Mensuration 2D

Square cm and one of its sides is 24 cm (in cm2) is:

1. The length of the diagonal of a ,d vk;r dk {ks=kiQy (oxZ ls-eh- es) D;k fdlh vk;r dh yEckbZ rFkk pkSM+kbZ dk vuqikr
square is ‘a’ cm. Which of the gS] ;fn bldk fod.kZ
25 ls-eh- gS vkSj bldh 3:2 gSrFkk ifjeki20cm gSA vk;r dk
following represents the area of ,d Hkqtk24 ls-eh- gS\ {ks=kiQy Kkr djaas\
the square (in sq. cm )? (a) 24 cm2 (b) 36 cm2
(a) 186 (b) 144
fdlh oxZ ds fod.kZ dh yEckbZ
'a' cm gSA (c) 48 cm2
(d) 12 cm2
(c) 132 (d) 168
fuEufyf[kr esa oxZ dk {ks=kiQy lseh- esa Kkr djsa\ 12. The perimeter of a rectangle
7. What is the area (in sq cm) of a and a square are 160 m each.
a
(a) 2a (b) rectangle of perimeter 90 cm The area of the rectangle is less
2 and breadth 20 cm? than that of the square by 100
(c) a 2 /2 (d) a 2 / 4 90 l s-eha- dh ifjf/ vkSj 20 ls-eha- pkSM+kbZ
sq m. The length of the rect-
2. If the length of the diagonal AC okys ,d vk;r dk {ks=kiQy (oxZ ls-eha esa)angle is
of a square ABCD is 5.2 cm, D;k gS\ ,d vk; r rFkk oxZ dk ifjeki 160 eh- gSA
then the area of the square is : vk;r dk {ks=kiQy] oxZ ds {ks=kiQy
100 ls
(a) 500 (b) 400
oxZABCD dk fod.kZAC dh yEckbZ
5.2 eh-2 de gSA vk;r dh yEckbZ Kkr djsa\
(c) 250 (d) 450 (a) 30 m (b) 60 m
cm gS
A oxZ dk {ks=kiQy Kkr djsa\
8. The perimeter of a rectangle is 160 (c) 40 m (d) 50 m
(a) 15.12 sq. cm (b) 13.52 sq. cm metres and the difference of two Triangle
(c) 12.62 sq. cm (d) 10 sq . cm sides is 48 metres. Find the side13. In a triangular field having
of a square whose area is equal to sides 30m, 72m and 78m, the
3. The diagonal of a square is
the area of this rectangle? length of the altitude to the side
4 2 cm. The diagonal of another ,d vk;r dk ifjeki 160 eh- gS rFkk measuring 72m is :
square whose area is double that mldh nks Hkqtkvksa dk ehVjgSA oxZ
48vUrj fdlh f=kHkqt dh Hkqtk,sas
30 eh-] 72 eh-RkFkk
of the first square is:
dh Hkqtk Kkr dhft, ftldk {ks=kiQy bl 78 eh- gSaA
72 ehVj Hkqtk ij Mkys x;s
fdlh oxZ dk fod.kZ vk;r ds {ks=kiQy ds cjkcj gSA 'kh"kZyEc dh yEckbZZ Kkr djsa\
4 2 lseh A nwljs
. gS
(a) 25 m (b) 28 m
oxZ dk fod.kZ Kkr djsa] ftldk {ks=kiQy]
(a) 32m(b) 8 m (c) 4 m (d) 16m
(c) 30 m (d) 35 m
izFke oxZ ds {ks=kiQy dk nks xquk9.gS\ The length of a rectangular hall 14. The two equal sides of an
is 5m more than its breadth.
(a) 8 2 cm (b) 16 cm isosceles triangle is 20 cm
The area of the hall is 750m2.
each and the third side is 30
The length of the hall is :
(c) 32 cm (d) 8 cm cm. What is the area (in cm²)
fdlh vk;rkdkj gkWy dh yEckbZ mldh pkSM+kbZ
of the triangle ?
4. The perimeter of two squares ls 5m vf/d gSA gkWy dk {ks=kiQy
750m2
are 24 cm and 32 cm. The pe- ,d lef}ckgq f=kHkqt dh nks leku20Hkqtk,¡
gS
A gkWy dh yEckbZ Kkr djsa\
rimeter (in cm) of a third
(a) 15 m (b) 22.5 m ls-eh- gSA rFkk rhljh 30
Hkqtk
cm gS] rks
square equal in area to the
(c) 25 m (d) 30 m f=kHkqt dk {ks=kiQy ²) (ls-eh-
D;k gS\
sum of the areas of these
10. The area (in m2) of the square (a) 50 5 (b) 100
squares is :
which has the same perim-
nksoxks± ds ifjeki
24 lseh- vkSj
32 lseh- e t e r a s a r e c t a n g l e w h os e (c) 75 7 (d) 175
gS bu oxksZ ds {ks=kiQyksa ds ;ksx dslength
cjkcj is 48 m and is 3 times
15. If the perimeter of a
{ks=kiQy okys ,d rhljs oxZ dk ifjeki gSAits breadth is: right-angled isosceles triangle
(a) 45 (b) 40 (c) 32 (d) 48 fdlh vk;r dh yEckbZ mldh pkSM+kbZ dh rhu
5. If each edge of a square be doubled. xquk gSA ml oxZ dk {ks=kiQy Kkr djsa ftldk
is 4 2  4  cm, the length of the
then the increase percentage in its ifjeki mi;qZDr vk;r ds cjkcj gSA ftldh hypotenuse is ;
area is yEckbZ 48 ehVjgSA l ef}ckgq ledks.k f=kHkqt dk ifjeki
fdlh oxZ dh Hkqtk dks nksxquk fd;k tk;s](a) 1000
rc {ks=kiQy %esai fjorZu Kkr djsa\
(b) 1024 4 2  4 lseh- gSA d.kZ dh yEckbZ Kkr djsa\
(c) 1600 (d) 1042 (a) 4 cm (b) 6 cm
(a) 200% (b) 250%
(c) 280% (d) 300% 11. If the length and breadth of a (c) 8 cm (d) 10 cm
Rectangle rectangle are in the ratio 3 : 2 16. The perimeter of a triangle is
and its perimeter is 20 cm, 40cm and its area is 60 cm2. If
6. What is the area (in sq cm) of a
then the area of the rectangle the largest side measures 17
rectangle if its diagonal is 25

