Maths by Amiya - Geometry - 3e Learning

7/23/2019 Maths by Amiya - Geometry - 3e Learning

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177 Geometry Questions


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Maths By Amiya, 3E Learning, www.facebook.com/MathsByAmiya

AMIYA KUMAR

1.

2.


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AMIYA KUMAR

3.

4.

https://www.youtube.com/watch?v=NBZawFsTrvc

5. If in a ABC , AB= 7cm , BC=8cm , CA=12 cm, points D,E,F are on BC,CA, & AB

respectively , such that AF=4 cm, CD=2cm and AE=5cm, Point O is on the intersection of lineAD and EF, then what would be ratio of area of AFO to that of AOE ?

a. 49:36 b. 36:49 c. 20:21 d. 21:20 e. NoT

ans: [e] 144:35


6. If in a ABC , points D,E,F are on BC,CA, & AB respectively , such that AE=3 cm, CD=2cm

and AC=7cm & BD= 5cm, CF is angle bisector of

ACB. Point O is on the intersection of line

DE and CF, then what would be ratio of area of EFO to that of DOC ?


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AMIYA KUMAR

a. 2:5 b. 5:2 c. 1:2 d. 2:1 e. NoT

ans: [e] 13:4


7. If smallest side of an integral right angled triangle is 23 cm then what would be digital sum of

perimeter of this triangle.

a. 2 b. 3 c. 7 d. 8 e. NoT

Sol: [b] 3, sides are 23, 264 , 265

8. If ABC is a right angled triangle with hypotenuse AC=15 cm , points M and N trisect the

side AC, then BM^2 + BN^2 =?

a. 100 b. 125 c. 175 d. 225 e. Not

Sol: [b] 125 , By apolloniusBM^2 + BN^2 =(5/9)*AC^2 => (5/9)*15^2 = 125, or use

coordinate, with origin as B and take AB and BC as 12 and 9 cm, then use section formula and

find coordinates of M & N and get answer.

9. In a triangle ABC, point F and D on side BC such that that BF:FD:DC = 1:2:3. Point E is on

AB and AE:EB = 2:3. If G is mid point of ED, then what would be ratio of area of quad BEGF

to that to that AEDC.

Ans : 2:7

10.In a triangle ABC , D, E & F are points on BC, CA & BA (resp). If D is mid point of BC,

CE=6 cm, EA = 4 cm ; AF : FB = 4:5 and area of quad BDEF is 47 cm^2 then what is the area

of triangle DEC.

Ans : 27

11.If AD = 18cm , BE= 24 cm and CF= 30 cm are medians of ABC and G is centroid. then what

would be area EFG

Ans : 24 ,

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12.If in a ABC, D is a point on side AB such that AD=4cm ,DB=5 cm and DC = 8 cm, then find

the perimeter of ABC if ABC=DCA.a. 27 b. 28 c. 30 d. data inadequate e. NoT

based on previous year MBA question

Ans: 27, sides are 10,12,6 , use similarity , ABC ~ACD


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AMIYA KUMAR

13.If 2,3,4 are altitudes of a triangle then what is the inradius of the triangle.

a. 11/12 b. 12/13 c. 13/12 d. Data inadequate e. NoT

Sol: [b] 12/13

Relation = + + ; where , & 1 = 12 + 13 + 14 = 1312 = 1213

14.

Ans :1315.If in a ABC , AB=7cm , BC=4cm and CA = 10CM . Point D is on BC such that AD is angle

bisector and I is incentre then AI:ID = ?

a. 17:4 b. 2:1 c. 11:10 d. 4:13 e. NoT

16.If in a ABC , AB=BC= 6m and CD = 10cm then what is the distance between incentre and

centroid of the triangle.

17.If is orthocentre of ABC, then which point would be orthocentre of OAC.

18.If in ABC , AB=BC, D is midpoint of BC, E is on AC and F is on AD such that DEF is an

equilateral triangle & AFE is an isosceles triangle. line FG ||AB where G is on BC thenFGD ?a. 30 b. 45 c. 50 d. Can't say e. NoT

19.If in a ABC side BC makes an angle 132at incentre then angle subtended by side BC atorthocentre is ????

a. 100 b. 104 c. 96 d. 86 e. NoT


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20.If in triangle distance between orthocentre and circum-centre is 9.9 cm then what is the

distance between centroid and orthocentre.

Ans: 6.6 , by euler line

21.


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Maths By Amiya, 3E Learning,

The height gain on each face w

journey.

So total distance =

4 10For n=5 , total distance = 10

Alternate :- Open the cube alo

=40cm in one rotation, since

Height gain is 10 but base mov

= 10

+ for number of rotation =5 , Tot

25.There is a solid cheese cube

cube from centre of all the s

similar air tunnels crossing

each tunnel is 1cm*1cm, th

a. 600 cm^2 b. 558 c

Sol : [d]

New surface area = old surface

= 600 + 40 + 36 + 36 - 2 -4 -4

26.What would be total volum

points of all 6 surfaces of a

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uld be 10/(4*n) where n is number of rotati

= 4 1 6 + 1 = 1 016 6 5 + 1 = 1 0 401ng faces , Height gain is height of cube 10c

oves along four sides, and for two rotation

ment is 40*(number of rotation)

0

= 1 0 1 + 4

l distance = 10 401

of dimension 10cm*10cm*10cm. if Jerry a

urfaces in such a way that the rest of the che

ach other at the centre of cube and dimensio

n what is total surface area of the rest chees

^2 c. 698 cm^2 d. 702 c

area + new faces created - faces destroyed

702

created by a 3-D figure, which is created b

cubical room of dimension 10m*10m*10m .

/MathsByAmiya

ns in ants total

+ 1

m but base is 10*4

ts 80.

rat eats the cheese

se cube has three

n of cross section of

cube.

^2 e. NoT

joining the mid


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AMIYA KUMAR

a. 250/3 m^3 b. 500/3 m^2 c. 1000/3 m^3 d. 166.67 m^2 e. NoT

Sol: [d]

The figure is Bi-pyramidal , with base dimension

52 52and height 5m.

so volume = = 52 52 5 = 27.If there is a frustum shaped plastic bucketwhose close bottom is a circle ofinner radius 70 cm

and the top is a circle ofinner radius 140 cm and height is 100 cm. if the total mass of the

bucket with water is 1600 kg then what is the mass of plastic used in bucket.

a. 6 kg b. 60 kg c. 6.6 kg d. 8 kg e. NoT

SOl: [e] Actually total mass would be much greater than given mass.

