Transcript
177 Geometry Questions
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1.
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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 line AD 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 https://www.youtube.com/watch?v=NBZawFsTrvc 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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a. 2:5
b. 5:2
c. 1:2
d. 2:1 e. NoT
ans: [e] 13:4 https://www.youtube.com/watch?v=NBZawFsTrvc 7. If smallest side of an integral inte gral right angled triangle is 23 cm then what would be digital s um 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 h ypotenuse 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 , https://www.facebook.com/MathsByAmiya/509385892446865
∠ ∠
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 based on previous year MBA question Ans: 27, sides are 10,12,6 , use similarity , �ABC Maths By Amiya, 3E Learning,
e. NoT
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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
= + + 1 1 13
1 = 12 + 3 + 4 = 12 = 1213
14. Ans :
; where
ℎ,ℎ&ℎ
√ 13
15. 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 then FGD ?
∠
a. 30
b. 45
c. 50
°
d. Can't say
e. NoT
19. If in a �ABC side BC makes an angle 132 at incentre then angle subtended by side BC at orthocentre is ???? a. 100
b. 104
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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.
PC) and touches smaller circle at B. If TAP=20 and TBP = 30 , then find BTA =& BTC...
∠ ° ∠ °
°
∠ ∠
Ans: Both are 10
23. A regular polygon with 959 vertices and another regular polygon with 1781 sides has a common circumscribe circle if they have some common vertices then digital sum of number of common vertices is a.2
b.3
c.5
d. 9
e. NoT
Sol: [a]They have same common multiple of central angle, central angle is 959 = 137*7 & 1781 =137*13 ; so 137 common verti ces , SoD(137) = 2
[By Sanket]
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24. There is a sugar cube of dimension 10cm*10cm*10cm. If an ant start moving with uniformly from one bottom corner to top corner of the same edge along all four faces of sugar cube uniformly in his entire journey. Then among options which one could be total distance travelled by the ant, consider the ant is shape zero. a. Sol: [d]
√ 401
√
b.
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c.5*
√ 401
10∗√ 401
d.
e.NoT
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The height gain on each face w uld be 10/(4*n) where n is number of rotati ns in ants total journey. So total distance =
4∗ 10 =4∗ √ 1 6∗ +1=10√ 16∗ +1 =10√ 6∗5 +1=10∗ √ 401
For n=5 , total distance
Alternate :- Open the cube along faces , Height gain is height of cube 10c m but base is 10*4 =40cm in one rotation, since oves along four sides, and for two rotation ts 80.
Height gain is 10 but base mov ment is 40*(number of rotation)
= 10 + 0∗ =10∗ 1 +4 10∗ √ 401 for number of rotation =5 , Tot l distance =
25. There is a solid cheese cube of dimension 10cm*10cm*10cm. if Jerry a rat eats the cheese cube from centre of all the surfaces in such a way that the rest of the che se cube has three similar air tunnels crossing ach other at the centre of cube and dimension of cross section of each tunnel is 1cm*1cm, th n what is total surface area of the rest chees cube. a. 600 cm^2
b. 558 c ^2
c. 698 cm^2
d. 702 c ^2
e. NoT
Sol : [d] New surface area = old surface area + new faces created - faces destroyed = 600 + 40 + 36 + 36 - 2 -4 -4
702
26. What would be total volum created by a 3-D figure, which is created b joining the mid points of all 6 surfaces of a cubical room of dimension 10m*10m*10m . Maths By Amiya, 3E Learning,
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a. 250/3 m^3 Sol: [d]
b. 500/3 m^2
c. 1000/3 m^3
e. NoT
5 2 ∗5 2 √ √ ∗ ∗ℎ= ∗5√ 2 ∗5√ 2 ∗5=
The figure is Bi-pyramidal , with base dimension so volume =
d. 166.67 m^2
and height 5m.
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 a rea.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 https://www.facebook.com/MathsByAmiya/photos/745195878865864/
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32. Inside an equilateral triangl there is a point from which the length of pe pendicular on all the three sides are 1cm, 2cm, & 3cm then. what would be area of equilateral triangle.
9∗ √ 3
a. (???)
cm^2
b 12cm^
c.
12∗ √ 3 ^2
d. Data i adequate
e. NoT
Sol: [c]
90°
33. In a quadrilateral ABCD if then its area is ......??? a. 1224 b. 2568
B=15cm , BC=144cm, CD=145cm and AD = 8 cm with c. 1284
d. Data inadequate
∠=
e. NoT
Sol: [c]JoinBD and get two rig t angled triangles BAD & BAC and find are of triangles then add the values.