Telegram Channel-Maths by Sultan Sir, Contact No.-8418077039 1

 cm, then the length (in cm) of sides are 3 cm 2 3 cm and 29 29
the smallest side of the (a) 1 4 8 cm2 (b) 2 48 cm2
5 3 cm. The perimeter ( in cm)
triangle is
of the triangle is 27 27
fdlh f=kHkqt dk ifjeki
40 cm rFkk {ks=kiQy (c) 1 cm2 (d) 2 cm2
60cm² gS A f=kHkqt dh lcls yEch Hkqtk fdlh leckgq f=kHkqt ds vH;karj ds fdlh 48 48
26. The area of a circle is increased
17cm gks] rc lcls NksVh Hkqtk dh yEckbZfcUnq ls rhuksa Hkqtkvksa dh yEcor
3 nwfj;k¡
by 22 cm², if its radius is in-
Kkr djsa\ lseh-]2 3 lseh- vkSj
5 3 lseh- gSA f=kHkqt creased by 1 cm. The original
(a) 4 (b) 6 (c) 8 (d) 15 dk ifjeki (lseh- esa) D;k gSaA radius of the circle is
17. The ratio of length of each (a) 64 (b) 32 (c) 48 (d) 24 ; fn fdlh o`Ùk dh f=kT;k1 dks
lseh- c<+k;k
equal side and the third side of 22. In an isosceles triangle, the 22 lseh-2 c<+ tkrk gSA
tk;s rks mldk {ks=kiQy
an isosceles triangle is 3 : 4. If measure of each of equal sides o`Ùk dh okLrfod f=kT;k Kkr djsa\
the area is 8 5 units². the is 10 cm and the angle between (a) 6 cm (b) 3.2 cm
them is 45°, then area of the (c) 3 cm (d) 3.5 cm
small side is triangle is 27. A copper wire is bent in the form
fdlh lef}ckgq f=kHkqt dh cjkcj Hkqtk esa lef}ckg
ls q f=kHkqt dh cjkcj Hkqtk,a 10 lseh-
of an equilateral triangle and
3 : 4 gSA ;fn
,d rFkk vleku Hkqtk dk vuqikr 45° gS
rFkk muds chp dks.k A f=kHkqt dk has area 121 3 cm2. If the same
8 5 unit² gks] rc NksVh Hkqtk Kkr djsa\
{ks=kiQy {ks=kiQy Kkr djsa\ wire is bent into the form of a
25
circle. the area (in cm 2 )
2 2
(a) 6 units (b) 2 5 units (a) 25 cm (b) 2
2 cm enclosed by the wire is
22
(c) 8 2 units (d) 12 units (c) 25 2 cm2 (d) 2 3 cm2 (take   )
7
18. The perimeter of an isosceles 23. The base and altitude of a right fdlh rkj dks leckgq f=kHkqt ds :i esa eksM+k
triangle is 64 cm and each of angled triangle are 12 cm and x;k] ftlds }kjk f?kjk {ks=kiQy
121 3
the equal sides is 5/6 times the 5 cm respectively. The perpen-
base. What is the area (in cm2) dicular distance of its hypotenuse lseh-² gS
aA ;fn leku rkj dks o`Ùk ds :i esa
of the triangle? from the opposite vertex is eksM+k tk;s] rks o`Ùk dk {ks=kiQy Kkr djsa \
,d lef}ckgq f=kHkqt dh ifjeki 64 ls-eh fdlh ledks.k f=kHkqt dk vk/kj
12 lseh- (a) 364.5 (b) 693.5
gS rFkk mldk vk/kj izR;sd cjkcj Hkqtk ds 5 lseh- gSA mlds fod.kZ dh
rFkk 'kh"kZyEc (c) 346.5 (d) 639.5

5/6 xq.kk gSA f=kHkqt dk {ks=kiQy

2 foijhr 'kh"kZ ls yEc nwjh Kkr djsa\ 28.
esa) (ls-eh
A 7 m wide road runs outside
around a circular park, whose
D;k gksxk\ 4 8 circumference is 176 m. The
(a) 4 cm (b) 4 cm
(a) 169 (b) 192 13 13 22
area of the road is : (use  )
(c) 196 (d) 184 (c) 5 (d) 7 cm 7