28.In a right triangle ABC. BD, DE, DF, FGand EH are perpendicular to AC, BC , AB and AD

& DC respectively, Then GD: DH = ?

a. 1:1 b. 1:2 c. 2:1 d. 2:3 e. 3:2

Sol:[a] 1:1

FBED is a rectangle and diagonals BD and EF intersect at point I, midpoint of diagonal EF.G, D

,H are the projections of F, I, E over line AC.Since I is the midpoint of EF ,so D is the midpoint of

GH.

29.There is a solid cubical box of dimension 10cm*10cm*10cm. If N is maximum number of

small cubes of dimension 1cm*1cm*1cm, we can cut from the cubical box such that the total

surface area of remaining box would same as the original box. Then which range best describe

N.

a. Less than 6 b. 7 to 16 c. 16 to 150 d. 150 to 300 e. More than 300

Sol: [e]

Can remove a cube of 9*9*9 from a corner without affecting surface area.so can remove 729

cubes max.

30.What would be maximum volume of a cube inside a semi-sphere of radius 10 cm

31.What would be maximum volume of a cuboid inside a semi-sphere of radius 10 cm

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32.Inside an equilateral triangl

three sides are 1cm, 2cm, &

a. 9

3cm^2 b 12cm^(???)

Sol: [c]

33.In a quadrilateral ABCD if90then its area is ......???a. 1224 b. 2568

Sol: [c]JoinBD and get two rig

the values.

34.If the perimeter of an integr

possible

a. 45 b. 48 c.

Sol: [b]

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35.If three tangential circles to

If we draw a circle such tha

of new circle, Then what is

a. 2 cm b. 2.5 cm

Sol:

Circle would be circum circ

Sides of triangle are 3 cm, 5

R - circum radius of triangl

Or triangle is a right angle

36.If paint used by all colour a

purpule color circle is 1 cm,

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there is a point from which the length of pe

3cm then. what would be area of equilateral

c. 12

3 ^2 d. Data i

B=15cm , BC=144cm, CD=145cm and AD

c. 1284 d. Data inadequate

t angled triangles BAD & BAC and find are

al sided triangle is 45 cm then how many dif

42 d. 56 e. NoT (???)

MathsByAmiya/photos/528057913912996/

ches each other from outside, and their radii

the centre of all three given tangential circl

radius of new circle

c. 3 cm d. 3.33 cm e. NoT

le of triangle formed by joining the centres o

cm & 4 cm

= 4 = 3 5 44 6 = 2.5

(required radius) , a, b , c are sides and istriangle , so R = half of hypotenuse.

e same and radius of smallest

then what is the thickness of

/MathsByAmiya

pendicular on all the

triangle.

adequate e. NoT

= 8 cm with = e. NoT

of triangles then add

erent triangles are

are 1cm, 2cm & 3cm.

s are on the perimeter

f tangential circle.

area of triangle


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balck colour , if thickness o

a.

b.

c. d.

e.NoT

Sol :[d]

Here we have 4 circles with

yellow circle and x is thick

Purple = Total Black = Tota 1 = 11 = 1By solving these = ;

Alternate- Take width of y

37.There is a triangular park A

horse is threaded outside of

cannot entre inside the trian

?????

a. 64*pi - 9 b.

d.61*pi e.

Sol[e]Area covered by horse = Ar

radius 8cm + area at side B

length of rope)

= 8 + =61*pi - com

38.In a triangle ABC , D pointAC=14 cm & AD= 5 cm th

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f balck colour is same with all circles

radius 1cm, (1+x)cm, y cm & (y+x)cm , wh

ess then according to question

l Yellow+ 1 + + = + 1 + + = 1 + = llow is y , then y = 2x (x is width of black)

C, has brick wall on its side. If AB=AC =

the part at vertex A with a rope of length 8 c

gle due to fence, then the maximum area cov

58.67*pi c. 17*pi

NoT

ea of sector (330withwith radius 2 cm (extra

2 mon area

is on BC such that AD is perpendicular on B n what is the circumradius of triangle ABC.

/MathsByAmiya

re y is radius of

1 +

and BAC= 30. Asuch that horse

ered by horse is ....

C. If AB= 40cm ,


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a. 77.77 cm b. 80 cm

Sol: [e] 56 cm

In fig s i n = = According to Sine Formula2 = = 2 = 402 = 56

39.In a triangle ABC, D is on

then =?a. 30 b.15ABC~BDC, Take DC=x

By sine law, = = 3 0

40.In a right triangle ABC. B

& DC respectively, If FG =

a. 4.5 b. 5

Sol: [c]

FBED is a rectangle and dia

of BD & EF so BD=2*ID.

FGHE is a trapezium with I

would be median of trapezi

So,

ID = (FG+EH)/2 = (4+2)/2


41.There are how many differe

is 30 unit

a. 13 b. 14

SOl: [e] 5

If 30 is not hypotenuse (tak

h^2 - b^2 = 30^2

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c. 70 cm d. 66.66 cm e.

C such that BD is medianand

BDC=

45, i

c.45 d.60 e., AC=2x, then BC=2x.

, DE, DF, FG and EH are perpendicular to

4 cm & EH = 2 cm then BD =?

c. 6 d. 7 e. NoT

gonals BD and EF intersect at point I (say) s

as midpoint of its unparallel sides, and ID ||

m,

3 cm, so BD = 6 cm.


nt integral sided right angled triangle are pos

c. 12 d. 15 e. NoT

30 as perpendicular) , then

[h & b must be even]

/MathsByAmiya

NoT

= =NoT

C, BC , AB and AD

o I would be midpoint

o parallel sides, so it

sible whose one side


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AMIYA KUMAR

By this case we would get 4 values = = 4 [ ] is GIFIf 30 is hypotenuse, then its factor should be crude hypotenuse , and factor of 30 only crude

hypotenuse is 5 (with 3,4,5) so 30 as hypotenuse would have only one integral triplet which is

18,24,30

SO total required triangles = 4+1 = 5

By NitinGuppta Sir-

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&type=1

42.If area of a trapezium ABCD is 180 unit square whose height is 20 unit and one parallel side is

10 unit. If P and Q are mid points of diagonals AC & BD then PQ = ?

a. 1 b. 2 c. 2.5 d. Cannot be determined e. Not (???)

