : 25 (B) 5:4
(C) 4:5 (D) 2 : 5
Areas of two similar triangles are in the ratio of
4 : 5, then the ratio of their corresponding sides is :
(A) 16 : 25 (B) 5:4
(C) 4:5 (D) 2 : 5
8. fp= esa] AB || QR, AB = 3 lseh, QR = 9 lseh vkSj
PR = 6 lseh, PB dh yEckbZ gS % 1
P
A B
Q R
(A) 4 lseh (B) 3 lseh
(C) 2 lseh (D) buesa ls dksbZ ugha
4803/(Set : C)
Fill in the blank using the correct word given in
bracket :
All ………… triangles are similar.
(isosceles, equilateral)
7. nks le:i f=Hkqtksa ds {ks=Qyksa dk vuqikr 4 : 5 gS] rks mudh
laxr Hkqtkvksa dk vuqikr gS % 1
(A) 16 : 25 (B) 5:4
(C) 4:5 (D) 2 : 5
Areas of two similar triangles are in the ratio of
4 : 5, then the ratio of their corresponding sides is :
(A) 16 : 25 (B) 5:4
(C) 4:5 (D) 2 : 5
8. fp= esa] AB || QR, AB = 3 lseh, QR = 9 lseh vkSj
PR = 6 lseh, PB dh yEckbZ gS % 1
P
A B
Q R
(A) 4 lseh (B) 3 lseh
(C) 2 lseh (D) buesa ls dksbZ ugha
4803/(Set : C)
Page 39
(7) 4803/(Set : C)
In figure, AB || QR, AB = 3 cm, QR = 9 cm and
PR = 6 cm, the length of PB is :
P
A B
Q R
(A) 4 cm (B) 3 cm
(C) 2 cm (D) None of these
9. P fcUnq ls] o`Ùk ij Li'kZ js[kk dh yEckbZ 12 lseh gS vkSj dsUæ
ls P dh nwjh 13 lseh gSA o`Ùk dh f=T;k Kkr dhft,A 1
From a point P, the length of tangent to a circle
is 12 cm and distance of P from centre is 13 cm.
Find the radius of circle.
10. (−1, 5) vkSj (7, 3) fcUnqvksa ds chp dh nwjh Kkr dhft,A 1
Find the distance between the points (−1, 5) and
(7, 3).
11. A ds funsZ'kkad Kkr dhft,] tgk¡ AB o`Ùk dk O;kl gS ftldk
dsUæ (2, −3) gS vkSj B(1, 4) gSA 1
Find the coordinates of A, where AB is diameter
of circle whose centre is (2, −3) and B is (1, 4).
4803/(Set : C) P. T. O.
In figure, AB || QR, AB = 3 cm, QR = 9 cm and
PR = 6 cm, the length of PB is :
P
A B
Q R
(A) 4 cm (B) 3 cm
(C) 2 cm (D) None of these
9. P fcUnq ls] o`Ùk ij Li'kZ js[kk dh yEckbZ 12 lseh gS vkSj dsUæ
ls P dh nwjh 13 lseh gSA o`Ùk dh f=T;k Kkr dhft,A 1
From a point P, the length of tangent to a circle
is 12 cm and distance of P from centre is 13 cm.
Find the radius of circle.
10. (−1, 5) vkSj (7, 3) fcUnqvksa ds chp dh nwjh Kkr dhft,A 1
Find the distance between the points (−1, 5) and
(7, 3).
11. A ds funsZ'kkad Kkr dhft,] tgk¡ AB o`Ùk dk O;kl gS ftldk
dsUæ (2, −3) gS vkSj B(1, 4) gSA 1
Find the coordinates of A, where AB is diameter
of circle whose centre is (2, −3) and B is (1, 4).
4803/(Set : C) P. T. O.
Page 40
(8) 4803/(Set : C)
cos 37 o
12. dk eku Kkr dhft,A 1
sin 53 o
cos 37 o
Find the value of .
sin 53 o
13. ;fn cot A = 8 , rks sin A gS % 1
15
15 8
(A) (B)
17 17
15
(C) (D) buesa ls dksbZ ugha
8
8
If cot A = , then sin A is :
15
15 8
(A) (B)
17 17
15
(C) (D) None of these
8
14. o`Ùk dh ifjf/k 22 lseh gSA o`Ùk dh f=T;k Kkr dhft,A 1
Circumference of a circle is 22 cm, find the
radius of the circle.
4803/(Set : C)
cos 37 o
12. dk eku Kkr dhft,A 1
sin 53 o
cos 37 o
Find the value of .
sin 53 o
13. ;fn cot A = 8 , rks sin A gS % 1
15
15 8
(A) (B)
17 17
15
(C) (D) buesa ls dksbZ ugha
8
8
If cot A = , then sin A is :
15
15 8
(A) (B)
17 17
15
(C) (D) None of these
8
14. o`Ùk dh ifjf/k 22 lseh gSA o`Ùk dh f=T;k Kkr dhft,A 1
Circumference of a circle is 22 cm, find the
radius of the circle.
4803/(Set : C)
Page 41
(9) 4803/(Set : C)
15. yEco`Ùkh; csyu ds vk/kkj dk O;kl 2r gS rFkk mldh Å¡pkbZ h
gSA csyu dk vk;ru gS % 1
(A) 2πr (r + h)
(B) πr 2h
(C) 2πrh
(D) buesa ls dksbZ ugha
The diameter of the base of right circular
cylinder is 2r and its height is h. The volume of
cylinder is :
(A) 2πr (r + h)
(B) πr 2h
(C) 2πrh
(D) None of these
16. ,d FkSys esa 3 uhyh xsan] 2 lQsn xsan vkSj 4 yky xsan gSaA ;fn
,d xsan FkSys ls ;kn`fPNd fudkyh tkrh gS] rks blds yky gksus
dh çkf;drk D;k gksxh \ 1
A bag contains 3 blue balls, 2 white balls and 4
red balls. If one ball is taken out at random from
the bag. What is the probability that it will be
Red ?
4803/(Set : C) P. T. O.
15. yEco`Ùkh; csyu ds vk/kkj dk O;kl 2r gS rFkk mldh Å¡pkbZ h
gSA csyu dk vk;ru gS % 1
(A) 2πr (r + h)
(B) πr 2h
(C) 2πrh
(D) buesa ls dksbZ ugha
The diameter of the base of right circular
cylinder is 2r and its height is h. The volume of
cylinder is :
(A) 2πr (r + h)
(B) πr 2h
(C) 2πrh
(D) None of these
16. ,d FkSys esa 3 uhyh xsan] 2 lQsn xsan vkSj 4 yky xsan gSaA ;fn
,d xsan FkSys ls ;kn`fPNd fudkyh tkrh gS] rks blds yky gksus
dh çkf;drk D;k gksxh \ 1
A bag contains 3 blue balls, 2 white balls and 4
red balls. If one ball is taken out at random from
the bag. What is the probability that it will be
Red ?
4803/(Set : C) P. T. O.