34. If the perimeter of an integr al sided triangle is 45 cm then how many dif erent triangles are possible a. 45 b. 48 c. 42 d. 56 e. NoT (???) Sol: [b] https://www.facebook.com/MathsByAmiya/photos/528057913912996/ 35. If three tangential circles to ches each other from outside, and their radii are 1cm, 2cm & 3cm. If we draw a circle such tha the centre of all three given tangential circl s are on the perimeter of new circle, Then what is radius of new circle a. 2 cm b. 2.5 cm c. 3 cm d. 3.33 cm e. NoT Sol: Circle would be circum circle of triangle formed by joining the centres of tangential circle. Sides of triangle are 3 cm, 5 cm & 4 cm
3∗5∗4 = ∗∗ = 4∗∆ 4∗6 =2.5 ∆
R - circum radius of triangl (required radius) , a, b , c are sides and
is area of triangle
Or triangle is a right angle triangle , so R = half of hypotenuse.
36. If paint used by all colour a e same and radius of smallest purpule color circle is 1 cm,then what is the thickness of
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balck colour , if thickness of balck colour is same with all circles
∗ √ √
a.
b.
c.
d.
∗ √ √
NoT
e.
Sol :[d] Here we have 4 circles with radius 1cm, (1+x)cm, y cm & (y+x)cm , wh re y is radius of yellow circle and x is thick ess then according to question Purple = Total Black = Total Yellow
1+ + ==∗ ∗1 = 1=∗ 11++11+++ 1+ = √ ; = ∗√
By solving these
Alternate- Take width of y llow is y , then y = 2x (x is width of black)
∠ 30°
37. There is a triangular park A C, has brick wall on its side. If AB=AC = and BAC= . A horse is threaded outside of the part at vertex A with a rope of length 8 c such that horse cannot entre inside the triangle due to fence, then the maximum area cov ered by horse is .... ????? a. 64*pi - 9 b. 58.67*pi c. 17*pi d.61*pi e. NoT
330°
Sol[e] Area covered by horse = Ar ea of sector ( with radius 8cm + area at side B with radius 2 cm (extra length of rope)
° ° ∗∗8 + ∗∗ 2 ° ° =
=61*pi - com mon area
38. In a triangle ABC , D point is on BC such that AD is perpendicular on B C. If AB= 40cm , AC=14 cm & AD= 5 cm th n what is the circumradius of triangle ABC. Maths By Amiya, 3E Learning,
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a. 77.77 cm
b. 80 cm
c. 70 cm
d. 66.66 cm
e. NoT
Sol: [e] 56 cm
sin= = 2= ⇒= 2 ∗ = 2∗40 =56 30°=? 15° 45° In fig
According to Sine Formula
39. In a triangle ABC, D is on then a. b.
c.
∆ABC~∆BDC, Take DC=x , AC=2x, then BC= By sine law,
=30°
∠ 45° ∠= ∠ = 60°
C such that BD is medianand BDC=
= √
,i
d.
√ 2
e. NoT
x.
40. In a right triangle ABC. B , DE, DF, FG and EH are perpendicular to & DC respectively, If FG = 4 cm & EH = 2 cm then BD =? a. 4.5
b. 5
c. 6
d. 7
C, BC , AB and AD
e. NoT
Sol: [c] FBED is a rectangle and dia gonals BD and EF intersect at point I (say) so I would be midpoint of BD & EF so BD=2*ID. FGHE is a trapezium with I as midpoint of its unparallel sides, and ID || o parallel sides, so it would be median of trapezi m, So, ID = (FG+EH)/2 = (4+2)/2 3 cm, so BD = 6 cm. https://www.facebook.com/MathsByAmiya/photos/550655228319931/ 41. There are how many differe nt integral sided right angled triangle are pos sible whose one side is 30 unit a. 13 b. 14 c. 12 d. 15 e. NoT SOl: [e] 5 If 30 is not hypotenuse (tak 30 as perpendicular) , then h^2 - b^2 = 30^2 [h & b must be even]
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By this case we would get 4 values =
= 4
[ ] is GIF
If 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 Sirhttps://www.facebook.com/photo.php?fbid=10152541092894878&set=p.10152541092894878 &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 triangle
√ 2 1 1 1 1 1 1 = = + + = 12 18 36 6 ∆ = = √ 6 ∗12∗18∗36=216 a. 36 cm^2
b. 108 cm^2
c. 108
cm^2
d. 216 cm^2
e. NoT
Sol: 216 cm^2
44. If I is incetnre of�ABC 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 Maths By Amiya, 3E Learning,
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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
1 =
Ans [e]
