CBSE Class 10 Question Paper 2022 Maths Basic (Solved)

Series PPQQA/1 SET~1
àíZ-nÌ H$moS>
Q.P. Code 430/1/1
amob Z§. narjmWu àíZ-nÌ H$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 (~w{Z`mXr)
MATHEMATICS (BASIC)

:2 : 40
Time allowed : 2 hours Maximum Marks : 40

.430/1/1 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$) `{X a = 50, d = 4 VWm Sn = 0 h¡, Vmo n H$m _mZ kmV
H$s{OE & 2
AWdm
(I) T>r H$s ghm`Vm go g§»`m 7 Ho$ 2 A§H$m| dmbo àW_ ~mah JwUOm| H$m
`moJ\$b kmV H$s{OE & 2

2. 3 go_r {ÌÁ`m dmbo YmVw Ho$ EH$ R>mg
o Jmobo H$mo {nKbmH$a 2 go_r {ÌÁ`m dmbo EH$ R>mog ~obZ
Ho$ AmH$ma _| T>mbm OmVm h¡ & ~obZ H$s D±$MmB© kmV H$s{OE & 2

3. (H$) {ÛKmV g_rH$aU x2 5x + 9 = 0 Ho$ _ybm| H$s àH¥${V kmV H$s{OE & 2
AWdm
(I) EH$ {ÛKmV g_rH$aU {b{IE {OgHo$ _yb 3 VWm 5 h¢ & 2

4. {ZåZ{b{IV ~ma§~maVm ~§Q>Z Ho$ {bE ~hþbH$ kmV H$s{OE : 2
0 20 20 40 40 60 60 80 80 100
8 7 12 5 3

.430/1/1 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) In an AP, if a = 50, d = 4 and Sn = 0, then find the value of n. 2

OR
(b) Find the sum of the first twelve 2-digit multiples of 7, using an AP. 2

2. A solid metallic sphere of radius 3 cm is melted and recast into the shape
of a solid cylinder of radius 2 cm. Find the height of the cylinder. 2

3. (a) Find the nature of the roots of the quadratic equation
x2 5x + 9 = 0. 2
OR
(b) Write a quadratic equation with roots 3 and 5. 2

4. Find the mode of the following frequency distribution : 2

Class 0 20 20 40 40 60 60 80 80 100

Frequency 8 7 12 5 3

.430/1/1 3 P.T.O.

5. {ÛKmV g_rH$aU 2x2 5x 1 = 0 H$mo x Ho$ {bE hb H$s{OE & 2

6. AmH¥${V 1 _|, `{X EH$ q~Xþ P go O Ho$ÝÐ dmbo {H$gr d¥Îm na PA, PB ñne©-aoImE± nañna
70 Ho$ H$moU na PwH$s h¢, Vmo POA H$s _mn kmV H$s{OE & 2

1

IÊS> I
7 10 3

7. ZrMo {XE JE ~ma§~maVm ~§Q>Z _| EH$ H$jm Ho$ 40 {dÚm{W©`m| H$m ^ma {XIm`m J`m h¡ &
{dÚm{W©`m| H$m _mÜ`H$ ^ma kmV H$s{OE & 3

40 45 9
45 50 5
50 55 8
55 60 9
60 65 6
65 70 3

8. (H$) 4 go_r {ÌÁ`m H$m EH$ d¥Îm It{ME & Ho$ÝÐ go 6 go_r Xÿa pñWV EH$ {~ÝXþ go d¥Îm na
EH$ ñne©-aoIm `w½_ H$s aMZm H$s{OE & 3
AWdm
(I) EH$ aoImIÊS> PQ = 7·5 go_r It{ME & Bg aoImIÊS> H$mo 3 : 1 Ho$ AZwnmV _|
{d^m{OV H$s{OE & 3

.430/1/1 4

5. Solve the quadratic equation 2x2 5x 1 = 0 for x. 2

6. In Figure 1, if tangents PA and PB drawn from a point P to a circle with
centre O, are inclined to each other at an angle of 70 , then find the
measure of POA. 2

Figure 1

SECTION B

Question numbers 7 to 10 carry 3 marks each.

7. The frequency distribution given below shows the weight of 40 students
of a class. Find the median weight of the students. 3

Weight (in kg) Number of Students

40 45 9
45 50 5
50 55 8
55 60 9
60 65 6
65 70 3

8. (a) Draw a circle of radius 4 cm. Construct a pair of tangents to the
circle from a point 6 cm away from its centre. 3
OR
(b) Draw a line segment PQ = 7·5 cm. Divide it in the ratio 3 : 1. 3

.430/1/1 5 P.T.O.

9. AmH¥${V 2 _|, _rQ>a D±$MmB© dmbr EH$ _rZma AB Ho$ AmYma go Am¡a EH$ gab aoIm _|
x m VWm y m Xÿar na pñWV Xmo {~ÝXwAm| P Am¡a Q go _rZma Ho$ {eIa Ho$ CÞ`Z H$moU
H«$_e: 60 VWm 30 h¢ & {gÕ H$s{OE {H$ h2 = xy. 3

2

10. {ZåZ{b{IV gmaUr {H$gr AñnVmb _| EH$ {deof gßVmh _| ^Vu hþ`o amo{J`m| H$s Am`w H$mo
Xem©Vr h¡ :
: 5 15 15 25 25 35 35 45 45 55 55 65
: 5 12 20 24 15 4
amo{J`m| H$s _mÜ` Am`w kmV H$s{OE & 3