Page 42
( 10 ) 4803/(Set : C)
[k.M & c
SECTION – B
17. fl) dhft, fd 5 ,d vifjes; la[;k gSA 3
Prove that 5 is an irrational number.
18. cgqin p ( x ) = x 3 − 3x 2 + 5 x − 3dks cgqin
2
q (x ) = x − 2 ds }kjk Hkkx dhft,A HkkxQy vkSj 'ks"kQy
Kkr dhft,A 3
3 2
Divide the polynomial p(x ) = x − 3x + 5x − 3
2
by the polynomial q (x ) = x − 2. Find the
quotient and remainder.
19. 6 eh0 yEckbZ okys ,d Å/okZ/kj LrEHk dh Hkwfe ij Nk;k dh
yEckbZ 4 eh0 gSA tcfd mlh le; ,d ehukj dh Nk;k dh
yEckbZ 28 eh0 gSA ehukj dh Å¡pkbZ Kkr dhft,A 3
A vertical pole of length 6 m casts a shadow 4 m
long on the ground and at the same time a tower
casts a shadow 28 m long. Find the height of the
tower.
20. fl) dhft, % 3
sin θ − cos θ + 1 1
=
sin θ + cos θ − 1 sec θ − tan θ
4803/(Set : C)
[k.M & c
SECTION – B
17. fl) dhft, fd 5 ,d vifjes; la[;k gSA 3
Prove that 5 is an irrational number.
18. cgqin p ( x ) = x 3 − 3x 2 + 5 x − 3dks cgqin
2
q (x ) = x − 2 ds }kjk Hkkx dhft,A HkkxQy vkSj 'ks"kQy
Kkr dhft,A 3
3 2
Divide the polynomial p(x ) = x − 3x + 5x − 3
2
by the polynomial q (x ) = x − 2. Find the
quotient and remainder.
19. 6 eh0 yEckbZ okys ,d Å/okZ/kj LrEHk dh Hkwfe ij Nk;k dh
yEckbZ 4 eh0 gSA tcfd mlh le; ,d ehukj dh Nk;k dh
yEckbZ 28 eh0 gSA ehukj dh Å¡pkbZ Kkr dhft,A 3
A vertical pole of length 6 m casts a shadow 4 m
long on the ground and at the same time a tower
casts a shadow 28 m long. Find the height of the
tower.
20. fl) dhft, % 3
sin θ − cos θ + 1 1
=
sin θ + cos θ − 1 sec θ − tan θ
4803/(Set : C)
Page 43
( 11 ) 4803/(Set : C)
Prove that :
sin θ − cos θ + 1 1
=
sin θ + cos θ − 1 sec θ − tan θ
21. v)Zo`Ùkh; vkÑfr dh ifjf/k 72 lseh gSA mldk {ks=Qy Kkr
dhft,A 3
The circumference of semi-circular piece of
design is 72 cm. Find its area.
[k.M & l
SECTION – C
1 1 1 1 13
22. + = 2 vkSj + = dks gy dhft,A 4
2x 3y 3x 2y 6
Solve :
1 1 1 1 13
+ = 2 and + =
2x 3y 3x 2y 6
23. 3 o"kZ iwoZ jgeku dh vk;q ¼o"kks± esa½ dk O;qRØe (reciprocal)
vkSj vc ls 5 o"kZ i'pkr~ vk;q ds O;qRØe dk ;ksx 1 gSA
3
mldh orZeku vk;q Kkr dhft,A 4
4803/(Set : C) P. T. O.
Prove that :
sin θ − cos θ + 1 1
=
sin θ + cos θ − 1 sec θ − tan θ
21. v)Zo`Ùkh; vkÑfr dh ifjf/k 72 lseh gSA mldk {ks=Qy Kkr
dhft,A 3
The circumference of semi-circular piece of
design is 72 cm. Find its area.
[k.M & l
SECTION – C
1 1 1 1 13
22. + = 2 vkSj + = dks gy dhft,A 4
2x 3y 3x 2y 6
Solve :
1 1 1 1 13
+ = 2 and + =
2x 3y 3x 2y 6
23. 3 o"kZ iwoZ jgeku dh vk;q ¼o"kks± esa½ dk O;qRØe (reciprocal)
vkSj vc ls 5 o"kZ i'pkr~ vk;q ds O;qRØe dk ;ksx 1 gSA
3
mldh orZeku vk;q Kkr dhft,A 4
4803/(Set : C) P. T. O.
Page 44
( 12 ) 4803/(Set : C)
The sum of the reciprocal of Rehman's age (in
years) 3 years ago and 5 years after from now is
1
. Find his present age.
3
24. ,sls çFke 40 /ku iw.kk±dksa dk ;ksx Kkr dhft, tks 6 ls foHkkT;
gSA 4
Find the sum of first 40 positive integers
divisible by 6.
25. fl) dhft, fd ,d o`Ùk dh thok ds fljksa ij [khaph x;h Li'kZ
js[kk thok ls cjkcj dks.k cukrh gSA 4
Prove that the tangents drawn at the ends of a
chord of a circle make equal angles with the
chord.
26. fcUnqvksa (−3, 10) vkSj (6, −8) dks tksM+us okys js[kk[k.M dks
fcUnq (−1, 6) fdl vuqikr esa foHkkftr djrk gS \ 4
In what ratio does the point (−1, 6) divides the
line segment joining the points (−3, 10) and
(6, −8).
4803/(Set : C)
The sum of the reciprocal of Rehman's age (in
years) 3 years ago and 5 years after from now is
1
. Find his present age.
3
24. ,sls çFke 40 /ku iw.kk±dksa dk ;ksx Kkr dhft, tks 6 ls foHkkT;
gSA 4
Find the sum of first 40 positive integers
divisible by 6.
25. fl) dhft, fd ,d o`Ùk dh thok ds fljksa ij [khaph x;h Li'kZ
js[kk thok ls cjkcj dks.k cukrh gSA 4
Prove that the tangents drawn at the ends of a
chord of a circle make equal angles with the
chord.
26. fcUnqvksa (−3, 10) vkSj (6, −8) dks tksM+us okys js[kk[k.M dks
fcUnq (−1, 6) fdl vuqikr esa foHkkftr djrk gS \ 4
In what ratio does the point (−1, 6) divides the
line segment joining the points (−3, 10) and
(6, −8).
4803/(Set : C)
Page 45
( 13 ) 4803/(Set : C)
27. ,d ikls dks ,d ckj Qsadk tkrk gSA fuEufyf[kr dks çkIr djus
dh çkf;drk Kkr dhft, (i) ,d vHkkT; la[;k (ii) 2 vkSj 6 ds
chp fLFkr dksbZ la[;k (iii) ,d fo"ke la[;kA 4
A die is thrown once. Find the probability of
getting (i) a prime number (ii) a number lying
between 2 and 6 (iii) an odd number.
[k.M & n
SECTION – D
28. iw.kZ oxZ cukdj lehdj.k 2x 2 − 7x + 3 = 0 dks gy
dhft,A 5
Solve the equation 2x 2 − 7x + 3 = 0 by
completing the square method.