19. What is the area (in sq cm) of 24. In an equilateral triangle ABC of fdlh 176 ehVji fjf/ okys o`Rrkdkj ikdZ ds
an equilateral triangle of side side 10 cm, the side BC is tri- 7 ehVjpkSM+k jkLrk gSA jkLrs dk
pkjksa vksj
14 cm? sected at D & E. Then the length {ks=kiQy gS%
(in cm) of AD is
14ls-eha- Hkqtk okys leckgq f=kHkqt dk {ks=kiQy (a) 1386 m2 (b) 1472 m2
10 cm Hk qtk okys leckgq f=kHkqt
 ABC 2
(d) 1760 m2
(oxZ ls-eha- esa) D;k gksxk\ (c) 1512 m
esa Hkqtk
BC dksfcUnqD rFkkE }kjk rhu 29. A circular road runs around a
(a) 49 3 (b) 98 3 cjkcj Hkkxksa esa ck¡Vk
AD dhx;kA
yEckbZ circular ground. If the differ-
cm esa Kkr djsa\ ence between the circumfer-
(c) 49 / 2 3 (d) 49 / 4 3 ence of the outer circle and the
(a) 3 7 (b) 7 3
20. One acute angle of a right inner circle is 66 meters, the
angled triangle is double the 10 7 7 10 width of the road is:
other. If the length of its hypot- (c) (d)
3 3 22
enuse is 10 cm, then its area is
Circle (Take   )
fdlh ledks.k f=kHkqt dk ,d dks.k] nwljs 7
25. The circumference of a circle is
dks.k dk nks xquk gSA ;fn d.kZ 10
dh yEckbZ dkj eSnku ds pkjksa vksj ,d pkSM+k
fdlh o`Ùkk
11 cm and the angle of a sector
] rc {ks=kiQy Kkr djsa \
lseh-gks of the circle is 60°. The area of jkLrk gSA ckgjh ifjf/ rFkk vakrfjd ifjf/
(a)
25
3 cm2 (b) 25 cm2 the sector is dk vUrj 66 ehVjgSA rc ekxZ dh pkSM+kbZ
2
(use  
22
)
Kkr djsa\
75 7
(c) 25 3 cm2 (d) cm2 (a) 10.5 metres (b) 7 metres
2
fdlh o`Ùk dh ifjf/11 lseh- gS rFkk ,d (c) 5.25 metres(d) 21 metres
21. From a point in the interior of
pki dsUnz 60°
ij dk dks.k varfjr djrh gSA 30. The four equal circles of radius
an equilateral triangle, the
f=kT;&[k.M dk {ks=kiQy Kkr djsa\ 4 cm drawn on the four corners
perpendicular distance of the

2 Telegram Channel-Maths by Sultan Sir, Contact No.-8418077039

 of a square touch each other makes 1000 revolutions in (c) 140 m (d) 145 m
externally. Then the area of the moving 440 m . The diameter 39. If the radius of a circle is in-
portion between the square and (in metre) of the wheel is creased by 14% its area in-
the four sectors is ,d ifg;k 440 eh-pyusa esa
1000 pDdj
fdlh oxZ ds dksuksa 4ij lseh-
cus f=kT;k okys creases by
iwjs
djrk gSA ifg;s dk O;kl gS\
pkj o`Rr ,d&nwljs dks ckgj ls Li'kZ djrs gSaA ; fn ,d o`Ùk dh f=kT;k esadh o`f¼ dh
14%
(a) 0.44 (b) 0.14
oxZ rFkk o`Rrksa ds chp fjDr LFkku dk {ks=kiQy tkrh gS] rks mldk {ks=kiQy fdrus izfr'kr c<+
(c) 0.24 (d) 0.34
Kkr djsa\ 35. A gear 12 cm in diameter is tk,xk\
(a) 9  – 4 sq. cm turning a gear 18 cm in diam- (a) 28% (b) 29.96%
eter. When the smaller gear (c) 14% (d) 14.98%
(b)16 4 – sq. cm has 42 revolutions. how many
40. A is the centre of circle whose
has the larger one made?
(c) 99  – 4  sq. cm radius is 8 and B is the centre
12cm O;kl okyk ,d ifg;k] 18cm of a circle whose diameter is 8.
(d) 169  – 4  sq. cm O;klokys nwljs ifg;s dks ?kqekrk gSA tc NksVk
If these two circles touch
31. At each corner of a triangular ifg;k 42 pDdj iwjs djrk gS]rc cM+s ifg;s externally, then the area of the
field of sides 26 m ,28 m and 30 }kjk r; pDdj Kkr djsa\ circle with diameter AB is
m, a cow is tethered by a rope (a) 28 (b) 20 (c) 15 (d) 24 8cm f=kT; A gSrFkk
k okys o`Ùk dk dsUæ
of length 7m, the area 36. A circle is inscribed in a square 8cm O;kl okys o`Ùk dk dsUæ A ;fn
B gS
(in m²-) ungrazed by the cows is whose length of the diagonal is nksuksa o`Ùk ckg~; #i ls Li'kZ djrs
AB gSa] rc
fdlh f=kHkqtuqek {ks=k 26 dh ehVj]
Hkqtk;sa O;kl okys o`Ùk dk {ks=kiQy Kkr djsa\
12 2 cm. An equilateral tri-
28 ehVj]rFkk30 ehVjgSaA izR;sd 'kh"kZ ij (a) 36 (b) 64
angle is inscribed in that circle.
7 eh-yEch jLlh }kjk xk;ksa dks ck¡/k x;kA
The length of the side of the (c) 144 (d) 256
xk;ksa }kjk fcuk pjk gqvk Hkkx dk {ks=kiQy
triangle is 41. A circle is inscribed in an
equilateral triangle and a
Kkr djsa\ fdlh oxZ dk fod.kZ
12 2 cm gSftlds square is inscribed in that
(a) 336(b) 259 (c) 154 (d) 77
vUnj ,d o`Ùk fLFkr gSA bl o`Ùk ds vUnjcircle. The ratio of the areas of
32. Three circles of diameter 10 cm
each are bound together by a rub- ,d leckgq f=kHkqt fLFkr gSA f=kHkqt dhthe
Hkqtk
triangle and the square is
Kkr djsa\ fdlh leckgq f=kHkqt ds vUnj ,d o`Ùk gSA o`Ùk
ber band as shown in the figure.
ds vUnj ,d oxZ gSA f=kHkqt rFkk oxZ ds {ks=kiQyks
(a) 4 3 cm (b) 8 3 cm
dk vuqikr Kkr djsa\
(c) 6 3 cm (d) 11 3 cm (a) (b)
3 :4 3 :8
37. The area of a circle is same as
(c) 3 3 : 2 (d) 3 3 :1
the area of a square. What is
the length of the rubber band the ratio of the diameter of the 42. If the length of a side of the
(in cm) if it is stretched is circle and diagonal of the square is equal to that of the
10 lseh- O;kl okys3 o`Rr,d&nwljs dks diameter of a circle, then the
square?
ratio of the area of the square
Li'kZ djrs gS rFkk mUgsa ,d jcj }kjk ck¡èkk
,d o`Ùk dk {ks=kiQy ,d oxZ ds {ks=kiQy ds
tkrk gSA jcj dh yEckbZ Kkr djsa\ 22
cjkcj gSA o`Ùk ds O;kl rFkk oxZ ds fod.kZand
dk that of the circle (  )
(a) 30 (b) 30 +10 7
vuwikr D;k gksxk\
(c) 10 (d) 60+20 fdlh oxZ dh Hkqtk fdlh o`r dk O;kl gS] rc
33. Three circles of radius a, b, c (a) 1:  (b) 2 :  oxZ rFkk o`r ds {ks=kiQy dk vuqikr Kkr djssa\
touch each other externally. (a) 14 : 11 (b) 7 : 11
The area of the triangle formed (c) 2 :  (d)1: (c) 11 : 14 (d) 11 : 7
by joining their centre is 43. If the numerical value of the
38. There is a rectangular tank of circumference and area of a
k okys rhu o`Ùk ,d nwljs dks length 180 m and breadth 120
a,b,c f=kT;
circle is same, then the area is
ckg; Li'kZ djrs gSaA muds dsUæksa dks feykdj]
m in a circular field, If the area fdlh o`r dh ifjf/ rFkk {ks=kiQy dk vafdd
izkIr f=kHkqt dk {ks=kiQy Kkr djsa\ of the land portion of the field
is 40000 m2, what is the ra- eku leku gSA {ks=kiQy Kkr djsa\
22
(a) 6 sq. units
(a) a  b  c abc dius of the field? ( Take  
7
)
(b) 4 sq. units
fdlh o`rkdkj eSnku180
esam yEck rFkk (c) 8 sq. units
(b) a  b  c  ab  bc  ca (d)12 sq. units
120 m pkSM+k vk;rkdkj VSad j[kk gqvk gSA
44. A circular wire of diameter 112
(c) ab + bc + ca ;fn esSnku esa Hkwfe dk40000
{ks=kiQy
m2 cm is cut and bent in the form
(d) None of the above ] rks eSnku dh f=kT;k Kkr djas\
gS of a rectangle whose sides are
34. The wheel of a motor car (a) 130 m (b) 135 m in the ratio of 9 : 7. The