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 property (sum of two sides is greater than third and difference is less than third side)
14>48 & 2< 48 ⇒3.42 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 perpendicular distance 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
√ 13
a. 3
b. 2
√ 14
c. 2
√ 13
d. 3
√ 14
Sol: [c]
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∠
tan= cot cosec sec >
68. If in a triangle �ABC, ABC= , such that how many integral value of k would be possible a. Not Possible for real K d. 5. Sol:
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and
b. Never Possible
then
c. 3
e. NoT
tan= cot⇒ =∗±45° www.facebook.com/MathsByAmiya ©AMIYA KUMAR
coseccosec sec >sec =√ 2 √ =∗±45° 2= 2√ 2 > ==0,±1 69. ∠ 20° ∠EBA = ? a.120°20° b. 70° c. 80° d. 100° e.NoT ; positive for
; it shows angle is in second quadrilateral,
where
If two circles of equal radius intersect at two different points C & D. If A & B are centre of these two circle, & line AC cuts other circle whose centre is B at E, such that EAB = then
Ans: [e]
, 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. 150
°
Sol: [d] http://youtu.be/Ouw21pvOyFA
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71. IF in �ABC, D, E and F are the points of trisection of respective sides, a shown in figure. Further, each of the ratio A : XD, BY : YE and CZ : ZF is 3 : 4. Find t he ratio of the areas of triangle XYZ and triangle BC
a. 2 :9
b. 1 : 7
c. 3 : 7
d. 4 : 9
Sol:[b] Since there is a unique answer ( as the options suggest, we can safely assume triangle ABC to be equilateral. This will reduce our work considerably. Now the non-overlapping areas that appear similarly placed about the three ertices will equal in area. Assuming the areas as x, y and z as sh wn in the figure, we have
= = ..
2+ 1 = ⟹3= . .= +2+ 2 3 Also, = = . . = ⟹4 +=3. Plugging x in terms of z, we have y =. We need to find the ratio of .. .. Alternatively :∗∗∗ = ∗∗ By Routh's theorem, here x= =z = 2; ht p://en.wikipedia.org/wiki/Ro th's_theorem Maths By Amiya, 3E Learning,
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72.Itfwtohreebiggercirclciersclande is a4cmstraiandght6.li2n5escmtouches each ot h er at si x di f e rent poi n t s &radi u s of then what would be radius of smallest circle in cm. a. 0.123 b. 1.234 c. 2.33 d. 1.66 e. NoT Sol:[e] Thitheorem] s is case of mutually tangent circle , looking for radius of smallest circle R3 [Descartes' 14 = 11 + 21 +2∗ 11 21 14 = 1004 + 6.10025 +2∗ 10046.10025 14 =81 ⇒4=1.23456790… =0.0123 73.There are how many dif erent integral sided triangle possible whose perimeter is 18 unit a.5 b. 6 c. 7 d. 8 Sol: c 7 By manual process: Dif erent 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=7 https://www.facebook.com/MathsByAmiya/photos/528057913912996/ 74.Forpossigibvlene, tperihenmwhateteriPs tunihetsumof trofiangldigeit,stofhereP ?are 12 dif erent integral sided triangle are a. 5 b. 6 c. 7 d. 8 Sol:[b] < 600 ⇒23.49 = Maths By Amiya, 3E Learning,
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113.a G.IPf seriradieisofthalenarea l fourofcir∆cl s arewoulconsecut i v e t e rms of d be equal to a.b. Largest radi u s among al l Product of smal l e st radi u s nd 3rd l a rgest radi u s c.d.Square of 2nd smal l e st radi s Product of 2nd smallest an 3rd smallest radius Sol: [d] ∆=rest are exradi∗us∗of atr∗iagnle. herer is inradius and 114.triaWhat i s t h e maxi m um al u e of r a ti o of area of i n c i r cl e of a tri a n l e t o area of ngla. 1e. b. pi c. pi / 3* sqrt3 d. 2 e. NoT Ans : [c] , for equilateral triangle. 115.oneWhat woul d be appro x area of a regul a r convex pol y gon wi t h 1 1 si d ed f i g whose sia. 472.de is9716cm. b.. 478.169 c. 458.916 d.480 SolFor:[ac]given perimeter , Ar a of a circle is maximum . Perimeter of this polygon is 77 cm , consi d er i t as a ci r cl e of ci cumf e rence = 77cm so t h e area of thi s ci r cl e i s approx472. so area of polygon should be less than 472 , hence [c] I f i n a t r i a ngl e B = 30, BC= 40 & CA = 50 , D and E ar e t o poi n t s on si d e AC such that Perimeter of ∆A E = Perimeter of ∆BEC & Area of ∆ABD = Area of ∆BDC, then 116. Lengt h of BD = ? a. 20 b. 25 c. 26. 6 6 d. 23. 3 3 e. NoT Ans : [b] - Median 117. Lengt h of BE a. 12 b. 12√ 5 c. 18 d. 18√ 5 e. NoT Ans :[b] , Best is coordinate geometry Direction :