Sol: [a]

Another parallel side would be 8 unit so PQ = (difference of parallel side )/2 = 1 unit

43.Ifexradii of a triangle are 12; 18 & 36 cm.Then find the area of trianglea. 36 cm^2 b. 108 cm^2 c. 1082cm^2 d. 216 cm^2 e. NoT

Sol: 216 cm^21 = 1 = 112 + 118 + 136 = 16 = = 6 1 2 1 8 3 6 = 2 1 6

44.If I is incetnre ofABC where AB=AC=15 cm , BC=24 cm & D is midpoint of BC then AI =

?

a. 3 cm b. 4cm c. 5cm d. 6 cm e. NoT

Ans : [c]

45.If in ABC , points E & are on sides AC & AB respectively such that AE:AC=2:5 &

AF:FB=4:1 and if BO= 15 cm then OE =? , where O is point of intersection of CF & BE.

a. 20 cm b. 24 cm c. 36 cm d. 40 cm e. NoT


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AMIYA KUMAR

Ans : [c]

46.In a PQR , points S & T are on PQ , such that QT=2*PS=2*ST=2 cm, point U is on QR such

that QU=3cm & UR = 2cm and point V is on PR such that RV=4cm & PV=3cm. M & N are

point of intersections of line "QV & RS" and "QV &UT" respectively, then MN/QV=?

a. 4/25 b. 3/5 c. 8/25 d. 6/25 e. NoT

Ans [e]1 = 47.How many triangles are possible whose two altitudes are 6cm & 8cm and other altitude is also

a natural number.

a. 18 b. 13 c. 20 d. 21 e. NoT

Sol:

Altitudes are - 6 , 8 & x (let) so side ratio is 8x : 6x : 48

By basic property14 > 48 & 2 < 48 (sum of two sides is greater than third and difference is less than thirdside)3.42


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52.If in a ABC, points D & E

such that AQ:QC=3:4. Poin

BQ" respectively. If OP:BQ

a. 2212 b. 316

Ans: [b] 81:235 , sum=316

53.If in a ABC AB=6cm, BC

median, points D & E lies o

BE then PE = ?

a. 2cm b. Ans: [d]

54.In a ABC , D lies on BC s

lies on CE such that CF:CE

a. 4:5 b. 1:5

55.In an isosceles ABC, if A

what is the distance betweea. 0.33 b. 0.25

Ans [d]

56.Total number of point of int

regular octagon

a. 28 b. 64

e. NoT

Sol: 4*8 + 3*8 + 1 = 57

A regular polygon makes sa

are 4 octagon, just need to c

outer side , which are 8-5=3

gravity.

57.Total number of point of int

hexagon

Ans :- 2*6 + 1*6 + 1 = 19

A regular polygon makes sa

hexagon, just need to check

side , which are 6-5=1 , and

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are on side BC such that BD:DE:EC = 2:3:4

ts O & P are points of intersections of line "

= m:n then m+n = ? (m & n are co-primes)

c. 4 d. 235 e. NoT

7 cm, CA= 8cm , AD is angle bisector of a

n sides BC & AC respectively. P is point of i

c. 4/5 d.106 /5

ch that BD:BC=1:2 , E lies on AD such that

= 1:4 , O is point of intersection of lines AD

c. 1:3 d. 1:4 e. NoT

=AC=10 cm , BC=16 cm , I and G are ince

I & Gc. 0.5 d. 0.66 e. NoT

ersections (PoI) of all diagonals of a

c. 33 d. 57

me fig with PoI of diagonals, there

heck points on second octagon from

, and one more point at centre of

ersections (PoI) of all diagonals of a regular

me fig with PoI of diagonals, there are 2

points on second hexagon from outer

one more point at centre of gravity.

/MathsByAmiya

& Q is on side AC

D & BQ" and "AE &

gle A , and BE is

ntersection of AD &

e. NoT

AE:AD = 1:3 & F

& BF then BO:BF =?

tre& centroid then


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58.If the area and perimeter of

side of triangle is 13 unit th

this triangle.

a. 1 b. 7

Sol: [c]

Sides of triangle are, 5,12&

59.In the fig. point A and C are

circles, point B lies on the b

that

ABC=

90; D & E lie

circle and these two are poiintersections of AC and circDBE=?a. 20 b.30c.45 d. Data ie.NoT

Sol:

DBE180BDEB60.In ABC, AC=14cm, point

then AD =?

a. 12 cm b.

Sol:

Draw DE (where E is midp

AD=AE = 7 cm, (MPT)

61.There are two concentric ci

which cuts smaller circle at

which is perpendicular on

igger circles respectively a

one is a correct relation

a. x + y + z = R - r

c. x + y + z = R + r

e. NoT

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a triangle have same numerical value which

n what is the different between longest side

c. 8 d. Cant Say e. NoT

13, by Heron's formula.

centre of these two

oth the circles such

s on the each

t ofles, then

adequate

ED1801/2(180A)1/2(180C)D is on BC such that, AD is median, BAD7 cm c. 14 cm d. Data inadequ

int of AC), by MPT AB||DE , and ADE is

cles with centreO, AB is chord of bigger cir

B and C. EB is a chord of smaller circle

B.If r & R are radii of smaller and

nd AB = x , BD= y & BE = z then which

b. x + y + z = 2(R - r )

d. x + y + z = 2(R + r )

/MathsByAmiya

s 30 and the longest

and smallest side of

1/2(AC)45= 50 &CAD= 80te e. NoT

n isosceles , so

le


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Sol: [d]

Hint:- Use Pythagoras & E

62.What is the approxcurve su

inner diagonal is 2.0cm and

a. 3.93 b.6.47

Sol:

Curve Surface Area = (pi^2

63.What would be ratio of side

hexagon

a. 3 + 3 b.Sol: [b]



e=1

64.What would be ratio of side

a. b.