IÊS> J
11 14 4

11. (H$) EH$ JmobmH$ma H$m±M Ho$ ~V©Z H$s EH$ ~obZ Ho$ AmH$ma H$s JX©Z h¡ {OgH$s D$±MmB©
8 go_r VWm {ÌÁ`m 1 go_r h¡ & JmobmH$ma ^mJ H$s {ÌÁ`m 9 go_r h¡ & kmV H$s{OE
{H$ nyam ^aZo na `h ~V©Z {H$VZm nmZr (brQ>a _|) aI gH$Vm h¡ & 4
AWdm
(I) D±$MmB© 2·4 go_r Am¡a ì`mg 1·4 go_r dmbo EH$ R>mog ~obZ _| go Bgr D±$MmB© Am¡a
Bgr ì`mg dmbm EH$ e§ (cavity) H$mQ> H$a {ZH$mbm OmVm h¡ & eof
~Mo R>mog H$m Hw$b n¥îR>r` joÌ\$b kmV H$s{OE & 4

.430/1/1 6

9. In Figure 2, the angles of elevation of the top of a tower AB of height

of the tower respectively and in the same straight line with it, are 60
and 30 , respectively. Prove that h2 = xy. 3

Figure 2

10. The following table shows the age of patients admitted in a hospital
during a particular week :

Age (in years) 5 15 15 25 25 35 35 45 45 55 55 65
Number of
5 12 20 24 15 4
Patients

Find the mean age of the patients. 3

SECTION C

Question numbers 11 to 14 carry 4 marks each.

11. (a) A spherical glass vessel has a cylindrical neck 8 cm long and 1 cm
in radius. The radius of the spherical part is 9 cm. Find the
amount of water (in litres) it can hold, when filled completely. 4
OR
(b) From a solid cylinder, whose height is 2·4 cm and diameter 1·4 cm,
a conical cavity of the same height and same diameter is hollowed
out. Find the total surface area of the remaining solid. 4

.430/1/1 7 P.T.O.

12. Xr JB© AmH¥${V 3 _|, l VWm m, O Ho$ÝÐ dmbo {H$gr d¥Îm na A Am¡a B na
ItMr JB© Xmo g_mÝVa ñne©-aoImE± h¢ Am¡a {~ÝXþ R na d¥Îm na ItMr JB© ñne©-aoIm PQ h¡ &
{gÕ H$s{OE {H$ POQ = 90 . 4

3

àH$aU AÜ``Z 1
13. Omo ~oH$ma g_P H$a \|$H$ {XE OmVo h¢, dmo Zm {g\

Oê$ar h¡ {H$ h_ {H$gr ^r àH$ma go
ZrMo {XE JE {MÌ _| XmBª Amoa EH$ nm`XmZ {XIm`m J`m h¡ Omo nwamZr Q>r-eQ>© Ho$ YmJo go
~Zm`m J`m h¡ & {MÌ H$m AdbmoH$Z H$aZo na Amn XoI|Jo {H$ ha d¥ÎmmH$ma n§{º$ _| \§$Xm| H$s
g§»`m n¡Q>Z© : 6, 12, 18, 24, ... _| h¡ &

Cn`w©º$ gyMZm Ho$ AmYma na, {ZåZ{b{IV àíZm| Ho$ CÎma Xr{OE :
(H$) Om± EH$ g_m§Va `{X hm±, Vmo gmd©
AÝVa VWm g_m§Va 2
(I) Bg g_m§Va ndm± nX {b{IE & Xgdt d¥ÎmmH$ma n§{º$ _| \§$Xm| H$s
g§»`m kmV H$s{OE & 2

.430/1/1 8

12. In Figure 3, the tangent l is parallel to the tangent m drawn at
points A and B respectively to a circle centred at O. PQ is a tangent to
the circle at R. Prove that POQ = 90 . 4

Figure 3

Case Study 1

13. Do you know old clothes which are thrown as waste not only fill the
landfill site but also produce very harmful greenhouse gas. So, it is very
important that we reuse old clothes in whatever way we can.
The picture given below on the right, shows a footmat (rug) made out of
old t-shirts yarn. Observing the picture, you will notice that a number of
stitches in circular rows are making a pattern : 6, 12, 18, 24, ...

Based on the above information, answer the following questions :
(a) Check whether the given pattern forms an AP. If yes, find the
common difference and the next term of the AP. 2
(b) Write the nth term of the AP. Hence, find the number of stitches in
the 10th circular row. 2

.430/1/1 9 P.T.O.

àH$aU AÜ``Z 2

14. {ZåZ Q>r.dr. Q>m°da, nrV_nwam, {Xëbr _| 1988 _| {Z{_©V {H$`m J`m Wm & ZrMo {XE JE {MÌ
H$mo Ü`mZnyd©H$ XoI| :

B

C

A

Q>r.dr. Q>m°da YaVr na D$ go Q>m°da Ho$ erf© ({~ÝXþ
) H$m CÞ`Z H$moU 60 h¡ & YaVr go 78 _r. (bJ^J) H$s D±$MmB© na Q>m°da na EH$ {~ÝXþ
h¡ & {~ÝXþ A go {~ÝXþ C H$m CÞ`Z H$moU 30 h¡ &
(H$) Cn`w©º$ gyMZm H$mo EH$ AÀN>r àH$ma go A§{H$V {MÌ Ho$ Ûmam Ambo{IV H$s{OE & 2

(I) Q>m°da H$s D±$MmB© VWm {~ÝXþ A go Q>m°da H$s Xÿar kmV H$s{OE & 2

.430/1/1 10

Case Study 2

14. The following TV Tower was built in 1988 and is located in Pitampura,
Delhi. It has an observation deck. Observe the picture given below :

B

C

A

The TV T
ground, the angle of elevation of top of the tower (p . There
.) above the ground.
The angle of elevation of the point C from point A is found to be 30 .
(a) Draw a well-labelled figure, based on the information given above. 2
(b) Find the height of the tower and the distance of the tower from
point A. 2

.430/1/1 11 P.T.O.