Telegram Channel-Maths by Sultan Sir, Contact No.-8418077039 3

 smaller side of the rectangle is D 4
fdlh 112 lseh- O;kl okys o`Ùk dks ,d A ;fn ifjf/ 1
22 : 7 gS rks o`Ùk
m, gks
4m 7
vk;r ds :i esa ifjofrZr fd;k x;k] ftldh A
: 7 gS
Hkqtkvksa esa9vuqikr A vk;r dh NksVh dh f=kT;k D;k gksxh\
O 45°
Hkqtk Kkr djsa\ 1 1
(a) m/eh- (b) m/eh-
(a) 77 cm (b) 97 cm 4 3
(c) 67 cm (d) 84 cm
3m B
1
45. Two equal maximum sized E (c) m/eh- (d) 1 m/eh-
circular plates are cut off from
2
11 11 55. Between a square of perimeter
a circular paper sheet of
circumference 352 cm. Then (a) m² (b) m² 44 cm and a circle of
16 8
the circumference of each circumference 44 cm, which
circular plate is 11 11 figure has larger area and by
(c) m² (d) m²
fdlh 352 l seh- ifjf/ okyh o`Ùkkdkj pknj esa 2 4 how much?
ls] nks cM+h ls cM+h cjkcj o`Ùkkdkj50. IysVIfdkVh
the circumference of a circle 44 lseh-ifjeki okys oxZ rFkk
44 lseh-
x;haA rc izR;sd IysV dh ifjf/ Kkr djsa\ 30 ifjeki okys o`r esa fdl vkÑfr dk {ks=kiQy
(a) 176 cm (b) 150 cm is

, then the diameter of the vf/d rFkk fdruk vf/d gS\
(c) 165 cm (d) 180 cm (a) Square, 33cm2
46. The difference between the cir- circle is
cumference and diameter of a (b) Circle, 33 cm2
30
circle is 150 m. The radius of ; fn o`Ùk dh ifjf/ gS] rks o`Ùk dk O;kl (c) Both have equal area.

