CBSE Class 10 Question Paper 2022 Maths Standard (Solved)

Series PPQQA/1 SET~1
àíZ-nÌ H$moS>
Q.P. Code 30/1/1
amob Z§. narjmWu àíZ-nÌ H$moS> >H$mo CÎma-nwpñVH$m Ho$
Roll No. _wI-n¥ð >na Adí` {bIo§ &
Candidates must write the Q.P. Code
on the title page of the answer-book.

NOTE
(I) (I) Please check that this question paper
11 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) (III) Please check that this question paper
14 contains 14 questions.
(IV) (IV) Please write down the serial
number of the question in the
answer-book before attempting it.
(V) 15 (V) 15 minute time has been allotted to
read this question paper. The
10.15 question paper will be distributed
10.15 10.30 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

.30/1/1 1 P.T.O.

:

:

(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. (H$) g_m§Va lo : 30, 24, 18, ..... Ho$ àW_ 30 nXm| H$m `moJ\$b kmV H$s{OE & 2
AWdm
(I) EH$ g_ _| `{X Sn = n (4n + 1) h¡, Vmo kmV H$s{OE & 2

2. 10·5 go_r {ÌÁ`m dmbo YmVw Ho$ EH$ R>mog Jmobo H$mo {nKbmH$a, 3·5 go_r {ÌÁ`m Am¡a 3 go_r
D±$MmB© Ho$ Hw$N> N>moQ>o-N>moQ>o e§Hw$ ~ZmE OmVo h¢ & Bg àH$ma ~ZmE JE e§Hw$Am| H$s g§»`m kmV
H$s{OE & 2

3. (H$) m Ho$ {H$g _mZ Ho$ {bE {ÛKmV g_rH$aU
(m 1) x2 + 2 (m 1) x + 1 = 0
Ho$ Xmo ~am~a Am¡a dmñV{dH$ _yb hm|Jo ? 2
AWdm
(I) {ZåZ {ÛKmV g_rH$aU H$mo, x Ho$ {bE hb H$s{OE : 2
3 x2 + 10x + 7 3 = 0

4. {ZåZ ~ma§~maVm ~§Q>Z H$m ~hþbH$ kmV H$s{OE : 2
10 20 20 30 30 40 40 50 50 60
15 10 12 17 4

.30/1/1 2

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. (a) Find the sum of first 30 terms of AP : 30, 24, 18, ..... . 2
OR
(b) In an AP if Sn = n (4n + 1), then find the AP. 2

2. A solid metallic sphere of radius 10·5 cm is melted and recast into a
number of smaller cones, each of radius 3·5 cm and height 3 cm. Find the
number of cones so formed. 2

3. (a) Find the value of m for which the quadratic equation
(m 1) x2 + 2 (m 1) x + 1 = 0
has two real and equal roots. 2
OR
(b) Solve the following quadratic equation for x : 2
3 x2 + 10x + 7 3 = 0

4. Find the mode of the following frequency distribution : 2
Class 10 20 20 30 30 40 40 50 50 60
Frequency 15 10 12 17 4

.30/1/1 3 P.T.O.

5. aohmZ H$s 5 df© nyd© Am`w (dfm] _|) VWm A~ go 7 df© CnamÝV CgH$s Am`w H$m JwUZ\$b
CgH$s dV©_mZ Am`w Ho$ Xmo JwZo go EH$ A{YH$ h¡ & CgH$s dV©_mZ Am`w kmV H$s{OE & 2

6. Xmo g§H$| Ðr` d¥Îmm| H$s {ÌÁ`mE± 4 go_r VWm 3 go_r h¢ &
kmV H$s{OE Omo N>moQ>o d¥Îm H$mo ñne© H$aVr hmo & 2

IÊS> I
7 10 3

7. x Ho$ {H$g _mZ Ho$ {bE {ZåZ{b{IV ~ma§~maVm ~§Q>Z H$m _mÜ`H$ 34·5 h¡ ? 3

0 10 3

10 20 5

20 30 11

30 40 10

40 50 x

50 60 3

60 70 2

8. 3 7 go_r H$s Xÿar
na Xmo q~Xþ P Am¡a Q br{OE & BZ XmoZm| q~XþAm| P Am¡a Q go d¥Îm na ñne©-aoImAm| H$s
aMZm H$s{OE & 3