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118. Lengt h of DE = ? a. 3 b. 4 c. 5 d. 6 e. NoT Ans : [c] 5, Best is coordinate geometry 119.movement If a robotpatonlh iysmoves i n st r ai g ht l i n e and onl y t a kes ei t h er l e f t or ri g ht t u rn and hi s marked by a LASER. One day he st a rt e d f r om a poi n t and reach at t h e same poi n t and f a ci n g same di r ect i o n as i n i t i a l y he was af t e r t a ki n g 20 ri g ht t u rns t h at how many l e f t t u rns he has t a ken, i f he never repeat e d or crossed a pat h whi c h i s al r eady markeda. 20and neverb.ta16ke more thanc.2one4 turn ond.a bpoinort. c e. NoT SolTake: [dLef] t turn as 90 degree and right turn as 270 as internal angle of a closed polygon, andHerewe know sum of all internal angles = 180n-2 , n is vertex 90*l + 270*r = 180 l+r-2 , by question r=20, we get l=24 Now, Take Lef t t u rn as 270 degree and ri g ht t u rn as 90 as i n t e rnal angl e of a cl o sed polHereygon, and we know sum of all internal angles = 180n-2 , n is vertex 270*l + 90*r = 180 l + r2 , by quest i o n r=20, we get l = 16 So either 24 or 16. 120.TR^2In =a ∆ST^2PQ=QR , a ngl e PQR = 90°and S and T are poi n t s on PR such t h at PS^2 + t h en angl e SQT = ? i n degre a. 30 b. 45 c. 60 d. 75 e. NoT Ans : [b] , solve by options or coordinate or sine formula 121.5,5If tthheenequat i o n of one si d e of an equi l a t e ral t r i a ngl e i s 3x+4y=5 and i t s one vert e x i s what i s i t s area a. 6√ 3 b. 12√ 3 c. 9√ 3 d. 15 e. NoT Ans : [b] 122.hexagon What is the ratio of side of a hexagon to a square of maximum area inside the same a. 3 root 3 b. 3 root 2 c. 2 root 3 d. 2 root 2 e. NoT Ans : [e] Direct formula = |left turn - - right turn| = 4 4
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https://www.facebook.co /MathsByAmiya/photos/58449419826 367/ 123. If perimeter of a triangl is 24 cm then how many different triangles ossible where only two sides are odd integer re t is even. a.12 b. 6 c. 3 d. NoT Ans : [d] 124. If length of minor arc cr eated of a chord AB is equal to radius of the circle .then angle OAB = ? (where O is the ce ntre of circle and A & B are on the centre) a. 1 rad b. 2pi -1 rad c. pi - (1/2) rad d.60 degree Ans : [c]
125.poinWhatt E suchwoulthdatbe, CE=2 diametc er, CD= of cir9clcme whose t w o chords AB and CD ake angl e of 90° at & EB= 3 cm. a. 12 cm b.. √ 122 c. √ 129 d. NoT Ans: [b] 126. https://www.faceboo .com/MathsByAmiya/photos/84041359 010758/ 127.radiWhat woul d be radi u s o f ci r cl e of maxi m um area i n si d e a sect o r f a ci r cl e whose ua. s6cmis 12 cm andb. 4centcmr l anglc.e of2√ sect3 or is 60°d.√ 12 e. NoT Ans: [b]4
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128. Ans: 10 cm^2 https://www.facebook.com/MathsByAmiya/photos/509985899053531/ 129.inteThere are how many convex pol y gon possi b l e such t h at i n t e gral angl e s are i n AP and ger and the smallest angle is 30 a. 8 b. 17 c. 3 d. 4 e. NoT Sol: [e]NoT 180*n-2=n/22a+n-1d, here a=30For convex polygon we get only 2 set of values ht2%29%3D%28n%2F2%29%282a%2B%28ntp://www.wolframalpha.com/input/?i=180*%28n1%29d%29%2C+a%3D30%2C+n%3E0%2C+d%3E0
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130. If angle ABC=angle BC A,BF=7 cm, CE= 5 cm , DE= 9 cmThen EF =? a. 3 cm d. 4 cm
b. 3.4 cm e. NoT
c. 3.6
Ans: [c]
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131. If in a �ABC, AB=16 c , BC= 30 cm & CA= 34 cm and I is incetre of the triangle then IA =? a. 6 cm
b. 2
Sol: [e]
√ 17
3√ 5 √ 6 +10 =√ 1 36=2 34 ° ∗√ °
c. 8 cm
inradius = 6 , so centre (6,6) an A=(0,16) so IA=
d.