29. vk/kkj 8 lseh vkSj Å¡pkbZ 4 lseh ds ,d lef}ckgq f=Hkqt dh
jpuk dhft, vkSj fQj ,d vU; f=Hkqt dh jpuk dhft,]
ftldh Hkqtk,¡ bl lef}ckgq f=Hkqt dh laxr Hkqtkvksa dh 1 1
2
xquh gksaA 5
Construct an isosceles triangle whose base is
8 cm and altitude 4 cm and then another
1
triangle whose sides are 1 times the
2
corresponding sides of the isosceles triangle.
4803/(Set : C) P. T. O.
27. ,d ikls dks ,d ckj Qsadk tkrk gSA fuEufyf[kr dks çkIr djus
dh çkf;drk Kkr dhft, (i) ,d vHkkT; la[;k (ii) 2 vkSj 6 ds
chp fLFkr dksbZ la[;k (iii) ,d fo"ke la[;kA 4
A die is thrown once. Find the probability of
getting (i) a prime number (ii) a number lying
between 2 and 6 (iii) an odd number.
[k.M & n
SECTION – D
28. iw.kZ oxZ cukdj lehdj.k 2x 2 − 7x + 3 = 0 dks gy
dhft,A 5
Solve the equation 2x 2 − 7x + 3 = 0 by
completing the square method.
29. vk/kkj 8 lseh vkSj Å¡pkbZ 4 lseh ds ,d lef}ckgq f=Hkqt dh
jpuk dhft, vkSj fQj ,d vU; f=Hkqt dh jpuk dhft,]
ftldh Hkqtk,¡ bl lef}ckgq f=Hkqt dh laxr Hkqtkvksa dh 1 1
2
xquh gksaA 5
Construct an isosceles triangle whose base is
8 cm and altitude 4 cm and then another
1
triangle whose sides are 1 times the
2
corresponding sides of the isosceles triangle.
4803/(Set : C) P. T. O.
Page 46
( 14 ) 4803/(Set : C)
30. fl) dhft, % 5
cos θ cos θ
+ = 2 sec θ
1 + sin θ 1 − sin θ
Prove that :
cos θ cos θ
+ = 2 sec θ
1 + sin θ 1 − sin θ
vFkok
OR
vk¡/kh vkus ls ,d isM+ VwV tkrk gS vkSj VwVk gqvk Hkkx bl
rjg eqM+ tkrk gS fd isM+ dk f'k[kj tehu dks Nwus yxrk gS
vkSj blls 30° dk dks.k cukrk gSA isM+ ds ikn fcUnq dh nwjh]
tgk¡ isM+ dk f'k[kj tehu dks Nwrk gS] 8 eh0 gSA isM+ dh Å¡pkbZ
Kkr dhft,A
A tree breaks due to storm and the broken part
bands so that the top of the tree touches the
ground making an angle 30° with it. The
distance between the foot of the tree to the point
where the top touches the ground is 8 m. Find
the height of the tree.
4803/(Set : C)
30. fl) dhft, % 5
cos θ cos θ
+ = 2 sec θ
1 + sin θ 1 − sin θ
Prove that :
cos θ cos θ
+ = 2 sec θ
1 + sin θ 1 − sin θ
vFkok
OR
vk¡/kh vkus ls ,d isM+ VwV tkrk gS vkSj VwVk gqvk Hkkx bl
rjg eqM+ tkrk gS fd isM+ dk f'k[kj tehu dks Nwus yxrk gS
vkSj blls 30° dk dks.k cukrk gSA isM+ ds ikn fcUnq dh nwjh]
tgk¡ isM+ dk f'k[kj tehu dks Nwrk gS] 8 eh0 gSA isM+ dh Å¡pkbZ
Kkr dhft,A
A tree breaks due to storm and the broken part
bands so that the top of the tree touches the
ground making an angle 30° with it. The
distance between the foot of the tree to the point
where the top touches the ground is 8 m. Find
the height of the tree.
4803/(Set : C)
Page 47
( 15 ) 4803/(Set : C)
31. ,d f[kykSuk f=T;k 3.5 lseh okys ,d 'kadq ds vkdkj dk gS] tks
mlh f=T;k okys ,d v)Zxksys ij v/;kjksfir gSA bl f[kykSus dh
lEiw.kZ Å¡pkbZ 15.5 lseh gSA bl f[kykSus dk lEiw.kZ i`"Bh;
{ks=Qy Kkr dhft,A 5
A toy is in the form of a cone mounted on a
hemisphere of radius 3.5 cm. The total height of
the toy is 15.5 cm. Find the total surface area of
the toy.
32. ,d VsyhQksu funsZf'kdk ls 100 dqyuke (surnames) fy,
x,A muesa ç;qDr vaxzsth o.kZekyk ds v{kjksa dh la[;k dk
fuEufyf[kr ckjackjrk caVu çkIr gqvk %
v{kjksa dh la[;k 1-4 4-7 7-10 10-13 13-16 16-19
dqyukeksa dh la[;k 6 30 40 16 4 4
dqyukeksa ds ek/;d v{kjksa dh la[;k Kkr dhft,A 5
100 surnames were picked from a telephone
directory and the frequency distribution of the
number of letters in the English alphabets in the
surnames was obtained as below :
Number of 1-4 4-7 7-10 10-13 13-16 16-19
Letters
Number of 6 30 40 16 4 4
Surnames
Determine the median number of letters in the
surnames.
4803/(Set : C) P. T. O.
31. ,d f[kykSuk f=T;k 3.5 lseh okys ,d 'kadq ds vkdkj dk gS] tks
mlh f=T;k okys ,d v)Zxksys ij v/;kjksfir gSA bl f[kykSus dh
lEiw.kZ Å¡pkbZ 15.5 lseh gSA bl f[kykSus dk lEiw.kZ i`"Bh;
{ks=Qy Kkr dhft,A 5
A toy is in the form of a cone mounted on a
hemisphere of radius 3.5 cm. The total height of
the toy is 15.5 cm. Find the total surface area of
the toy.
32. ,d VsyhQksu funsZf'kdk ls 100 dqyuke (surnames) fy,
x,A muesa ç;qDr vaxzsth o.kZekyk ds v{kjksa dh la[;k dk
fuEufyf[kr ckjackjrk caVu çkIr gqvk %
v{kjksa dh la[;k 1-4 4-7 7-10 10-13 13-16 16-19
dqyukeksa dh la[;k 6 30 40 16 4 4
dqyukeksa ds ek/;d v{kjksa dh la[;k Kkr dhft,A 5
100 surnames were picked from a telephone
directory and the frequency distribution of the
number of letters in the English alphabets in the
surnames was obtained as below :
Number of 1-4 4-7 7-10 10-13 13-16 16-19
Letters
Number of 6 30 40 16 4 4
Surnames
Determine the median number of letters in the
surnames.
4803/(Set : C) P. T. O.