9. (H$) EH$ _rZma Ho$ nmX-q~Xþ go EH$ ^dZ Ho$ {eIa H$m CÞ`Z H$moU 30 h¡ Am¡a ^dZ Ho$
nmX-q~Xþ go _rZma Ho$ {eIa H$m CÞ`Z H$moU 60 h¡ & `{X _rZma 50 _r. D±$Mr h¡,
Vmo ^dZ H$s D±$MmB© kmV H$s{OE & 3
AWdm
(I) EH$ ZXr Ho$ nwb Ho$ EH$ q~Xþ go ZXr Ho$ gå_wI {H$Zmam| Ho$ AdZ_Z
30 Am¡a 45 h¢ & `{X nwb {H$Zmam| go 3
kmV H$s{OE & 3

.30/1/1 4

5. is age 7 years
from now, is one more than twice his present age. Find his present age. 2

6. Two concentric circles are of radii 4 cm and 3 cm. Find the length of the
chord of the larger circle which touches the smaller circle. 2

SECTION B

Question numbers 7 to 10 carry 3 marks each.

7. For what value of x, is the median of the following frequency distribution
34·5 ? 3

Class Frequency

0 10 3

10 20 5

20 30 11

30 40 10

40 50 x

50 60 3

60 70 2

8. Draw a circle of radius 3 cm. Take two points P and Q on one of its
extended diameter each at a distance of 7 cm from its centre. Construct
tangents to the circle from these two points P and Q. 3

9. (a) The angle of elevation of the top of a building from the foot of the
tower is 30 and the angle of elevation of the top of the tower from
the foot of the building is 60 . If the tower is 50 m high, then find
the height of the building. 3
OR
(b) From a point on a bridge across a river, the angles 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,
then find the width of the river. 3

.30/1/1 5 P.T.O.

10. {H$gr H$ånZr Ho$ 30 H$_©Mm[a`m| Ho$ ImZo Ho$ X¡{ZH$ IM© {ZåZ h¢ :

100 120 8

120 140 3

140 160 8

160 180 6

180 200 5

H$_©Mm[a`m| H$m _mÜ` X¡{ZH$ IM© kmV H$s{OE & 3

IÊS> J

11 14 4

11. (H$) D±$MmB© 30 go_r VWm {ÌÁ`m 7 go_r dmbo EH$ R>mog ~obZ _| go 24 go_r D±$MmB© VWm
Bg H$mQ>H$a {ZH$mb {b`m OmVm h¡ & eof ~Mo
R>mog H$m gånyU© n¥ð>r` joÌ\$b kmV H$s{OE & 4
AWdm
(I) 8 _r. 6 _r. Jhar EH$ Zha _| nmZr 12 {H$_r/K§Q>o H$s Mmb go ~h ahm
h¡ & 1 K§Q>o _| `h Zha {H$VZo joÌ\$b H$s qgMmB© H$a nmEJr, `{X qgMmB© Ho$ {bE
0·05 _r. Aàdmhr nmZr H$s Amdí`H$Vm hmoVr h¡ ? 4

.30/1/1 6

10. Following is the daily expenditure on lunch by 30 employees of a
company :

Daily Expenditure Number of
(in Rupees) Employees
100 120 8

120 140 3

140 160 8

160 180 6

180 200 5

Find the mean daily expenditure of the employees. 3

SECTION C

Question numbers 11 to 14 carry 4 marks each.

11. (a) From a solid cylinder of height 30 cm and radius 7 cm, a conical
cavity of height 24 cm and same radius is hollowed out. Find the
total surface area of the remaining solid. 4

OR
(b) Water in a canal, 8 m wide and 6 m deep, is flowing with a speed of
12 km/hour. How much area will it irrigate in one hour, if 0·05 m
of standing water is required ? 4

.30/1/1 7 P.T.O.