e. NoT
132. What would be side of i scribed square PQRS having maximum are inside a triangle ABC such PQ lies on side C, angle ABC=30 , angle ACB=60 and side AC= 6 cm
∗√ √
a. Sol: [c]
b.
∗√ √
∗√ √
c.
d.
√
e. NoT
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133. If in a triangle ABC, A is also a side of a regular hexagon and AC is side of a regular pentagon then what is the easurement (in degree) of angle BAC ? a. 60 b. 114 c. 120 d. 108 e. NoT Ans: [e] cannot be determined 134. https://www.facebook.c m/MathsByAmiya/photos/859153280803456 Ans: [b] 135. If the semi-perimeter of right angled triangle is 154 cm and smallest what would be area of the tr iangle. a.1600 cm^2
b. 1440 cm^2
c. 1540 cm^2
edian is 72 cm then
d . Data inadequate
e. Not Maths By Amiya, 3E Learning,
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Sol: [c] Area = (s – c)*s = 1540 cm^2 https://www.facebook.com/MathsByAmiya/photos/861355437249907/
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136.
137. How many set of data g ven below is (are) sufficient to construct an nique triangle ABC. [P= Perimeter, A , B, & C a re angles & a,b & c are sides to corresponding angles]
I. P = 16 cm , c = 9 cm, A= II. a=b= 12 cm, A=
60�
III. A= 60� ; B = 30� ; C = IV. A= 60� ; B =
6 �
90�
45� ; a = 4cm, b= 3 cm
a. Only one set of data
b. Two set of data
c. Three sets of data
d. By all we can construct uniq e triangle
e. NoT Ans : [a] only II is possible 138.
How many statements a e correct
I. ��� 1�
��� 1
I . �
IV � V. ���5�
III. �
��� 5
VI �
Ans: 4 Maths By Amiya, 3E Learning,
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139. How many different set S are possible, if S is set having three elements, all elements of set S are positive integers in w ich two are odd and one is even, it is known that sum of any two elements is greater than third element and sum of all elements is 80.
a. 133
b. 33
c. 100
d. 80
e. NoT
Ans: [c] , question is of triangle whose perimeter is 80. https://youtu.be/Pv hMly9cFY
140. How many triangles are possible whose two sides are 50 unit and 47 unit and third side is a prime number.
a. 25
b. 24
c. 23
d. 22
e. NoT
Ans: [d]
141.
In the given fig ,QA:AB = RB:BC =PC:PA = 1:3 , then
∆ ? ∆
142.
In the given fig ,QA:AB = RB:BC =PC:PA = 1:3 , then
∆ ? ∆ Ans: 36:13
143. If in a right angled ∆ , point D lies on AC such that angle A AD= 4 cm & CD = 9 cm th n area of ∆ ? [in cm^2]
90�
Ans: 39 cm^2
144. In given ∆ , PR:RJ Ans: 1:7
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1:3 , AQ:QP = 3:4 then QO:OJ = ?
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145.
In given ∆ , PR:RJ
1:3 , AQ:QP = 3:4 then AO:AR = ?
Ans: 1:1
146.
In given ∆ , PR:RJ
5:3 , AQ:QP = 3:5 then
? Ans: 1:1 147.
In given ∆ , PR:RJ
5:3 , AQ:QP = 3:5 then
∎ ? ∆ Ans: 25:52 148.
In given ∆ , PR:RJ
4:3 , AQ:QP = 3:5 & AS:SJ = 2:3
then
∎ ? ∆ 149. In given ∆ , PR:RJ 2:3 then
4:3 , AQ:QP = 3:5 & AS:SJ =
∆ ? ∆ Ans: 5:4 150.
In given ∆ , PR:RJ
3:2 , AO:OR = 4:3 then AQ:QP = ?