Sol: [b]


65.If PQ & PR are two tangent

AB on the same circle touc

respectively. If Radius of th

a. 26 cm b. 24 cm

Sol:[b]

Perimeter of PAB = PA+

66.What would be ratio of area

that of blue coloured shape

a. 4:3 b. 3:4

c. 1:1 c. 9:8

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is diameter of smaller circle and AB=CD

face area of an uniform circular ring in cm^

outer diagonal is 3.0 cm

c. 12.34 d.15.78 e.NoT

*(R^2 - r^2) = (pi^2)*(1.5^2 - 1^2)= 12.34

of a largest square inside a regular hexagon

3 3 c. d. MathsByAmiya/photos/584494198269367/

photo.php?fbid=744000315659641&set=p.7

of a largest regular hexagon inside a square

c.

d.

e.


s from a outside point P on a given circle. A

es circle at C and points A & B lie on the ta

e circle is 5 cm and CP is 8 cm then what is

c. 30 cm d. 21 cm

B+AB = PA+PB+AC+BC= PA+PB+AQ+B

of pink coloured shape to

/MathsByAmiya

(wedding ring) if its

m^2

o that of regular

e. Not

4000315659641&typ

o that of square

NoT

d another tangent

gents PQ & PR

erimeter of PAB

= PQ + PR = 24cm


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AMIYA KUMAR

Sol: [c]

Let side of the square : 4r ; Then Total area of 4 small circles 4*(pi*r^2)=4(w + blue area)

Where w - white area inside small circles.

Now Area of big circle =>4*pi*r^2=4(w + pink area)

=> Pink area = Blue area.

67.Let L , M & N are three parallel lines , M is in the middle on two, such that the perpendiculardistance between LM & MN are 2cm &5 cm respectively. Points A, B &C are lines L, M &

N respectively such that ABC form an equilateral triangle then what is the length of ABC

a. 313 b. 214 c. 2 13 d. 3 14Sol: [c]


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68.If in a triangle ABC, ABC= , such that tan= cotand cosec sec >thenhow many integral value of k would be possible

a. Not Possible for real K b. Never Possible c. 3

d. 5. e. NoT

Sol:

tan = cot = 45


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AMIYA KUMAR

cosec sec >; positive for = 4 5 ; it shows angle is in second quadrilateral,where cosec sec = 2 2 = 22 > = = 0 , 1

69.If two circles of equal radius intersect at two different points C & D. If A & B are centre ofthese two circle, & line AC cuts other circle whose centre is B at E, such that EAB = 20thenEBA = ?a. 20 b. 70 c. 80 d. 100 e.NoT

Ans: [e]120, isosceles triage property.70.There are four points A, B , C & D are in a plane such that AB=BC=CA=DA, If Line AD

intersect Line BC at E such that ED:AE = 1:10 then BDC = ?a. 60 b. 120 c. 135 d. 150Sol: [d]

http://youtu.be/Ouw21pvOyFA


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71.IF in ABC, D, E and F are

Further, each of the ratio A

triangle XYZ and triangle

a. 2 :9 b.

Sol:[b]

Since there is a unique answer (

equilateral. This will reduce ou

Now the non-overlapping areas

Alternatively : By Routh's theorem, here x=

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the points of trisection of respective sides, a

: XD, BY : YE and CZ : ZF is 3 : 4. Find t

BC

1 : 7 c. 3 : 7 d. 4 : 9

as the options suggest, we can safely assume

r work considerably.

that appear similarly placed about the three

area. Assuming the areas as x, y and z as sh

have = = ..2 + + 2 + = 12 3 = .Also, = = .. = 4Plugging x in terms of z, we have y = .We need to find the ratio of ..

= =z = 2;http://en.wikipedia.org/wiki/Ro

/MathsByAmiya

shown in figure.

he ratio of the areas of

triangle ABC to be

ertices will equal in

wn in the figure, we

. = 3+ = 3 .

..

th's_theorem


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AMIYA KUMAR

72.If three circles and a straight lines touches each other at six different points &radius of

two bigger circle is 4cm and 6.25 cm then what would be radius of smallest circle in cm.a. 0.123 b. 1.234 c. 2.33 d. 1.66 e. NoTSol:[e]This is case of mutually tangent circle , looking for radius of smallest circle R3 [Descartes'theorem]1

4= 1

1+ 1

2+ 2 1

1 1

2

14 = 1004 + 1006.25 + 2 1004 1006.25 14 = 81 4 = 1.23456790 = 0.0123

73.There are how many different integral sided triangle possible whose perimeter is 18 unita.5 b. 6 c. 7 d. 8Sol: c 7

By manual process: Different triangles are{2,8,8},{3,7,8},{4,7,7},{4,6,8},{5,6,7},{5,5,8},{6,6,6}

By Formula :Total number of integral triangles = Nearest Integral value of

= 6 . 7 5 = 7https://www.facebook.com/MathsByAmiya/photos/528057913912996/ 74.For given perimeter P unit of triangle , there are 12 different integral sided triangle arepossible, then what is the sum of digits of P ?a. 5 b. 6 c. 7 d. 8

Sol:[b]If P is even then 11.5


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There is no such odd PSO only 24 Unit perimeter w

P is 6https://www.facebook.com/75.In the given fig, ABCD is aA rectangle DEFG with EFED & DG lies on side of sqcircle. Then find the area

a. 900 cm^2 b.c. 994 cm^2 d.e. NoT ???

Sol: [e]Construct the same fig, SO inare in Pythagoras, So by solviR=35 cmSo side of square = 70 cmArea of Shaded Region = AreArea of Rectangle= 70^2 - 22/7*35*35 - 7*1= 952 cm^2

76.What would be area of riglongest side and smallesta. 10.8 b. 21.6

Sol: [c]Since sides are in AP of rightdifference = 1.8 given so si

Required area = 1/2*5.4 *www.facebook.co

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will get 12 different integral sided triangl

athsByAmiya/photos/52805791391299 square, circumscribing a circle .7cm & FG=14cm, whose sidesare & one vertex F is on thef shaded region [take pi=22/7]

. 936 cm^2. Cannot be determined

FOP , R radius, R-7 and R-14g we will getof square - Area of circle -

t angled triangle whose sides are in AP aide is 3.6 cm.c. 19.44 d. 43.2 e. NoT

ngles triangle so , it should be multiple ofes would be 1.8*3,4,5 = 5.4, 7.2 & 9.