Page 48
( 16 ) 4803/(Set : C)
vFkok
OR
fuEufyf[kr vk¡dM+s 75 fctyh midj.kksa ds çsf{kr thoudky
¼?kaVksa esa½ dh lwpuk nsrs gSa %
thoudky 0-20 20-40 40-60 60-80 80-100 100-120
¼?k.Vksa esa½
ckjackjrk 10 15 12 21 8 9
midj.kksa dk ek/; thoudky Kkr dhft,A
The following data gives the information on the
life-time (in hours) of 75 electrical instruments :
Life-time (in 0-20 20-40 40-60 60-80 80-100 100-120
hours)
Frequency 10 15 12 21 8 9
Find the mean life time of the instruments.
4803/(Set : C)
vFkok
OR
fuEufyf[kr vk¡dM+s 75 fctyh midj.kksa ds çsf{kr thoudky
¼?kaVksa esa½ dh lwpuk nsrs gSa %
thoudky 0-20 20-40 40-60 60-80 80-100 100-120
¼?k.Vksa esa½
ckjackjrk 10 15 12 21 8 9
midj.kksa dk ek/; thoudky Kkr dhft,A
The following data gives the information on the
life-time (in hours) of 75 electrical instruments :
Life-time (in 0-20 20-40 40-60 60-80 80-100 100-120
hours)
Frequency 10 15 12 21 8 9
Find the mean life time of the instruments.
4803/(Set : C)
Page 49
CLASS : 10th (Secondary) Code No. 4803
Series : Sec. M/2020
Roll No. SET : D
xf.kr
MATHEMATICS
(Academic/Open)
[ fgUnh ,oa vaxzsth ek/;e ]
[ Hindi and English Medium ]
(Only for Fresh/Re-appear Candidates)
le; % 3 ?k.Vs ] [ iw.kkZad % 80
Time allowed : 3 hours ] [ Maximum Marks : 80
• Ñi;k tk¡p dj ysa fd bl iz'u-i= esa eqfnzr i`"B 16 rFkk
iz'u 32 gSaA
Please make sure that the printed pages in this
question paper are 16 in number and it contains
32 questions.
• iz'u-i= esa nkfgus gkFk dh vksj fn;s x;s dksM uEcj rFkk lsV dks
Nk= mÙkj-iqfLrdk ds eq[;-i`"B ij fy[ksaA
The Code No. and Set on the right side of the
question paper should be written by the candidate
on the front page of the answer-book.
• Ñi;k iz'u dk mÙkj fy[kuk 'kq: djus ls igys] iz'u dk Øekad
vo'; fy[ksaA
Before beginning to answer a question, its Serial
Number must be written.
4803/(Set : D) P. T. O.
Series : Sec. M/2020
Roll No. SET : D
xf.kr
MATHEMATICS
(Academic/Open)
[ fgUnh ,oa vaxzsth ek/;e ]
[ Hindi and English Medium ]
(Only for Fresh/Re-appear Candidates)
le; % 3 ?k.Vs ] [ iw.kkZad % 80
Time allowed : 3 hours ] [ Maximum Marks : 80
• Ñi;k tk¡p dj ysa fd bl iz'u-i= esa eqfnzr i`"B 16 rFkk
iz'u 32 gSaA
Please make sure that the printed pages in this
question paper are 16 in number and it contains
32 questions.
• iz'u-i= esa nkfgus gkFk dh vksj fn;s x;s dksM uEcj rFkk lsV dks
Nk= mÙkj-iqfLrdk ds eq[;-i`"B ij fy[ksaA
The Code No. and Set on the right side of the
question paper should be written by the candidate
on the front page of the answer-book.
• Ñi;k iz'u dk mÙkj fy[kuk 'kq: djus ls igys] iz'u dk Øekad
vo'; fy[ksaA
Before beginning to answer a question, its Serial
Number must be written.
4803/(Set : D) P. T. O.
Page 50
(2) 4803/(Set : D)
• mÙkj-iqfLrdk ds chp esa [kkyh iUuk / iUus u NksMsa+A
Don’t leave blank page/pages in your answer-book.
• mÙkj-iqfLrdk ds vfrfjDr dksbZ vU; 'khV ugha feysxhA vr%
vko';drkuqlkj gh fy[ksa vkSj fy[kk mÙkj u dkVsaA
Except answer-book, no extra sheet will be given.
Write to the point and do not strike the written
answer.
• ijh{kkFkhZ viuk jksy ua0 iz'u&i= ij vo'; fy[ksaA
Candidates must write their Roll Number on the
question paper.
• d`i;k iz'uksa dk mÙkj nsus lss iwoZ ;g lqfuf'pr dj ysa fd iz'u-i=
iw.kZ o lgh gS] ijh{kk ds mijkUr bl lEcU/k esa dksbZ Hkh nkok
Lohdkj ugha fd;k tk;sxkA
Before answering the questions, ensure that you
have been supplied the correct and complete
question paper, no claim in this regard, will be
entertained after examination.
lkekU; funsZ'k %
General Instruction :
(i) lHkh iz'u vfuok;Z gSaA
All questions are compulsory.
(ii) bl iz'u-i= esa dqy 32 iz'u gSa tks fd pkj [k.Mksa v]
c] l vkSj n esa ck¡Vs x;s gSa %
This question paper consists of 32 questions
in all which are divided into four Sections :
A, B, C and D :
4803/(Set : D)
• mÙkj-iqfLrdk ds chp esa [kkyh iUuk / iUus u NksMsa+A
Don’t leave blank page/pages in your answer-book.
• mÙkj-iqfLrdk ds vfrfjDr dksbZ vU; 'khV ugha feysxhA vr%
vko';drkuqlkj gh fy[ksa vkSj fy[kk mÙkj u dkVsaA
Except answer-book, no extra sheet will be given.
Write to the point and do not strike the written
answer.
• ijh{kkFkhZ viuk jksy ua0 iz'u&i= ij vo'; fy[ksaA
Candidates must write their Roll Number on the
question paper.
• d`i;k iz'uksa dk mÙkj nsus lss iwoZ ;g lqfuf'pr dj ysa fd iz'u-i=
iw.kZ o lgh gS] ijh{kk ds mijkUr bl lEcU/k esa dksbZ Hkh nkok
Lohdkj ugha fd;k tk;sxkA
Before answering the questions, ensure that you
have been supplied the correct and complete
question paper, no claim in this regard, will be
entertained after examination.
lkekU; funsZ'k %
General Instruction :
(i) lHkh iz'u vfuok;Z gSaA
All questions are compulsory.
(ii) bl iz'u-i= esa dqy 32 iz'u gSa tks fd pkj [k.Mksa v]
c] l vkSj n esa ck¡Vs x;s gSa %
This question paper consists of 32 questions
in all which are divided into four Sections :
A, B, C and D :
4803/(Set : D)
Page 51
(3) 4803/(Set : D)
[k.M v % bl [k.M esa 1 ls 16 rd dqy 16 iz'u gSa]
izR;sd iz'u 1 vad dk gSA
Section A : There are 16 questions from 1
to 16, each of 1 mark.
[k.M c % bl [k.M esa 17 ls 21 rd dqy 5 iz'u gSa]
izR;sd iz'u 3 vad dk gSA
Section B : There are 5 questions from 17
to 21, each of 3 marks.