22 (d) circle ,495 cm2
that circle is ( Take   ) Kkr djsa \
7 56. The perimeter of a square and a
15 30
fdlh o`Ùk dh ifjf/ rFkk O;kl dk vUrj (a) 30 (b) (c) 60 (d) circular field are same. If the area
150 eh-gSA o`Ùk dh f=kT;k Kkr djsa\  ² of the circular field is 3850 sq
(a) 25 metre (b) 35 metre 51. The outer and inner diameter meter. What is the area (in m2) of
(c) 30 metre (d) 40 metre of a circular path be 728 cm and the square ?
700 cm respectively. The breadth
47. The perimeters of a circle, a of the path is fdlh oxZ rFkk o`r dk ifjeki leku gSA ;fn
square and an equilateral ; fn ,d o`Ùkkdkj iFk dk cká ,oa vkarfjd 3850 ehVj
o`r dk {ks=kiQy 2
gks
] rc oxZ dk
{ks=kiQy Kkr djsa\
triangle are same and their ar- O;kl Øe'k%728 cm vkSj700 cm gks ]
eas are C, S and T respectively. (a) 4225 (b) 3025
Which of the following state-
rks iFk dh pkSM+kbZ fdruh gksxh\
(a) 7 cm (b) 14 cm (c) 2500 (d) 2025
ment is true?
(c) 28 cm (d) 20 cm 57. If the circumference of a circle
fdlh o`Ùk] oxZ rFkk leckgq f=kHkqt dk
52. The area of a circle is 324
C, S rFkk
ifjeki leku gS rFkk {ks=kiQYk T
 sq.cm. The length of its long-
increases from 4 to 8 , what
gSaA lgh dFku Kkr djsa\ est chord (in cm.) is
change occurs in its area?
(a) C = S = T (b) C > S > T fdlh o`Ùk dh ifjf/ dks 4 ls 8 rd
,d o`Ùk dk {ks=kiQy
324  oxZlseh gSA
(c) C < S < T (d) S < C < T c<+k;k x;kA {ks=kiQy esa o`f¼ Kkr djsa\
48. The perimeter of a sheet of pa- mldh nh?kZÙke thok dh yackbZ (lseh esa)
(a) It doubles (b) It triples
per in the shape of a quadrant fdruh gS\ (c) It quadruples(d) It is halved
of a circle is 75 cm. Its area (a) 36 (b) 38 (c) 28 (d) 32
Rhombus
22 53. One of the angles of a right-
would be (  = ) angled triangle is 15°, and the 58. The perimeter of a rhombus is
7 40 m and its height is 5m its
hypotenuse is 1 m. The area
o`Ùk ds prqFkk±'k ds vkdkj esa ,d dkxt dh of the triangle (in sq. cm.) is area is :
'khV dk ifjeki75 lsñehñgS] rks mldk ,d led ks.kh; f=kHkqt dk ,d 15°
dks.k
gS , d leprqHkZqt dk ifjeki 40 ehVj gS
{ks=kiQy Kkr djsaA v kSj d.kZ
1 eh gSA f=kHkqt dk {ks=kiQy vkSj bldh mQ¡pkbZ
5 eh- gS rks bldk
(a) 512.25 cm² (b) 346.5 cm²
fdruk gS\
(oxZ lseh esa) {ks=kiQy D;k gS\
(c) 100 cm² (d) 693 cm² (a) 60 m2 (b) 50 m2
(a) 1220 (b) 1250
49. In the figure, OED and OBA are (c) 45 m 2
(d) 55 m2
(c) 1200 (d) 1215
sectors of a circle with centre O. 59. The area of a rhombus is 150
The area of the shaded portion. 54. The ratio of circumference and
diameter of a circle is 22 : 7. If cm2. The length of one of its di-
fn, x, fp=k esa
OED vkSjOBA ,d o`Rr agonals is 10 cm. The length of
ds f=kT;[kaM gS ftudk O dsanz
gS
] rks jaxs gq, 4 the other diagonal is :
Hkkx dk {ks=kiQy Kkr djsa \ the circumference be 1 m,
7 fdlh le&prqHkqZt dk {ks=kiQy150cm2
then the radius of the circle is: rFkk,d fod.kZ dh yEckbZ10cm gS A nwljs
,d o`Ùk dh ifjf/ vkSj O;kl dk vuqikr