.2 = 19.44/MathsByAmiya

e, so sum of digits of

/

d difference of

,4,5 , and common


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AMIYA KUMAR

77.There are how many different integral angled triangles are possible

a. 180 b. 1800 c. 1980 d. 2700 e. NoTSol: [d]https://www.facebook.com/MathsByAmiya/photos/604561656262621/

78.Ans: a ,Since triangle ABC is isosceles so ABC=ACB=80AndEBF=40 and FCE=30 By SASTriangle DfAE congruent to Tri. CAbE case SASSo FE=CE and CFE= ECF =30In , CFE + x=50 ;30 + x=50; x=20


24/45


Direction for questions 78Direction for questions 78Direction for questions 78Direction for questions 78as shown in the fig then

79.APD =?a. 130 b. 160Ans: [e] 15080.CPD =?a. 45 b. 60Ans: [c] 75

81.BPC= ?a. 30 b. 60

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AMIYA KUMAR

to 8to 8to 8to 84444::::----There are four congruent circles wi

c. 175 d. 105 e. 150

c. 75 d. 90 e. NoT

c. 75 d. 45 e. NoT/MathsByAmiya

h centres A,B, C & D


25/45


Ans: [b] 6082.PAQ =?

a. 30 b. 60Ans: [b]6083.SBP =?a. 30 b. 15

Ans : [a]30

84.

QSC =?a. 30 b. 60Ans: [d] 10585.QPD =?a. 30 b. 60

Ans: [e]15086.If in a ABC , AD is mediaAC= 14 cm then AD =?

a. 7* sin30 b. 7* sinSol: [d] 7

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AMIYA KUMAR

c. 75 d. 45 e. NoTc. 20 d. 22.5 e. 27.5

c. 75 d. 105 e. NoT

c. 75 d. 105 e. 150

& D lies on side BC such that BAD = 805 c. 7* sin60 d. 7* sin

/MathsByAmiya

DAC=20 and0 d. NoT


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87.A regular polygon with 527

common circumscribe circl

vertices are

a.13 b.17

Sol: [b] HCF (527, 221)=17http

88.If two altitudes of a triangnatural number in cm thea. 5 b. 8Ans: [d]

89.If in the given fig AB=BC=a. 36 b. 72Ans : [b] 72

90.If in a triangle ABC , poinCE:AE= 2:3 & AF:AB=3 :of triangle AFEa. 29:55 b. 27:50Ans: [d] By ratio of side a

91.If in the given fig P,Q & R, BC=2*CP & 2*CA=3*QA ;a. 11:3 b. 14:3Ans: [b] ; By ratio of side a

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AMIYA KUMAR

vertices and another regular polygon with 2

if they have some common vertices thentot

c.31 d. 30 e. NoT

://youtu.be/JEKl2VN-oNY

es are 3cm and 4cm and magnitude of anhow many different triangles are possiblc. 9 d. 10 e. NoT

CD=DE=EA then BFD = ?c. 40 d.80 e.NoT

ts D,E & F are on sides BC, AC & AB such tthen what would be ratio of area of quad c. 55: 29 d. 50:27 e. NoTd area sine formulare on the extended sides of BC, CA & AB, sthen arthen arthen arthen arPQR: arABC= ?PQR: arABC= ?PQR: arABC= ?PQR: arABC= ?c. 13:3 d. 4:1 e. NoTnd area sine formula

/MathsByAmiya

1vertices has a

l number of common

ther altitude is a.

at BD:DC=1:2 ;ilateral BDEF to area

ch that AB:BR =1:1


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AMIYA KUMAR

92.If in a ABC , points D,E & F lies on side BC, CA & AB . If Centroid "G" lies on AD and pointsE & F are mid points of their respective sides. If EF & AD intersect at point I, then AI:GD=?a. 1:2 b. 2:1 c. 2:3 d. 3:2 e. NoTAns : [d] By MPG AI:IG:GD = 3:1:2

93.To save a circular grass land of diameter 28 m from sheep there is an uniformentrenchment all around the grass land which is 14 m wide at top 10 m wide at bottomand 10 m deep, which is completely field with water. Then how much litter water is usedto fill the entrenchment.a. 2.112 * 10^7 lit b. 1.584 * 10^7 lit c. 2.64*10^7 litd. NoTSol: [b]Area of entrancement = 1/2*14+10*10 [Shape is of an trapezoid]= 120 m^2

If we cut the entrancement and open wide it would be a prism , whose length =2*pi*14+7 = 2*22/7*21= 132m

SO vol of entrenchment = 120*132 =15840 m^31m^3 = 1000 lit waterSo water capacity of entrenchment = 15840000 lit = 1.584 * 10^7 lit94.A old rectangular carom board isa home of four ANTs. They live in the each hole of theboard. Carom has four holes one in each corner One day 3 of them decided to meet atone place then go to fourth home all together. If the distance between meeting point andhome of three antsare39 cm, 52 cm &60 cm, then what would be the maximum distance

covered by any one of the three ants to reach the home of fourth ant from its home if allof them cover distances in straight line and ants which covers distance 39 cm and 52 cmlive in opposite cornersa. 75 cm b. 80 cm c. 85 cm d. Can't be determined e. NoTAns :[c]

95. If in a ABC , a+b+c= 30 cm , where a,b& c are sides of and s is semi perimeter then = ?a. 30 b. 0 c. 1 d. 15 e. NoTAns: [c]


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AMIYA KUMAR

96.If sides of a parallelogram is 12 cm and 13 cm and its area is 60 cm^2 then what is the approx

length of its major diagonal.

a. 24 cm b. 24.5 cm c. 26 cm d. 27 cm

Ans: [b] 601=24.597.In a right angled ABC , right angle is at B. If AC= 10 cm, median AD= 2 cm then whatwould be length of median CFa. 10 cm b. 11cm c. 12 cm d. Can't Be e. NoT

Sol:DATA IN THE QUESTION IS WRONG

In any triangleIn any triangleIn any triangleIn any triangle + + = + + ;where ,&are respective mediansso in right angled at B , = 23 + + & = 10 = 2 + 5 + x= 11Alternative :In Right angled triangle at "B"In Right angled triangle at "B"In Right angled triangle at "B"In Right angled triangle at "B" + = 2 + = 5 5 =11But median of any triangle cant be more than the hypotenuse , so the data of the questionBut median of any triangle cant be more than the hypotenuse , so the data of the questionBut median of any triangle cant be more than the hypotenuse , so the data of the questionBut median of any triangle cant be more than the hypotenuse , so the data of the questionis wrong.is wrong.is wrong.is wrong.MAIN REASON TO POST THIS QUESTION IS TO LET YOU KNOW ALL FOUR CONCEPTS

98.What would be ratio of inradius tocircum radius of a triangle whose angles are in theratio of 1:1:4a. b. 3 + c. 3 d.Sol: [c]Angles are 30, 30 & 120 so = cos30 + cos30+ cos120 1= 3 32