[k.M l % bl [k.M esa 22 ls 27 rd dqy 6 iz'u gSa]
izR;sd iz'u 4 vad dk gSA
Section C : There are 6 questions from 22
to 27, each of 4 marks.
[k.M n % bl [k.M esa 28 ls 32 rd dqy 5 iz'u gSa]
izR;sd iz'u 5 vad dk gSA
Section D : There are 5 questions from 28
to 32, each of 5 marks.
(iii) [k.M n esa nks iz'uksa esa vkUrfjd fodYi fn;s x;s gSaA
mlesa ls ,d iz'u dks pquuk gSA
Section D contains two questions where
internal choice have been provided. You
have to choose one of them.
4803/(Set : D) P. T. O.
[k.M v % bl [k.M esa 1 ls 16 rd dqy 16 iz'u gSa]
izR;sd iz'u 1 vad dk gSA
Section A : There are 16 questions from 1
to 16, each of 1 mark.
[k.M c % bl [k.M esa 17 ls 21 rd dqy 5 iz'u gSa]
izR;sd iz'u 3 vad dk gSA
Section B : There are 5 questions from 17
to 21, each of 3 marks.
[k.M l % bl [k.M esa 22 ls 27 rd dqy 6 iz'u gSa]
izR;sd iz'u 4 vad dk gSA
Section C : There are 6 questions from 22
to 27, each of 4 marks.
[k.M n % bl [k.M esa 28 ls 32 rd dqy 5 iz'u gSa]
izR;sd iz'u 5 vad dk gSA
Section D : There are 5 questions from 28
to 32, each of 5 marks.
(iii) [k.M n esa nks iz'uksa esa vkUrfjd fodYi fn;s x;s gSaA
mlesa ls ,d iz'u dks pquuk gSA
Section D contains two questions where
internal choice have been provided. You
have to choose one of them.
4803/(Set : D) P. T. O.
Page 52
(4) 4803/(Set : D)
[k.M & v
SECTION – A
p
1. 0.125 dks ds :i eas O;Dr dhft,A 1
q
p
Express 0.125 in the form .
q
2. 3x 2 + 4x + 1 ds 'kwU;d gSa % 1
1
(A) − 1, −
3
1
(B) − 1,
3
1
(C) 1, −
3
1
(D) 1,
3
The zeroes of 3x 2 + 4x + 1 are :
1
(A) − 1, −
3
1
(B) − 1,
3
1
(C) 1, −
3
1
(D) 1,
3
4803/(Set : D)
[k.M & v
SECTION – A
p
1. 0.125 dks ds :i eas O;Dr dhft,A 1
q
p
Express 0.125 in the form .
q
2. 3x 2 + 4x + 1 ds 'kwU;d gSa % 1
1
(A) − 1, −
3
1
(B) − 1,
3
1
(C) 1, −
3
1
(D) 1,
3
The zeroes of 3x 2 + 4x + 1 are :
1
(A) − 1, −
3
1
(B) − 1,
3
1
(C) 1, −
3
1
(D) 1,
3
4803/(Set : D)
Page 53
(5) 4803/(Set : D)
3. 3x + 4y = 10 vkSj x − y = 1 dks gy dhft,A 1
Solve :
3x + 4y = 10 and x − y = 1
4. dkSu&lh ,d Js.kh A. P. gS \ 1
(A) −1.2, −3.2, −5.2, …….
(B) 2, 5, 7, 9, ……
(C) 1, 22 , 32 , 42 , ……
(D) buesa ls dksbZ ugha
Which one is an A. P. series ?
(A) −1.2, −3.2, −5.2, …….
(B) 2, 5, 7, 9, ……
(C) 1, 22 , 32 , 42 , ……
(D) None of these
1
5. −3, − , 2, …… A. P. dk 11ok¡ in Kkr dhft,A 1
2
1
Find the 11th term of A. P. −3, − , 2, …… .
2
6. dks"Bd esa fn, 'kCnksa esa ls lgh 'kCnksa dk iz;ksx djrs gq,] fjDr
LFkku dks Hkfj, % 1
Hkqtkvksa dh leku la[;k okys nks cgqHkqt le:i gksrs gSa] ;fn
muds laxr dks.k ---------- gksaA ¼cjkcj] lekuqikrh½
4803/(Set : D) P. T. O.
3. 3x + 4y = 10 vkSj x − y = 1 dks gy dhft,A 1
Solve :
3x + 4y = 10 and x − y = 1
4. dkSu&lh ,d Js.kh A. P. gS \ 1
(A) −1.2, −3.2, −5.2, …….
(B) 2, 5, 7, 9, ……
(C) 1, 22 , 32 , 42 , ……
(D) buesa ls dksbZ ugha
Which one is an A. P. series ?
(A) −1.2, −3.2, −5.2, …….
(B) 2, 5, 7, 9, ……
(C) 1, 22 , 32 , 42 , ……
(D) None of these
1
5. −3, − , 2, …… A. P. dk 11ok¡ in Kkr dhft,A 1
2
1
Find the 11th term of A. P. −3, − , 2, …… .
2
6. dks"Bd esa fn, 'kCnksa esa ls lgh 'kCnksa dk iz;ksx djrs gq,] fjDr
LFkku dks Hkfj, % 1
Hkqtkvksa dh leku la[;k okys nks cgqHkqt le:i gksrs gSa] ;fn
muds laxr dks.k ---------- gksaA ¼cjkcj] lekuqikrh½
4803/(Set : D) P. T. O.
Page 54
(6) 4803/(Set : D)
Fill in the blank using correct word given in
bracket :
Two polygons of the same number of sides are
similar, if their corresponding angles are
………… . (equal, proportional)
7. nks le:i f=Hkqtksa ds {ks=Qyksa dk vuqikr 7 : 3 gS] rks mudh
laxr Hkqtkvksa dk vuqikr gS % 1
(A) 7 : 3 (B) 7: 3
(C) 7 :3 (D) buesa ls dksbZ ugha
Area of two similar triangles are in the ratio of 7 : 3,
then the ratio of their corresponding sides is :
(A) 7 : 3 (B) 7: 3
(C) 7 :3 (D) None of these
8. ;fn nks le:i f=Hkqtksa dh Hkqtkvksa dk vuqikr 5 : 7 gS] rks mu
f=Hkqtksa ds {ks=Qyksa dk vuqikr gS % 1
(A) 15 : 14 (B) 25 : 49
(C) 49 : 25 (D) buesa ls dksbZ ugha
4803/(Set : D)
Fill in the blank using correct word given in
bracket :
Two polygons of the same number of sides are
similar, if their corresponding angles are
………… . (equal, proportional)
7. nks le:i f=Hkqtksa ds {ks=Qyksa dk vuqikr 7 : 3 gS] rks mudh
laxr Hkqtkvksa dk vuqikr gS % 1
(A) 7 : 3 (B) 7: 3
(C) 7 :3 (D) buesa ls dksbZ ugha
Area of two similar triangles are in the ratio of 7 : 3,
then the ratio of their corresponding sides is :
(A) 7 : 3 (B) 7: 3
(C) 7 :3 (D) None of these
8. ;fn nks le:i f=Hkqtksa dh Hkqtkvksa dk vuqikr 5 : 7 gS] rks mu
f=Hkqtksa ds {ks=Qyksa dk vuqikr gS % 1
(A) 15 : 14 (B) 25 : 49
(C) 49 : 25 (D) buesa ls dksbZ ugha
4803/(Set : D)
Page 55
(7) 4803/(Set : D)
If sides of two similar triangles are in the ratio
5 : 7, then areas of their triangles are in the
ratio :
(A) 15 : 14 (B) 25 : 49
(C) 49 : 25 (D) None of these
9. ,d fcUnq ls ,d o`Ùk ij Li'kZ js[kk dh yEckbZ Kkr dhft,
ftldh o`Ùk ds dsUæ ls nwjh 25 lseh gSA o`Ùk dh f=T;k 7 lseh
nh gqbZ gSA 1
Find the length of tangent drawn from a point
whose distance from the centre of a circle is
25 cm. Given the radius of circle is 7 cm.