4 Telegram Channel-Maths by Sultan Sir, Contact No.-8418077039

 fod.kZdh yEckbZ Kkr djas\ its height is: (a) 42 cm2 (b) 60 cm2
(a) 25 cm (b) 30 cm , d leyEc dh nks lekarj Hkqtkvksa dh yackbZ (c) 84 cm 2
(d) 96 cm2
(c) 35 cm (d) 40 cm Øe'k%15 cm vkSj20 cm gS A ;fn bldk 70. ABCD is parallelogram. P and
Q are the mid- points of sides
60. The length of one side of a {ks=kiQy175 oxZlseh gS rks mldh Å¡pkbZ
BC and CD respectively. If the
rhombus is 6.5 cm and its fdruh gksxh\ area of  ABC is 12 cm2, then
altitude is 10 cm. If the length of
(a) 25 cm/ lseh (b) 10 cm/ lseh
its diagonal be 26 cm, the length the area of APQ is
of the other diagonal will be: (c) 20 cm/ lseh (d) 15 cm/ lseh
ABCD , d lekukUrj prqHkqZt gSA BC Hkqtk
fdlh leprqHkqZt dh Hkqtk 6.5 lseh-, rFkk 66. The ratio of the length of the rFkk CD ds eè; fcUnq P rFkk
Q gSaA ;fn
mldk 'kh"kZyEc
10 lseh- gSA ;fn mlds ,d parallel sides of a trapezium is
3 : 2. The shortest distance be-  ABC dk {ks=kiQy 12cm² rc  APQ
fod.kZ dh yEckbZ 26 lseh- gks] rks nwljs dk {ks=kiQy Kkr djsa\
tween them is 15 cm. If the
fod.kZ dh yEckbZ Kkr djsa\ area of the trapezium is 450 (a) 12 cm2 (b) 8 cm2
(a) 5 cm (b) 10 cm 2
cm , the sum of the length of (c) 9 cm 2
(d) 10 cm2
(c) 6.5 cm (d) 26 cm the parallel sides is 71. ABCD is a parallelogram in
61. The measure of each of two fdlh leyEc dh lekukUrj Hkqtkvksa dk vuqikr which diagonals AC and BD in-
opposite angles of a rhombus is tersect at O. If E, F, G and H are
3:2 gSA muds chp dh nwjh 15 lseh- gSA ;fn
60° and the measure of one of the mid- points of AO, DO, CO
its sides is 10 cm. The length of leyEc dk {ks=kiQy 450 lseh² gks] rc and BO respectively, then the
its smaller diagonal is : lekukUrj Hkqtkvksa dk ;ksx Kkr djsa \ ratio of the perimeter of the
fdlh le&prqHkqZt ds nks foijhr 60°dks.k (a) 15 cm (b) 36 cm quadrilateral EFGH to the perim-
gS 10 lseh- gSA mlds NksVs (c) 42 cm
a rFkk mldh Hkqtk (d) 60 cm eter of parallelogram ABCD is
fod.kZ dh yEckbZ Kkr djsa\ 67. The area of an isosceles tra- ABCD ,d lekukUrj prqHkqZt gS rFkk fod.kZ
(a) 10cm (b) 10 3 cm
pezium is 176 cm² and the AC, BD ,d&nwljs dks fcUnq O ij dkVrs
height is 2/11th of the sum of
gSaA ;fn]
E, F, G rFkkH, AO, DO, CO
5 its parallel sides. If the ratio of
(c) 10 2 cm (d) 2 2 cm the length of the parallel sides rFkk BO ds eè; fcUnq gSaA prqHkqZt
EFGH
62. If the diagonals of a rhombus is 4 : 7, then the length of a di- ds ifjeki rFkk lekukUrj prqHkqZt
ABCD ds
are 8 cm and 6 cm, then the agonal (in cm) is ifjeki dk vuqikr Kkr djsa\
area of square having same ,d lef}ckgq leyac dk {ks=kiQy 176 cm² (a) 1 : 4 (b) 2 : 3
side as that of rhombus is gSvkSj Å¡pkbZ bldh lekarj Hkqtkvksa ds ;ksx (c) 1 : 2 (d) 1 : 3
fdlh le prqHkqZt ds fod.kZ 8cm rFkk dk 2/11 gS A ;fn lekarj Hkqtkvksa dh yackbZ
72. PQRS is a paralleogram and its
6cm gS aZA mlds cjkcj Hkqtk okys oxZ dk dk vuqikr4 : 7 gS] rks fod.kZ dh yackbZ D;k area is 300 cm2 side PQ is ex-
{ks=kiQy Kkr djsa\ gS\(cm es)a tended to X such that PQ = QX.
(a) 25 (b) 55 (c) 64 (d) 36 If XS intersects QR at Y, then
63. The perimeter of a non-square (a) 2 137 (b) 24
what is the area (in cm2) of tri-
rhombus is 20 cm. One its di- angle SYR?
(c) 137 (d) 28
agonal is 8 cm. The area of the
rhombus is Parallelogram PQRS , d lekUrj prqHkZt gS rFkk mldk
fdlh le&prqHkZqt dk ifjeki
20cm gSA fod.kZ 68. Two adjacent sides of a paral- {ks=kiQy 300ls-eh-2
gSA HkqtkPQ d ksX rd
dh yEckbZ 8cm gSA {ks=kiQy Kkr djsa\ lelogram are of length 15 cm
and 18 cm, If the distance be-
bl rjg c<+k;k x;k fdPQ=QX gSA ;fn
(a) 28 sq. cm (b) 20 sq. cm
tween two smaller sides is 12 XS,QR d ksY i j dkVrk gS] rks f=kHkqt
(c) 22 sq. cm (d) 24 sq. cm
64. The area of a rhombus is 256
cm, then the distance between SYR d k {ks=kiQy (ls-eh- 2
esa) D;k gS\
two bigger sides is
sq.cm. and one of its diagonal (a) 75 (b) 50
is twice the other in
fdlh lekukUrj prqHkqZtksa dh vleku Hkqtk,sa
length.Then length of its larger 15cm rFkk18 cm gS aA ;fn NksVh Hkqtkvksa (c) 120 (d) 100
diagonal is ds chp nwjh
12 cm gS
] rc cM+h Hkqtkvksa ds Quadrilateral
,d leprqHkZt dk {ks=kiQy256 oxZ lseh gS chp nwjh Kkr djsa\ 73. In the given figure, PQRS is a
(a) 8 cm (b) 10 cm quadrilateral. If QR = 18 cm and
vkSj mldk ,d fod.kZ nwljs ls yackbZ esa (c) 12 cm (d) 15 cm PS = 9 cm, then what is the
nksxquk gS] rks mlds cM+s fod.kZ69. dh A
yackbZ
parallelogram has sides 15 area (in cm 2) of quadrilateral
fdruh gS\ cm and 7 cm long. The length of PQRS?
(a) 32 cm (b) 48 cm one of the diagonals is 20 cm.
(c) 36 cm (d) 24 cm The area of the parallelogram is nh xbZ vkÑfr esa] PQRS , , d prZqHkqt gSA
Trapezium fdlh lekUrj prqHkZqt dh Hkqtkvksa dh yEckbZ ;fn QR = 18 l s-eh- rFkk PS= 9 l s-eh-
65. The length of two parallel sides 15 lseh- rFkk7 lseh- gSA ;fn ,d fod.kZ dh gSa] rks prqHkZqt
PQRS d k {ks=kiQy (ls-eh 2

of a trapezium are 15 cm and 20 yEckbZ 20 lseh- gks] rc lekUrj prqHkZqt dk esa) D;k gksxk\
cm. If its area is 175 sq.cm, then {ks=kiQy Kkr djsa \