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AMIYA KUMAR

99.If AD, BF & CE are the altitude of ABC, such that AO= 4

cm, OD= 3cm & BO=6 cm then among option which could

be a possible length of altitude CE

a. 3.7 b. 59 c. 54.55 d. 56

Sol: [c]

We know,

AO*OD=BO*OE=CO*OF

4*3 = 6*OF OF = 2cmSo, AD= 7cm & BF= 8cmThus Range of CE would be7 87 + 8 < < 7 88 7 3 . 7 3 3 < < 5 6By checking options only 55.01 comes in the range hence chttps://www.facebook.com/MathsByAmiya/photos/794476340604484/

100. If 3cm, 4cm & 5cm are altitudes of a triangle then what would be in radius of thattriangle

a. 1/12 b. 30/47 c. 60/47 d. 47/30Sol: [c]We know , = + + = + + = r= 101. If ABCD is a trapezium such that AB||CD and AB= 80cm & CD= 20 cm. Points M & Nare n non parallel sides, MN is||AB it divides trapezium in two equal halves then lengthof MN =?

a. 30 cm b. 40 cm c. 50 cm d. NoTAnd :d. NoT = 1034https://www.facebook.com/MathsByAmiya/photos/528568450528609/ 102. If two adjacent sides of a parallelogram is 10cm and 12 cm and one diagonal is 8 cm. Then

what is the length of another diagonala. 8 b. 2 106 c.106 d. Data adequate or NoT

Sol: By Apollonius ,

10 + 12 = 2 4 + ; where a is half of another diagonal.

so diagonal = 2 106


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AMIYA KUMAR

103. If a cone of radius 10 cm and of height 10 cm is filled till 5cm from its close end (tip) then

sealed with a circular sheet (of negligible width) then turned upside down, then what would be

the range of height of water surface inside the cone (from circular base & Assume all figures

are under 100% spirit levelled)

a.[0,1] b. ]1,2] c. ]2,3] d. ]3,4] e. ]4,5]

Sol:

Vol of water (tip is downside) = 5

Vol of water (circular base downside) = 1 0 + 10 + 1 0 1 0

1 0

+

10

+

1 0 1 0 =

5 3 0 + 3 0 0 1 2 5 = 0 = 5 2 7 0.43104. If side of an equilateral triangle ABC is 3 cm and point D is on BC such that BD=1cmthen AD=?a. 2.7 cm b. 7 c. 8 cm d. NoT ???

Sol: [b]If = then 9 = 7

105. If in a plan there are four points such that AB=BC=CA=DA and angle BDC = x degree, where x is less than 180 degree , then maximum possible value of x= ?Ans : 150 degree

106.

If AB, AC & DE are common tangents to two given circles whose centre are P & Q asshown in fig, such that AD= 6 cm , AE = 10 cm & DE= 8cm then what is the distancebetween P & Q.a. 42 cm b 82 cm c. 45 cm d. NoT


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Sol: [c]We have Radius of Circleand Radius of circle of cenSince ADE is a right angleAssume D is originSo coordinate of Q = 2,-2& co-ordinate of P = -6,-So QP = 45 cmhttps://www.facebook.co107. If 6cm and 8cm are lenradius of circle inscribed i

a. 2.5 b. 2.4Sol: [b] = 6 8

2 6

+ 8 =2.4

or can apply = www.facebook.co

AMIYA KUMAR

f centre Q = 2 cm [inradius of tri tre P = 6 cm [ ex radius = triangle so we can work on this by co-or [IVth quadrant] [IIIrdQuard][By Distance Formula]/MathsByAmiya/photos/81228309215

gth of diagonals of a rhombus then whatthis rhombusc. 5 d. 6 e

/MathsByAmiya

ngle, = ]]inate geometry .

142/ould be length of

. NoT


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AMIYA KUMAR

108. If in an isosceles triangle ABC , BC=4cm and circum-radius is a square of a primenumber who is even then angle C = ?

Ans: 15or30or 75 or 120 degreesince angle A=30 or 150 degree, and we dont know whichtwo angles or sides are equal109. If in triangle ABC , D,E & F are points on side BC, CA & AB such that BE is median ,BD:DC=1:2 & BF:FA = 2:3 then BO:OE=? [if O is point of intersection of BE & DF

a. 7:4 b. 4:7 c. 5:6 d. 6:5 e. NoT

Ans :[b]110. If in triangle ABC , D,E & F are points on sides BC=4cm, CA=5cm& AB=3cm such thatAD, BE & CFal angle bisector and I in in-centre then AO:IO =? , [if O is point ofintersection of EF&AD]a. 14:5 b. 5:15 c. 3:1 d. 1:3 e. NoT

Ans: [c]111. If in a triangle ABC . D lies on the side BC and on line AD , O is point such that

AO:OD=BD:DC=2:3 if we join points B & O and extend it to line AC then it cuts the line ACat E. Then AE:EC=?a. 19:4 b. 4:19 c. 4:15 d. 15:19 e. NoTAns : [c]112. If side ratio of a triangle is 10:11:12 then what is the ratio of circum radius to in-radius

a. 13:7 b. 40:19 c. 80:39 d. Can't Say e. NoTSol: = 4 & = = 4 = 4 = 4

For a=10x , b=11x& c=12x => =


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113. If radii of all four circl

a G.P series thenarea of a. Largest radius among allb. Product of smallest radiusc. Square of 2nd smallest radid. Product of 2nd smallest an

Sol: [d]= rest are exradius of a triagnle.114. What is the maximumtriangle.a. 1 b. pi

Ans : [c] , for equilateral tr115. What would be approone side is 7 cm.a. 472.916 b.Sol:[c]For a given perimeter , Arconsider it as a circle of ciarea of polygon should beDirection :Direction :Direction :Direction :If in a trianglesuch that Perimeter of A

116. Length of BD = ?a. 20 b. 25Ans : [b] - Median

117.