10. (1, −3) vkSj (4, 1) fcUnqvksa ds chp dh nwjh Kkr dhft,A 1
Find the distance between the points (1, −3) and
(4, 1).
11. js[kk[k.M dk e/;fcUnq Kkr dhft, ftlds fljs (4, 5) vkSj
(2, –1) gSaA 1
Find the mid point of the line segment whose
end points are (4, 5) and (2, –1).
4803/(Set : D) P. T. O.
If sides of two similar triangles are in the ratio
5 : 7, then areas of their triangles are in the
ratio :
(A) 15 : 14 (B) 25 : 49
(C) 49 : 25 (D) None of these
9. ,d fcUnq ls ,d o`Ùk ij Li'kZ js[kk dh yEckbZ Kkr dhft,
ftldh o`Ùk ds dsUæ ls nwjh 25 lseh gSA o`Ùk dh f=T;k 7 lseh
nh gqbZ gSA 1
Find the length of tangent drawn from a point
whose distance from the centre of a circle is
25 cm. Given the radius of circle is 7 cm.
10. (1, −3) vkSj (4, 1) fcUnqvksa ds chp dh nwjh Kkr dhft,A 1
Find the distance between the points (1, −3) and
(4, 1).
11. js[kk[k.M dk e/;fcUnq Kkr dhft, ftlds fljs (4, 5) vkSj
(2, –1) gSaA 1
Find the mid point of the line segment whose
end points are (4, 5) and (2, –1).
4803/(Set : D) P. T. O.
Page 56
(8) 4803/(Set : D)
tan 25 o
12. dk eku Kkr dhft,A 1
cot 65 o
tan 25 o
Find the value of .
cot 65 o
13. ;fn cot A = 8 , rks sec A gS % 1
15
17 8
(A) (B)
8 17
15
(C) (D) buesa ls dksbZ ugha
17
8
If cot A = , then sec A is :
15
17 8
(A) (B)
8 17
15
(C) (D) None of these
17
14. 21 lseh f=T;k okys ,d o`Ùk ds f=T;k[k.M dk {ks=Qy Kkr
dhft,] ;fn [k.M dk dks.k 60° gSA 1
Find the area of sector of circle with radius
21 cm, if angle of the sector is 60°.
4803/(Set : D)
tan 25 o
12. dk eku Kkr dhft,A 1
cot 65 o
tan 25 o
Find the value of .
cot 65 o
13. ;fn cot A = 8 , rks sec A gS % 1
15
17 8
(A) (B)
8 17
15
(C) (D) buesa ls dksbZ ugha
17
8
If cot A = , then sec A is :
15
17 8
(A) (B)
8 17
15
(C) (D) None of these
17
14. 21 lseh f=T;k okys ,d o`Ùk ds f=T;k[k.M dk {ks=Qy Kkr
dhft,] ;fn [k.M dk dks.k 60° gSA 1
Find the area of sector of circle with radius
21 cm, if angle of the sector is 60°.
4803/(Set : D)
Page 57
(9) 4803/(Set : D)
15. yEco`Ùkh; 'kadq ds vk/kkj dk O;kl 2r gS rFkk mldh Å¡pkbZ h
gS rFkk fr;Zd Å¡pkbZ l gSA 'kadq dk vk;ru gS % 1
(A) πrl
(B) πr 2h
1 2
(C) πr h
3
(D) buesa ls dksbZ ugha
The diameter of the base of right circular cone is
2r and its height h and slant height l. The
volume of the cone is :
(A) πrl
(B) πr 2h
1 2
(C) πr h
3
(D) None of these
16. ,d FkSys esa 3 yky xsan vkSj 5 dkyh xsan gSaA ;fn ,d xsan FkSys
ls ;kn`fPNd fudkyh tkrh gS] rks blds yky gksus dh çkf;drk
D;k gksxh \ 1
A bag contains 3 red and 5 black balls. If one
ball is taken out at random from the bag. What
is the probability that it will be Red ?
4803/(Set : D) P. T. O.
15. yEco`Ùkh; 'kadq ds vk/kkj dk O;kl 2r gS rFkk mldh Å¡pkbZ h
gS rFkk fr;Zd Å¡pkbZ l gSA 'kadq dk vk;ru gS % 1
(A) πrl
(B) πr 2h
1 2
(C) πr h
3
(D) buesa ls dksbZ ugha
The diameter of the base of right circular cone is
2r and its height h and slant height l. The
volume of the cone is :
(A) πrl
(B) πr 2h
1 2
(C) πr h
3
(D) None of these
16. ,d FkSys esa 3 yky xsan vkSj 5 dkyh xsan gSaA ;fn ,d xsan FkSys
ls ;kn`fPNd fudkyh tkrh gS] rks blds yky gksus dh çkf;drk
D;k gksxh \ 1
A bag contains 3 red and 5 black balls. If one
ball is taken out at random from the bag. What
is the probability that it will be Red ?
4803/(Set : D) P. T. O.
Page 58
( 10 ) 4803/(Set : D)
[k.M & c
SECTION – B
17. fl) dhft, fd 3 2 ,d vifjes; la[;k gSA 3
Prove that 3 2 is an irrational number.
18. cgqin p ( x ) = x 4 − 3x 2 + 4x + 5 dks cgqin
2
q (x ) = x − x +1 ds }kjk Hkkx dhft,A HkkxQy vkSj
'ks"kQy Kkr dhft,A 3
4 2
Divide the polynomial p(x ) = x − 3x + 4x + 5
2
by the polynomial q (x ) = x − x + 1 . Find the
quotient and remainder.
19. ,d lh<+h fdlh nhokj ij bl çdkj fVdh gqbZ gS fd bldk
fupyk fljk nhokj ls 2.5 eh0 dh nwjh ij gS rFkk bldk Åijh
fljk Hkwfe ls 6 eh0 dh Å¡pkbZ ij cuh ,d f[kM+dh rd
igq¡prk gSA lh<+h dh yEckbZ Kkr dhft,A 3
A ladder is placed against a wall such that its
foot is at a distance of 2.5 m from the wall and
its top reaches a window 6 m above the ground.