Telegram Channel-Maths by Sultan Sir, Contact No.-8418077039 5

 S 77. A straight line parallel to the sides of triangle ABC. AB = 21
base BC of the triangle ABC cm, BC = 28 cm and AC = 35
P intersects AB and AC at the cm. What is the area (in cm2)
points D and E respectively. If the of the shaded part?
150°
area of the ABE be 36 sq. cm. nh xbZ vkÑfr esa f=kHkqt
ABC dh rhuksa
then the area of the  A C D is Hkqtkvksa ij 3 v/Zo`Rr cuk;sAB x;s=gSaA
60° 60°
R  ABC ds vk/kj BC ds lekukUrj js[kk 21 ls-eh-BC = 28 ls-eh- rFkk
AC = 35
Q AB rFkkAC dks Øe'k% fcUnq
D rFkkE i j ls-eh- gSA Nk;kafdr Hkkx dk {ks=kiQy
2
) (ls-eh
(64 3) (177 3) ;fn dk {ks=kiQy
izfrPNsfnr djrh gSaAABE esa D;k gS\
(a) (b)
3 2 36 l seh-
² gks] rc
 A C D dk {ks=kiQy Kkr djsa\

(135 3) (98 3) (a) 18 sq.cm (b) 36 sq. cm

(c) (d) (c) 22 sq.cm (d) 60 sq.cm
2 3
Miscellaneous 78. Four equal sized maximum
circular plates are cut off from
74. D and E are points on side AB
a square paper sheet of area
and AC of  ABC. DE is paral- 784 sq. cm. The circumference
lel to BC. If AD:DB = 1:4 and area
22
of  ADE is 6 sq cm, what is of each plate is ( Take   ) (a) 588 (b) 324
7
the ratio of area of  ADE: area pkj leku vf/dre vkdkj dh o`Ùkkdkj (c) 294 (d) 286
of quadrilateral BDEC? IysVksa dks ,d oxkZdkj dkxt dh 'khV ftldk82. In the given figure, PQR is a
 ABC dh Hk qtkvksa
AB vkSjAC ij D {ks=kiQy 784 oxZehVj gS ls dkVk x;k gSA quadrant whose radius is 7 cm.
A circle is inscribed in the
DE, BC d s lekarj gSaA ;fn izR;sd IysV dh ifjf/ D;k gS\
vkSjE fcanq gSaA
quadrant as shown in the fig-
AD:DB = 1:4 vkSj ADE d k {ks=kiQy (a) 22 cm (b) 44 cm
ure. What is the area (in cm2 of
6 oxZ ls-eh- gSa]
rksADE d s {ks=kiQy% (c) 66 cm (d) 88 cm the circle?
79. The area of the shaded region
BDEC ds {ks=kiQy dk vuqikr D;k gSa\
prqHkqZt nh xbZ vkÑfr esa]
PQR ,d o`Ùk[k.M gS]
in the figure given below is
(a) 1:12 (b) 1:6 ftldh f=kT;k
fn;s x;s fp=k esa] Nk;kafdr Hkkx dk {ks=kiQy Kkr djsa\ 7 ls-eh- gSA tSlk fd vkÑfr
(c) 1:16 (d) 1:24 esa] n'kkZ;k x;k fd o`Ùk[k.M esa ,d o`Ùk dks
75. A man is running at the speed a vafdr fd;k x;k gSA o`Ùk dk {ks=kiQy
of 20km/hrs. What is time (in c (ls-eh-
2
esa) D;k gS\
seconds) taken by man to cover P
one round of a circular garden
of radius 350 metres?
a 2  
,d O;fDr 20 fdeh@?kaVk dh xfr ls nkSM+(a) 2  2 – 1  sq. units
 
jgk gSaA ,d o`Ùkkdkj cxhpk ftldh f=kT;k 2
(b) a  – 1 sq. units
350 ehVj gS] dks ikj djus esa O;fDr }kjk
fdruk le; (lsd.M esa) fy;k tk;sxk\  2 
(c) a  2 – 1  sq. units
 
(a) 412 (b) 336
a2
(c) 396 (d) 376 (d)  – 1 sq. units Q R
b2
76. In the given figure, two
80. The outer circumference of a (a) 385  221 2 (b) 308  154 2
squares of sides 8cm and 20cm
are given. What is the area (in circular race-track is 528
(c) 154  77 2 (d) 462  308 2
cm²) of the shaded part? metre. The track is every-
where 14 metre wide. Cost of 83. In the given figure, PQRS is
nhxbZ vkÑfr esa]
8ls-eh
- rFkk20 ls-eh
- levelling the track at the rate square whose side is 8 cm. PQS
Hkqtk okys nks oxZ fn;s gSA Nk;kafdr Hkkx
of `10dkper sq. metre is : and QPR are two quadrants. A
{ks=kiQy (ls-eh-
2
esa) D;k gS\ ,d o`Ùkkdkj nkSM+ iFk dh ckgjh528 ifjf/ circle is placed touching both
ehVjgSA iFk lc txg ls14 ehVjpkSM+k gSA the quadrants and the square as
`10 izfroxZehVj dh nj ij iFk dks lery shown in the figure. What is the
djus dh ykxr D;k gksxh\ area (in cm²) of the circle?
(a) ` 77660 (b) ` 67760 nhxbZ vkÑfr esa]
PQRS ,d oxZ gS ftldh
(c) ` 66760 (d) ` 76760 8 lseh-gSA
Hkqtk PQS rFkkQPR o`Ù
k ds nks
(a) 120/7 (b) 160/7 81. In the given figure, 3 semi- prqFkZ Hkkx gSaA ,d o`Ùk] o`Ùk ds nksuksa pr
(c) 180/7 (d) 240/13 circles are drawn on three Hkkxksa rFkk oxZ dks Li'kZ dj jgk gS tSlk fd