Ans: 8:15
151. In given ∆ , QO:OJ = 3:2 , AO:OR = 4:3 then AQ:QP =?
Ans: 1:15 152.
In given ∆ , PQ:QR:RJ = 2:2:3 , AS:SJ = 4:3 then PM:MN = ?
Ans: 10 : 7
153. ?
In given ∆ , PQ:QR:RJ = 2:2:3 , AS:SJ = 4:3 then PS:MN
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=
154.
In given ∆ , PQ:QR:RJ = 2:2:3 , AS:SJ = 4:3 then
∆ ? ∆ 155.
In given ∆ , PQ:QR:RJ = 2:2:3 , AS:SJ = 4:3 then
∎ ? ∎ Ans: 8:17 156. ∆ is a right angled triangle at B, in which AB= 9 cm & BC = 8 m. Point D & E lie on AB & BC such that AD: B = BC:BE = 2:1 . O is the mind point of li ne segment DE then what is the distance length f BO (in cm)
a. √ 5 Ans: [c]
b. √ 7
c. 2.5
157. If are three altitudes of a. 3 cm b. 6 cm
d. 3
e. NoT
triangle is √ 3 cm then what is the perimeter of triangle c. 4.5 cm d. CBD e. NoT
Ans: [a] If 3, 2 & 2 are three altitudes of a triangle then what is in-radius of the triangle a. 4/3 b. 3/4 c. 1 d. 1.5 e. NoT Ans: [b]
158.
159. If O is orthocentre of tri angle ABC , and AD, & BE are altitudes, suc h that AO= 3 cm, OH = 2 cm, BO = 6 cm then O = ? a. 1.5 cm b. 1 cm c. 0.5 cm d. CBD e. NoT Ans: [b] 160. How many different triangle are possible whose two altitudes are 7 c altitude is an even number. Ans: 19 161.
If 3, 2 & 2 are three altitudes of a triangle then what is the area of the triangle b. 9/(4 √ )
a. 12 Ans: [d] 162.
a. 6
& 6cm and third
d. (9√ 2) / 4
c. 6
e. NoT
If 3, 2 & 2 are three altitudes of a triangle then what is the perimeter of the triangle b. 6√ 2
c. 6√ 3
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d. 7
e. NoT
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Ans : 6√ 2 163. If in a ∆ , AD, BE & CF are altitudes such that, AD = 6 cm, BE = 9 cm & CF = 12 cm then angle A = ? a. 67 b. 85 c. 90 d. 30 e. NoT
Ans: [e] NoT it should be o tuse 164. If in a length f altitudes are 30 cm , 40 cm & 24 cm then argest angle of triangle is a. 150 b. 115 c. 90 d. 120 e. NoT Ans: [c]
If in ∆ , AB= 2 cm , BC= 4 cm & CA = 3 cm. AD, BE & CF a re angle bisector & I is the in centre of the triangle hen what is the ratio of area of ∆ to area of ∆ ? a. 5:4 b. 13: 30 c. 15:28 d. 5:6 e. NoT Ans: [c]
165.
166. If in ∆ , AB= 10 c , BC= 6 cm & CA = 8 cm & I is the in cen re of the triangle then what is the area of ∆ ? a. 6 cm^2 b. 8 cm^ c. 10 cm^2 d. 12 cm^2 e. NoT Ans: [c] 167. If ABCD is a square tar et and all arcs are quarter circle whose radius is equal to side of square ABCD, then what is the approx probability to hit coloured (shaded) area.
a. 20 %
b. 50%
c. 31.5 %
d. 40.5%
e. 45%
Ans: [c]
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Directions : If in given image circle is in-circle of ∆ , and lines DI, EF & H are tangents to the circle and DI || AB , EF||BC & GH|| AC. If AB= 6 cm , BC = 5 cm & AC = 7 cm th en find 168.
EF = ?
169.
ED = ?
170.
Ratio of Area of
∆ to Area of ∆
171.
Ratio of Area of
to Area of
∆ 172. If a polygon has only t o types of internal angles, one is 60 degree a other is 300 degree. If there are 30, 300 degree a ngles then there are how many 60 degrees a gles are in this polygon. Ans: 33 If ABCD is a square of 10 cm then 173.
What is the length of P
174.
What is the length of P
175.
What is the length of P
176.
What is the measureme t of ∡PDQ
177. If ABC is a quarter circle and PQRS is square of side "a". Find the ra dius of quarter circle in terms of "a" if CS =PB
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