Find the length of the ladder.
20. fl) dhft, % 3
tan θ cot θ
+ = 1 + sec θ cosec θ
1 − cot θ 1 − tan θ
4803/(Set : D)
[k.M & c
SECTION – B
17. fl) dhft, fd 3 2 ,d vifjes; la[;k gSA 3
Prove that 3 2 is an irrational number.
18. cgqin p ( x ) = x 4 − 3x 2 + 4x + 5 dks cgqin
2
q (x ) = x − x +1 ds }kjk Hkkx dhft,A HkkxQy vkSj
'ks"kQy Kkr dhft,A 3
4 2
Divide the polynomial p(x ) = x − 3x + 4x + 5
2
by the polynomial q (x ) = x − x + 1 . Find the
quotient and remainder.
19. ,d lh<+h fdlh nhokj ij bl çdkj fVdh gqbZ gS fd bldk
fupyk fljk nhokj ls 2.5 eh0 dh nwjh ij gS rFkk bldk Åijh
fljk Hkwfe ls 6 eh0 dh Å¡pkbZ ij cuh ,d f[kM+dh rd
igq¡prk gSA lh<+h dh yEckbZ Kkr dhft,A 3
A ladder is placed against a wall such that its
foot is at a distance of 2.5 m from the wall and
its top reaches a window 6 m above the ground.
Find the length of the ladder.
20. fl) dhft, % 3
tan θ cot θ
+ = 1 + sec θ cosec θ
1 − cot θ 1 − tan θ
4803/(Set : D)
Page 59
( 11 ) 4803/(Set : D)
Prove that :
tan θ cot θ
+ = 1 + sec θ cosec θ
1 − cot θ 1 − tan θ
21. ,d o`Ùk dh ifjf/k O;kl ls 33.6 lseh vf/kd gSA o`Ùk dk
{ks=Qy Kkr dhft,A 3
The circumference of a circle exceeds the
diameter by 33.6 cm. Find the area of the circle.
[k.M & l
SECTION – C
22. gy dhft, % 4
5 1 6 3
+ = 2, − =1
x −1 y − 2 x −1 y − 2
Solve :
5 1 6 3
+ = 2, − =1
x −1 y − 2 x −1 y − 2
23. ,d eksVj cksV] ftldh fLFkj ty esa pky 15 fdeh/?k.Vk gS]
30 fdeh /kkjk ds vuqdwy tkus vkSj okilh djus esa 4 ?kaVs 30
feuV yxrs gSaA ty dh pky Kkr dhft,A 4
4803/(Set : D) P. T. O.
Prove that :
tan θ cot θ
+ = 1 + sec θ cosec θ
1 − cot θ 1 − tan θ
21. ,d o`Ùk dh ifjf/k O;kl ls 33.6 lseh vf/kd gSA o`Ùk dk
{ks=Qy Kkr dhft,A 3
The circumference of a circle exceeds the
diameter by 33.6 cm. Find the area of the circle.
[k.M & l
SECTION – C
22. gy dhft, % 4
5 1 6 3
+ = 2, − =1
x −1 y − 2 x −1 y − 2
Solve :
5 1 6 3
+ = 2, − =1
x −1 y − 2 x −1 y − 2
23. ,d eksVj cksV] ftldh fLFkj ty esa pky 15 fdeh/?k.Vk gS]
30 fdeh /kkjk ds vuqdwy tkus vkSj okilh djus esa 4 ?kaVs 30
feuV yxrs gSaA ty dh pky Kkr dhft,A 4
4803/(Set : D) P. T. O.
Page 60
( 12 ) 4803/(Set : D)
A motor boat whose speed is 15 km/h in still
water goes 30 km downstream and comes back
in a total of 4 hours 30 minutes. Determine the
speed of water.
24. Js.kh 1, 4, 7, 10, …… ds fdrus in fy, tk,¡] rkfd mudk
;ksx 176 gks \ 4
How many terms of sequence 1, 4, 7, 10, ……
should be taken so that their sum is 176 ?
25. cká fcUnq ls o`Ùk ij [khaph xbZ Li'kZ js[kkvksa dh yEckb;k¡
cjkcj gksrh gS] fl) dhft,A 4
Prove that the length of tangents drawn from an
external point to a circle are equal.
26. og vuqikr Kkr dhft, ftlesa fcUnqvksa A(1, −5) vkSj
B(−4, 5) dks feykus okyk js[kk[k.M x-v{k ls foHkkftr gksrk
gSA bl foHkktu fcUnq ds funsZ'kkad Hkh Kkr dhft,A 4
Find the ratio in which the line segment joining
the points A(1, −5) and B(−4, 5) is divided by the
x-axis. Also find the coordinates of the point of
division.
4803/(Set : D)
A motor boat whose speed is 15 km/h in still
water goes 30 km downstream and comes back
in a total of 4 hours 30 minutes. Determine the
speed of water.
24. Js.kh 1, 4, 7, 10, …… ds fdrus in fy, tk,¡] rkfd mudk
;ksx 176 gks \ 4
How many terms of sequence 1, 4, 7, 10, ……
should be taken so that their sum is 176 ?
25. cká fcUnq ls o`Ùk ij [khaph xbZ Li'kZ js[kkvksa dh yEckb;k¡
cjkcj gksrh gS] fl) dhft,A 4
Prove that the length of tangents drawn from an
external point to a circle are equal.
26. og vuqikr Kkr dhft, ftlesa fcUnqvksa A(1, −5) vkSj
B(−4, 5) dks feykus okyk js[kk[k.M x-v{k ls foHkkftr gksrk
gSA bl foHkktu fcUnq ds funsZ'kkad Hkh Kkr dhft,A 4
Find the ratio in which the line segment joining
the points A(1, −5) and B(−4, 5) is divided by the
x-axis. Also find the coordinates of the point of
division.
4803/(Set : D)
Page 61
( 13 ) 4803/(Set : D)
27. 52 iÙkksa dh vPNh çdkj ls QsaVh xbZ ,d xM~Mh esa ls ,d iÙkk
fudkyk tkrk gSA çkIr gksus dh çkf;drk Kkr dhft, (i) yky
jax dk ckn'kkg] (ii) ,d Qsl dkMZA 4
One card is drawn from a well-shuffled deck of
52 cards. Find the probability of getting (i) a king
of red colour (ii) a face card.
[k.M & n
SECTION – D
28. iw.kZ oxZ cukus dh fof/k ls lehdj.k 2x 2 + x − 4 = 0 dks
gy dhft,A 5
Solve the equation 2x 2 + x − 4 = 0 by completing
the square method.
29. ,d f=Hkqt ABC dh jpuk dhft, ftldh Hkqtk,¡ BC = 6 lseh,
AB = 5 lseh vkSj ∠ABC = 60° gSaA ,d le:i f=Hkqt dh
jpuk dhft, ftldh Hkqtk,¡ fn, gq, f=Hkqt dh laxr Hkqtkvksa
dh 3 xquh gksaA 5
4
Construct a triangle ABC whose sides are
BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then
3
construct a similar triangle whose sides are th
4
of corresponding sides of given triangle.