6 Telegram Channel-Maths by Sultan Sir, Contact No.-8418077039

 vkÑfr esa n'kkZ;k x;k gSA o`Ùk dk {ks=kiQy
(c) 62.72 (d) 156.8 PQRST , d le iapHkqt gSA ;fn
PR rFkk
(lseh-² esa)D;k gS\ 86. In the given figure area of isos- QT ,d nwljs dksX ij izfrPNsn djrs gSa]
celes triangle ABE is 72 cm2 and rks TXR eku (fMxzh esa) D;k gS\
BE = AB and AB = 2 AD, AE DC , (a) 98 (b) 90
then what is the area (in cm2) (c) 72 (d) 108
of the trapezium ABCD? 90. In the given figure, ABCDEF is a
nh xbZ vkÑfr esa lef}ckgq f=kHkqt
ABE dk regular hexagon whose side is 12
cm. What is the shaded area (in
(a) 13/17 (b) 11/14 {ks=kiQy 2
BE = AB rFkk
72 ls-eh gS rFkk cm2)?
(c) 19/31 (d) 15/19 AB = 2 AD, AE DC gS] rks leyEc nh xbZ vkÑfrABCDEF
esa] , d le "kVHkqt
84. ABCD passes through the ABCD dk {ks=kiQy (ls-eh-
prqHkqZt 2
esa) gS ftldh Hkqtk12 ls-eh- gSA vkPNkfnr
centres of the three circles as D;k gksxk\ Hkkx dk {ks=kiQy2 (ls-eh-
esa) D;k gS\
shown in the figure. AB = 2cm
A D B C
and CD = 1 cm. If the area of
middle circle is the average of
the areas of the other two A D
circles, then what is the length
(in cm) of BC?
t Slk fd vkÑfr esa n'kkZ;k x;k
ABCD gS] B E C F E

rhuksa o`Ùkksa ds dsUnzksa AB =ls2 xqtjrh gSA

(a) 108 (b) 124 (a) 54 3 (b) 36 3
l seh- rFkk
CD = 1 l seh- gSA ;fn eè; o`Ùk dk (c) 136 (d) 144
(c) 48 3 (d) 52 3
{ks=kiQy] 'ks"k nksuksa o`Ùkksa {ks=kiQyksa dk vkSlr gS] 91. Each interior angle of a regu-
Hexagon
rksBC dh yEckbZ (lseh- esa) D;k gS\ lar polygon is 140º. The num-
A 87. What is the area (in sq cm) of a ber of sides is:
regular hexagon of side 6 cm? (a) 9 (b) 5
6 lsa-eh Hkqtk okys ,d fu;fer "kV~dks.k dk
(c) 7 (d) 10
B
{ks=kiQy (oxZ lsa-eh- esa) D;k gksxk\
92. Each interior angle of a regu-
C lar hexagon is:
(a) 27 3 (b) 54 3
(a) 72° (b) 102°
(c) 54 (d) 27 (c) 60° (d) 120°
D 88. In the given figure, ABCDEF is 93. If one of the interior angles of
a regular hexagon of side 12 cm a regular polygon is equal to
(a)  6 – 1 (b)  6  1 P, Q and R are the mid points of 5/6 times of one of the inte-
rior angles of a regular penta-
the sides AB, CD and EF respec-
(c)  6   4 (d)  6   3 gon, then the number of sides
tively. What is the area (in cm²)
of the polygon is:
85. In the given figure, radius of a of triangle PQR?
(a) 9 (b) 4
circle is 14 2 cm. PQRS is a
nh xbZ vkd`fr esa]
ABCDEF ,d le

square. EFGH, ABCD, WXYZ and

"kV~Hkqt gS ftldh Hkqtk 12 P,lseh
Q gSA (c) 7 (d) 10
94. The sum of the interior angles
LMNO are four identical RkFkk
R Øe'k% Hkqtkvks
AB, CD RkFkk
EF
of a polygon is 1260º. The num-
squares. What is the total area ds eè; fcUnq gSA f=kHkqt
PQR dk {ks=kIkQy ber of sides of the polygon is:
(in cm2) of all small squares? (ls-eh-
2
esa
) D;kgS\ (a) 9 (b) 4
nhxbZ vkd`fr esa] ,d o`Ùk dh14
f=kT;k
2 E D
(c) 7 (d) 10
R Q
ls-eh- gSAPQRS ,d oxZ gSA EFGH, 95. If each interior angle of a regu-
F C
ABCD, WXYZ rFkkLMNO pkj leku lar polygon is 3 times its exte-
oxZ gSA lHkh NksVs oxksZa dk dqy {ks=kiQy (ls- rior angle, the number of sides
A P B of the polygon is:
eh-2 esa) D;k gS\
W X (a) 27 6 (b) 81 3 (a) 9 (b) 4
P
Y
Q
(c) 8 (d) 10
Z
(c) 54 3 (d) 54 6
A B E F
96. Difference between the interior
D C H G
89. PQRST is a regular pentagon. and exterior angles of regular
L M
If PR and QT intersects each polygon is 60º. The number of
other at X, then what is the sides in the polygon is:
O N
value (in degrees) of  TXR? (a) 5 (b) 6
(a) 31.36 (b) 125.44

Telegram Channel-Maths by Sultan Sir, Contact No.-8418077039 7

 (c) 8 (d) 9
97. A polygon has 54 diagonals. The
number of sides in the polygon
is:
(a) 7 (b) 9
(c) 12 (d) None of these
98. The ratio between the number
of sides of two regular polygon
1 : 2 and the ratio between their
interior angle is 3 : 4. The num-
ber of sides of these polygons
are respectively:
(a) 3, 6 (b) 4, 8
(c) 6, 9 (d) 5, 10
99. The sum of all the interior
angles of a regular polygon is
four times the sum of its exte-
rior angles. The polygon is:
(a) hexagon (b) triangle
(c) decagon (d) nonagon
100. The ratio of the measure of
an interior angle of a regular
nonagon to the measure of its
exterior angle is:
(a) 3 : 5 (b) 5 : 2
(c) 7 : 2 (d) 4 : 5

8 Telegram Channel-Maths by Sultan Sir, Contact No.-8418077039