Length of BEa. 12 b. 125Ans :[b] , Best is coordinatwww.facebook.co

AMIYA KUMAR

s are consecutive terms of

would be equal tond 3rd largest radiuss3rd smallest radius

herer is inradius andalue of ratio of area of in-circle of a trian

c. pi / 3* sqrt3 d. 2

iangle.x area of a regular convex polygon with 1. 478.169 c. 458.916 d

a of a circle is maximum . Perimeter of thicumference = 77cm so the area of this cirless than 472 , hence [c]B = 30, BC= 40 & CA = 50 , D and E are tE = Perimeter of BEC & Area of ABD =

c. 26.66 d. 23.33 e. NoT

c. 18 d. 18 5e geometry/MathsByAmiya

le to area ofe. NoT

1 sided fig whose.480s polygon is 77 cm ,cle is approx472. soo points on side ACArea of BDC, then

e. NoT


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AMIYA KUMAR

118. Length of DE = ?a. 3 b. 4 c. 5 d. 6 e. NoTAns : [c] 5, Best is coordinate geometry119. If a robot only moves in straight line and only takes either left or right turn and hismovement path is marked by a LASER. One day he started from a point and reach at thesame point and facing same direction as initially he was after taking 20 right turns thathow many left turns he has taken, if he never repeated or crossed a path which is alreadymarked and never take more than one turn on a point.a. 20 b. 16 c.24 d. b or c e. NoT

Sol: [d]Take Left turn as 90 degree and right turn as 270 as internal angle of a closed polygon,and we know sum of all internal angles = 180n-2 , n is vertexHere90*l + 270*r = 180 l+r-2 , by question r=20, we get l=24Now, Take Left turn as 270 degree and right turn as 90 as internal angle of a closedpolygon, and we know sum of all internal angles = 180n-2 , n is vertexHere270*l + 90*r = 180 l+r-2 , by question r=20, we get l=16So either 24 or 16.Direct formula = |left turnDirect formula = |left turnDirect formula = |left turnDirect formula = |left turn ---- right turn| = 4right turn| = 4right turn| = 4right turn| = 4

120. In a PQ=QR ,angle PQR = 90and S and T are points on PR such that PS^2 +TR^2 = ST^2 then angle SQT = ? in degrea. 30 b. 45 c. 60 d. 75 e. NoT

Ans : [b] , solve by options or coordinate or sine formula121. If the equation of one side of an equilateral triangle is 3x+4y=5 and its one vertex is5,5 then what is its areaa. 63 b. 123 c. 93 d. 15 e. NoTAns : [b]

122. What is the ratio of side of a hexagon to a square of maximum area inside the same

hexagona. 3 - root 3 b. 3 - root 2 c. 2 - root 3 d. 2 - root 2 e. NoTAns : [e]


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https://www.facebook.co123. If perimeter of a triangl

two sides are odd integer re

a.12 b. 6

Ans : [d]

124. If length of minor arc cr

OAB = ? (where O is the ce

a. 1 rad b. 2pi -1

Ans : [c]

125. What would be diametpoint E such that , CE=2 ca. 12 cm b.Ans: [b]

126. https://www.faceboo127. What would be radiusradius is 12 cm and centra. 6cm b. 4 cm

Ans: [b]4

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AMIYA KUMAR

/MathsByAmiya/photos/58449419826is 24 cm then how many different triangles

t is even.

c. 3 d. NoT

eated of a chord AB is equal to radius of the

ntre of circle and A & B are on the centre)

rad c. pi - (1/2) rad d

er of circle whose two chords AB and CD, CD= 9 cm & EB= 3 cm.. 122 c. 129 d

.com/MathsByAmiya/photos/84041359of circle of maximum area inside a sectorl angle of sector is 60c. 23 d. 12 e. NoT

/MathsByAmiya

367/ossible where only

circle .then angle

.60 degree

ake angle of 90 at. NoT

010758/f a circle whose


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AMIYA KUMAR

128.Ans: 10 cm^2


129. There are how many convex polygon possible such that integral angles are in AP andinteger and the smallest angle is 30a. 8 b. 17 c. 3 d. 4 e. NoT

Sol: [e]NoT180*n-2=n/22a+n-1d, here a=30For convex polygon we get only 2 set of values

http://www.wolframalpha.com/input/?i=180*%28n-2%29%3D%28n%2F2%29%282a%2B%28n-1%29d%29%2C+a%3D30%2C+n%3E0%2C+d%3E0


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130. If angle ABC=angle BC

cm , DE= 9 cmThen EF =?

a. 3 cm b.

d. 4 cm e.

Ans: [c]

https://www.facebook.com/Mat

131. If in a ABC, AB=16 c

IA =?

a. 6 cm b. 217Sol: [e]

inradius = 6 , so centre (6,6) an

132. What would be side of i

ABC such PQ lies on side

a. b.

Sol: [c]

https://www.facebook.com/Mat

133. If in a triangle ABC, A

pentagon then what is the

a. 60 b. 114

Ans: [e] cannot be determined

134. https://www.facebook.c

Ans: [b]

135. If the semi-perimeter of

what would be area of the tr

a.1600 cm^2 b.

e. Not

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AMIYA KUMAR

A,BF=7 cm, CE= 5

3.4 cm c. 3.6

NoT

hsByAmiya/photos/853093624742755/

, BC= 30 cm & CA= 34 cm and I is incetre

c. 8 cm d. 35 e.A=(0,16) so IA= 6 + 10 = 1 3 6 = 2

scribed square PQRS having maximum are

C, angle ABC=30, angle ACB=60and sidec.

d. e. NoT

hsByAmiya/photos/532772120108242/

is also a side of a regular hexagon and AC

easurement (in degree) of angle BAC ?

c. 120 d. 108 e. NoT

m/MathsByAmiya/photos/85915328080345

right angled triangle is 154 cm and smallest

iangle.

1440 cm^2 c. 1540 cm^2 d

/MathsByAmiya

of the triangle then

NoT

34inside a triangle

AC= 6 cm

is side of a regular

6

edian is 72 cm then

. Data inadequate


38/45


AMIYA KUMAR

Sol: [c]

Area = (s c)*s = 1540 cm^2



39/45


136.

137. How many set of data g

[P= Perimeter, A , B, & C a

I. P = 16 cm , c = 9 cm, A= 6

II. a=b= 12 cm, A= 60

III. A= 60; B = 30; C = 90

IV. A= 60; B = 45; a = 4cm

a. Only one set of data

c. Three sets of data

e. NoT

Ans : [a] only II is possible

138. How many statements a

I. 1 1 I

IV VAns: 4

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AMIYA KUMAR

ven below is (are) sufficient to construct an

re angles & a,b & c are sides to correspondin

, b= 3 cm

b. Two set of data

d. By all we can construct uniq

e correct

. III.