4803/(Set : D) P. T. O.
27. 52 iÙkksa dh vPNh çdkj ls QsaVh xbZ ,d xM~Mh esa ls ,d iÙkk
fudkyk tkrk gSA çkIr gksus dh çkf;drk Kkr dhft, (i) yky
jax dk ckn'kkg] (ii) ,d Qsl dkMZA 4
One card is drawn from a well-shuffled deck of
52 cards. Find the probability of getting (i) a king
of red colour (ii) a face card.
[k.M & n
SECTION – D
28. iw.kZ oxZ cukus dh fof/k ls lehdj.k 2x 2 + x − 4 = 0 dks
gy dhft,A 5
Solve the equation 2x 2 + x − 4 = 0 by completing
the square method.
29. ,d f=Hkqt ABC dh jpuk dhft, ftldh Hkqtk,¡ BC = 6 lseh,
AB = 5 lseh vkSj ∠ABC = 60° gSaA ,d le:i f=Hkqt dh
jpuk dhft, ftldh Hkqtk,¡ fn, gq, f=Hkqt dh laxr Hkqtkvksa
dh 3 xquh gksaA 5
4
Construct a triangle ABC whose sides are
BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then
3
construct a similar triangle whose sides are th
4
of corresponding sides of given triangle.
4803/(Set : D) P. T. O.
Page 62
( 14 ) 4803/(Set : D)
30. fl) dhft, % 5
1 + sin A
= sec A + tan A
1 − sin A
Prove that :
1 + sin A
= sec A + tan A
1 − sin A
vFkok
OR
1.5 eh yack ,d vkneh ,d fpeuh ls 28.5 eh0 dh nwjh ij
gSA mldh vk¡[kksa ls fpeuh ds f'k[kj dk mUu;u dks.k 45° gSA
fpeuh dh Å¡pkbZ crkb,A
A man 1.5 m tall is 28.5 m away from a
chimney. The angle of elevation of the top of the
chimney from his eyes is 45°. What is the height
of chimney ?
31. Hkqtk 7 lseh okys ,d ?kukdkj CykWd ds Åij ,d v/kZxksyk j[kk
gqvk gSA v/kZxksys dk vf/kdre O;kl D;k gks ldrk gS \ bl
çdkj cus Bksl dk i`"Bh; {ks=Qy Kkr dhft,A 5
A cubical block of side 7 cm is surmounted by a
hemisphere. What is the greatest diameter of the
hemisphere can have ? Find the total surface
area of the solid.
4803/(Set : D)
30. fl) dhft, % 5
1 + sin A
= sec A + tan A
1 − sin A
Prove that :
1 + sin A
= sec A + tan A
1 − sin A
vFkok
OR
1.5 eh yack ,d vkneh ,d fpeuh ls 28.5 eh0 dh nwjh ij
gSA mldh vk¡[kksa ls fpeuh ds f'k[kj dk mUu;u dks.k 45° gSA
fpeuh dh Å¡pkbZ crkb,A
A man 1.5 m tall is 28.5 m away from a
chimney. The angle of elevation of the top of the
chimney from his eyes is 45°. What is the height
of chimney ?
31. Hkqtk 7 lseh okys ,d ?kukdkj CykWd ds Åij ,d v/kZxksyk j[kk
gqvk gSA v/kZxksys dk vf/kdre O;kl D;k gks ldrk gS \ bl
çdkj cus Bksl dk i`"Bh; {ks=Qy Kkr dhft,A 5
A cubical block of side 7 cm is surmounted by a
hemisphere. What is the greatest diameter of the
hemisphere can have ? Find the total surface
area of the solid.
4803/(Set : D)
Page 63
( 15 ) 4803/(Set : D)
32. fuEufyf[kr lkj.kh esa ,d Ldwy ds fo|kfFkZ;ksa dk nSfud tsc
[kpZ fn;k x;k gS % 5
nSfud tsc [kpZ 11-13 13-15 15-17 17-19 19-21 21-23 23-25
¼#0 esa½
fo|kfFkZ;ksa dh 7 6 9 13 20 5 4
la[;k
bl Ldwy ds cPpksa dk vkSlr tsc [kpZ Kkr dhft,A
The following distribution shows the daily pocket
money of children of a school :
Daily Pocket 11-13 13-15 15-17 17-19 19-21 21-23 23-25
money (Rs.)
Number of 7 6 9 13 20 5 4
Children
Find the mean of daily pocket money of children.
vFkok
OR
,d ikS/ks dh 40 ifÙk;ksa dh yEckb;k¡ fuEu lkj.kh esa feeh esa nh
xbZ gSa %
yEckb;k¡ ¼feeh esa½ 18-27 27-36 36-45 45-54 54-63 63-72
ifÙk;ksa dh la[;k 3 5 10 13 5 4
ifÙk;ksa dh ek/;d yEckbZ Kkr dhft,A
4803/(Set : D) P. T. O.
32. fuEufyf[kr lkj.kh esa ,d Ldwy ds fo|kfFkZ;ksa dk nSfud tsc
[kpZ fn;k x;k gS % 5
nSfud tsc [kpZ 11-13 13-15 15-17 17-19 19-21 21-23 23-25
¼#0 esa½
fo|kfFkZ;ksa dh 7 6 9 13 20 5 4
la[;k
bl Ldwy ds cPpksa dk vkSlr tsc [kpZ Kkr dhft,A
The following distribution shows the daily pocket
money of children of a school :
Daily Pocket 11-13 13-15 15-17 17-19 19-21 21-23 23-25
money (Rs.)
Number of 7 6 9 13 20 5 4
Children
Find the mean of daily pocket money of children.
vFkok
OR
,d ikS/ks dh 40 ifÙk;ksa dh yEckb;k¡ fuEu lkj.kh esa feeh esa nh
xbZ gSa %
yEckb;k¡ ¼feeh esa½ 18-27 27-36 36-45 45-54 54-63 63-72
ifÙk;ksa dh la[;k 3 5 10 13 5 4
ifÙk;ksa dh ek/;d yEckbZ Kkr dhft,A
4803/(Set : D) P. T. O.
Page 64
( 16 ) 4803/(Set : D)
The length of 40 leaves of a plant are measured
in mm and are given in the following table :
Length (mm) 18-27 27-36 36-45 45-54 54-63 63-72
Numbers of Leaves 3 5 10 13 5 4
Find the median length of the leaves.
4803/(Set : D)
The length of 40 leaves of a plant are measured
in mm and are given in the following table :
Length (mm) 18-27 27-36 36-45 45-54 54-63 63-72
Numbers of Leaves 3 5 10 13 5 4
Find the median length of the leaves.
4803/(Set : D)
Document Details
| Board / Org | Haryana Board |
| Exam | Class 10 |
| Type | Question Paper |
| Pages | 64 |
| Updated | 22 Jul 2026 |