12. AmH¥${V 1 _|, {Ì^wO ABC Xem©`m J`m h¡ {Og_| B = 90 h¡ & AB H$mo ì`mg boVo hþE
EH$ d¥Îm ItMm J`m h¡, Omo AC H$mo q~Xþ P na à{VÀN>Xo H$aVm h¡ & {gÕ H$s{OE {H$ q~Xþ P
na ItMr JB© ñne© aoIm BC H$mo g_{Û^m{OV H$aVr h¡ & 4

1

àH$aU AÜ``Z 1

13. J{UV _| g§~§Ym| H$mo H$B© àH$ma go ì`º$ {H$`m Om gH$Vm h¡ & _m{Mg H$s Vr{b`m| go ~ZmE
JE n¡Q>Z© aoIr` g§~§Ym| na AmYm[aV h¢ & AbJ-AbJ AmH¥${V`m| _| à`wº$ _m{Mg H$s
Vr{b`m| H$s g§»`m kmV H$aZo Ho$ {bE {^Þ `w{º$`m± à`wº$ H$s Om gH$Vr h¢ &
EH$ Eogm hr n¡Q>Z© ZrMo Xem©`m J`m h¡ & n¡Q>Z© H$mo Ü`mZnyd©H$ Xo{IE VWm g_m§Va H$m
Cn`moJ H$aVo hþE {ZåZ àíZm| Ho$ CÎma Xr{OE :

1 2 3

(H$) AmH¥${V`m| _| à`wº$ {Ì^wOm| H$s g§»`m H$mo
H$m ndm± nX ^r {b{IE & 2

(I) {H$g AmH¥${V _| 61 _m{Mg H$s Vr{b`m| H$m Cn`moJ hþAm h¡ ? 2

.30/1/1 8

12. In Figure 1, a triangle ABC with B = 90 is shown. Taking AB as
diameter, a circle has been drawn intersecting AC at point P. Prove that
the tangent drawn at point P bisects BC. 4

Figure 1

Case Study 1

13. In Mathematics, relations can be expressed in various ways. The
matchstick patterns are based on linear relations. Different strategies
can be used to calculate the number of matchsticks used in different
figures.

One such pattern is shown below. Observe the pattern and answer the
following questions using Arithmetic Progression :

Figure 1 Figure 2 Figure 3

(a) Write the AP for the number of triangles used in the figures. Also,
write the nth term of this AP. 2

(b) Which figure has 61 matchsticks ? 2

.30/1/1 9 P.T.O.

àH$aU AÜ``Z 2

14. J ga Prb amOñWmZ Ho$ O¡gb_oa {Obo _| pñWV h¡ & BgH$mo O¡gb_oa Ho$ amOm Zo ~Zdm`m
Wm VWm 14 Xþ~mam ~Zdm`m & Bg Prb _| ~hþV-gr N>V[a`m±
~Zr hþB© h¢ & CZ_| go EH$ N>Var H$mo ZrMo Xem©`m J`m h¡ :

B

A

C

{MÌ H$mo Ü`mZnyd©H$ Xo{IE & nmZr H$s gVh go h _r. D±$MmB© na pñWV q~Xþ A go N>Var Ho$
erf© (q~Xþ B) H$m CÞ`Z H$moU 45 h¡ VWm Bgr q~Xþ go nmZr _| N>Var Ho$ à{V{~å~
(q~Xþ C) H$m AdZ_Z H$moU 60 h¡ & nmZr H$s gVh Ho$ D$na N>Var H$s D±$MmB© `{X 10 _r.
hmo, Vmo
(H$) Cn`w©º$ gyMZm Ho$ AmYma na AÀN>r àH$ma go A§{H$V EH$ AmH¥${V It{ME & 2

(I) nmZr H$s gVh go q~Xþ A H$s D±$MmB© (h) kmV H$s{OE &
( 3 = 1·73 H$m à`moJ H$s{OE) 2

.30/1/1 10

Case Study 2

14. Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was
built by the King of Jaisalmer and rebuilt by Gadsi Singh in 14th century.
The lake has many Chhatris. One of them is shown below :

B

A

C

Observe the picture. From a point A h m above from water level, the
angle of elevation of top of Chhatri (point B) is 45 and angle of
depression of its reflection in water (point C) is 60 . If the height of
Chhatri above water level is (approximately) 10 m, then

(a) draw a well-labelled figure based on the above information; 2

(b) find the height (h) of the point A above water level.
(Use 3 = 1·73) 2

.30/1/1 11 P.T.O.