. 5 5 VI

/MathsByAmiya

nique triangle ABC.

g angles]

e triangle


40/45


139. How many different set

S are positive integers in w

elements is greater than thir

a. 133 b. 33

Ans: [c] , question is of triangle

140. How many triangles are

prime number.

a. 25 b. 24

Ans: [d]

141. In the given fig ,QA:AB

142. In the given fig ,QA:AB

Ans: 36:13

143.

If in a right angled AD= 4 cm & CD = 9 cm th

Ans: 39 cm^2

144. In given , PR:RJAns: 1:7

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AMIYA KUMAR

S are possible, if S is set having three eleme

ich two are odd and one is even, it is known

d element and sum of all elements is 80.

c. 100 d. 80 e. NoT

whose perimeter is 80.https://youtu.be/Pv

possible whose two sides are 50 unit and 47

c. 23 d. 22 e. NoT

= RB:BC =PC:PA = 1:3 , then

?

= RB:BC =PC:PA = 1:3 , then

?

, point D lies on AC such that angle A n area of ?[in cm^2]

1:3 , AQ:QP = 3:4 then QO:OJ = ?

/MathsByAmiya

nts, all elements of set

that sum of any two

hMly9cFY

unit and third side is a

90


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145. In given , PR:RJ

Ans: 1:1


Ans: 1:1


Ans: 25:52


149. In given , PR:RJ2:3 then

Ans: 5:4


Ans: 8:15

151. In given , QO:OJ= ?

Ans: 1:15

152. In given , PQ:QR:

Ans: 10 : 7

153. In given , PQ:QR:?

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AMIYA KUMAR

1:3 , AQ:QP = 3:4 then AO:AR = ?

5:3 , AQ:QP = 3:5 then

?

5:3 , AQ:QP = 3:5 then

?

4:3 , AQ:QP = 3:5 & AS:SJ = 2:3

?

4:3 , AQ:QP = 3:5 & AS:SJ =

?

3:2 , AO:OR = 4:3 then AQ:QP = ?

= 3:2 , AO:OR = 4:3 then AQ:QP

RJ = 2:2:3 , AS:SJ = 4:3 then PM:MN = ?

RJ = 2:2:3 , AS:SJ = 4:3 then PS:MN

/MathsByAmiya

then

=


42/45




Ans: 8:17

156. is a right angledon AB & BC such that AD:

what is the distance length

a. 5 b. 7Ans: [c]

157. If are three altitudes of

a. 3 cm b. 6 cm

Ans: [a]

158.

If 3, 2 & 2 are three altit a. 4/3 b. 3/4

Ans: [b]

159. If O is orthocentre of tri

= 2 cm, BO = 6 cm then O

a. 1.5 cm b. 1 cm

Ans: [b]

160. How many different tria

altitude is an even number.

Ans: 19

161. If 3, 2 & 2 are three altit

a. 12 b. 9/(4Ans: [d]

162. If 3, 2 & 2 are three altit

a. 6 b. 62 c.

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AMIYA KUMAR

RJ = 2:2:3 , AS:SJ = 4:3 then

?

RJ = 2:2:3 , AS:SJ = 4:3 then

?

triangle at B, in which AB= 9 cm & BC = 8

B = BC:BE = 2:1 . O is the mind point of li

f BO (in cm)

c. 2.5 d. 3 e. NoT

triangle is 3cm then what is the perimeterc. 4.5 cm d. CBD e. NoT

udes of a triangle then what is in-radius of thc. 1 d. 1.5 e. NoT

angle ABC , and AD, & BE are altitudes, suc

= ?

c. 0.5 cm d. CBD e. NoT

ngle are possible whose two altitudes are 7 c

udes of a triangle then what is the area of the

) c. 6 d. (92) / 4 e.

udes of a triangle then what is the perimeter

63 d. 7 e. NoT

/MathsByAmiya

m. Point D & E lie

ne segment DE then

of triangle

e triangle

h that AO= 3 cm, OH

& 6cm and third

triangle

NoT

of the triangle


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Ans : 62

163. If in a , AD, BEcm then angle A = ?

a. 67 b. 85

Ans: [e] NoT it should be o

164. If in a lengthtriangle is

a. 150 b. 115

Ans: [c]

165.

If in , AB= 2 cmthe in centre of the triangle

a. 5:4 b. 13: 30

Ans: [c]

166. If in , AB= 10 cwhat is the area of ?

a. 6 cm^2 b. 8 cm^

Ans: [c]

167. If ABCD is a square tar

square ABCD, then what is

a. 20 % b. 50%

Ans: [c]

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AMIYA KUMAR

& CF are altitudes such that, AD = 6 cm, BE

c. 90 d. 30 e. NoT

tuse

f altitudes are 30 cm , 40 cm & 24 cm then

c. 90 d. 120 e. NoT

, BC= 4 cm & CA = 3 cm. AD, BE & CF are

hen what is the ratio of area of to areac. 15:28 d. 5:6 e. NoT

, BC= 6 cm & CA = 8 cm & I is the in cen

c. 10 cm^2 d. 12 cm^2

et and all arcs are quarter circle whose radiu

the approx probability to hit coloured (shade

c. 31.5 % d. 40.5% e. 45%

/MathsByAmiya

= 9 cm & CF = 12

argest angle of

angle bisector & I is

of ?

re of the triangle then

e. NoT

s is equal to side of

d) area.


44/45


Directions :If in given ima

, and lines DI, EF &circle and DI || AB , EF||BC

BC = 5 cm & AC = 7 cm th

168. EF = ?

169. ED = ?

170. Ratio of Area of

171. Ratio of Area of

172. If a polygon has only t

If there are 30, 300 degree a

polygon.

Ans: 33

If ABCD is a square of 10

173. What is the length of P



176. What is the measureme

177. If ABC is a quarter circl

in terms of "a" if CS =PB

CHECK FACEBOOK P

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AMIYA KUMAR

ge circle is in-circle of

H are tangents to the

& GH|| AC. If AB= 6 cm ,

en find

to Area of

to Area of

o types of internal angles, one is 60 degree a

ngles then there are how many 60 degrees a

cm then

t of PDQ

e and PQRS is square of side "a". Find the ra

GE OR GROUP FOR SOLUTIONS OF Q

ARE NOT GIVEN HER

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other is 300 degree.

gles are in this

dius of quarter circle

ESTIONS WHICH


45/45

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Maths by Amiya - Geometry - 3e Learning

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Transcript of Maths by Amiya - Geometry - 3e Learning