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This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 201. |
Write the name of(a) vertices(b) edges, and(c) faces of the prism shown in given figure. |
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Answer» (a) Vertices : A, B, C, D, E and F. (b) Edges : AB, BC, AC, DF, FC, BD, EF, ED and AE. (c) Faces : EACF, EDBA, ABC, DEF and DBCF. |
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| 202. |
How many points are marked in Fig. 2.43? |
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Answer» The correct answer is Two |
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| 203. |
In Fig. 2.44, how many points are marked? Name them. |
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Answer» The correct answer is Three A,B,C |
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| 204. |
In Fig. 2.45 how many points are marked? Name them. |
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Answer» The correct answer is Four A,B,C,D |
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| 205. |
Can we have two obtuse angles whose sum is(a) a reflex angle? Why or why not?(b) a complete angle? Why or why not? |
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Answer» (a) Yes, ∵ the sum of two obtuse angles is always greater than 180°. E.g., 135° and 100° are two obtuse angles and their sum = 135° + 100° = 235°, which is greater than 180°. (b) No, ∵ the sum of two obtuse angles is greater than 180° but less than 360°. In the above example, we can see that the sum of 135° and 100° i.e., 235° is greater than 180° but less than 360°. |
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| 206. |
In Fig. 2.46, how many points are marked? Name them. |
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Answer» The correct answer is Five A,B,C,D,E |
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| 207. |
How many line segments are there in Fig. 2.44? Name them. |
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Answer» The correct answer is Three AB,BC,AC |
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| 208. |
In Fig. 2.45 how many line segments are there? Name them. |
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Answer» The correct answer is Six, AB, AC, AD, BC, BD, CD |
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| 209. |
Can we have two obtuse angles whose sum is (a) a reflex angle? Why or why not?(b) a complete angle? Why or why not? |
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Answer» (a) Yes. The sum of two obtuse angles is always greater then 180°. (b) No. The sum of two obtuse angles is always greater than 180°, but less than 360°. |
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| 210. |
In Fig. 2.46 how many line segments are there? Name them. |
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Answer» The correct answer is Ten, AB, AD, AE, AC, BD, BE, BC, DE, DC, EC |
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| 211. |
Can we have two acute angles whose sum is(a) an acute angle? Why or why not?(b) a right angle? Why or why not?(c) an obtuse angle? Why or why not?(d) a straight angle? Why or why not?(e) a reflex angle? Why or why not? |
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Answer» (a) Yes. The sum of two acute angles may be less than a right angle.(b) Yes. The sum of two acute angles may be equal to a right angle.(c) Yes. The sum of two acute angles may be more than a right angle.(d) No. The sum of two acute angles is always less than 180°.(e) No. The sum of two acute angles is always less than 180°. |
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| 212. |
In Fig. 2.47, O is the centre of the circle.Name a chord, which is not the diameter of the circle. |
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Answer» The correct answer is CP |
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| 213. |
In Fig. 2.47, O is the centre of the circle. (a) Name all chords of the circle.(b) Name all radii of the circle. |
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Answer» The correct answer is (a) CP and AB (b) OA, OB, OC, OP |
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| 214. |
`angleA and angleB` are two complementary angles. If `angleA` is `20^(@)` more than `angleB`, then find the angles of `angleA and angleB`. |
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Answer» Given that : `angleA+angleB=90^(@)` `angleB+20^(@)+angleB=90^(@)` `2angleB=70^(@)` `angleB=35^(@)` `therefore angleA=90^(@)-35^(@)` `angleA=55^(@)` |
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| 215. |
`angleP and angleQ` are two supplementary angles. If `angleP` is three times of `angleQ`, then find the measurement of the angles P and Q. |
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Answer» Given, `angleP+angleQ=180^(@)` `3angleQ+angleQ=180^(@)` `4angleQ=180^(@)` `angleQ=45^(@)` `angleP=3angleQ` `=3xx45^(@)` `angleP=135^(@)` |
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| 216. |
Find the value of x in the given figure. |
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Answer» In the cyclic quadrilateral ABCD ∠ABC = 180° – 120° = 60° ∠BCA = 90° ∴ x = ∠BAC = 180°- (90° + 60°) = 30° |
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| 217. |
In the given figure at right, side BC of ∆ABC is produced to D. Find ∠A and ∠C. |
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Answer» From the figure Exterior angle = 120° ⇒ ∠C = 180° – 120° = 60° (linear pair) ∴ ∠A = 180° – (40° + 60°) = 80° |
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| 218. |
In the above figure (not to scale ), `bar(GF)||bar(BD),bar(B)||bar(PQ)` and `bar(AC)||bar(PR)` If `/_ x =40^(@)` and `/_ y= 110^(@)`, then find `/_ QPR`.A. `70^(@)`B. `80^(@)`C. `60^(@)`D. None of these |
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Answer» Correct Answer - a (i) Sum of the angles of a triangle is `180^(@)`. Extend QP to meet AE. Corresponding angles are equal. (ii) Produce the lines PQ and PR to intersect the line BC at M and N respectively. (iii) Find `/_PMN` and `/_ PNM` by using the given conditions. (iv) `/_ QPR =180^(@)- ( /_ PMN + /_ PNM )`. |
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| 219. |
In the above figure , O is the centre of the circle, AB and CD are diameters. `/_ COB =50^(@)=50^(@)` . If E is the midpoint of AF, then find `/_ ADF`A. `130^(@)`B. `100^(@)`C. `110^(@)`D. `120^(@)` |
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Answer» Correct Answer - a `/_ COB= /_ AOD =50^(@)` (Vertically opposite angles ). Since E is the mid-point of AF,`/_ OEA = /_ OEF=90^(@)`. `implies /_OAE =/_OFE =40^(@)` `implies /_DOF =50^(@)` `:. /_ADF =1//2 `( reflex `( /_AOF) =130^(@)` |
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| 220. |
The angles of a quadrilateral are in the ratio 3:4:5:6. Which of the following can be conclude ?A. Exactly two angles are acute.B. Two pairs of angles are supplementary.C. Either (a) or (b)D. Neither (a) nor (b) |
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Answer» Correct Answer - C Let the angles be (3x), (4x) , (5x) and (6x) `3x+4x+5x+6x=360^(@)` `x=20^(@)` `3x=60^(@), 4x=80^(@),5x=100^(@), and 6x=120^(@)` 3x and 4x are acute. And `3x+6x=4x+5x=180^(@)` Option (a) and (b) follow. Hence, the correct option is ( c). |
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| 221. |
In the figure above, `angleQ=2angleS and angleQRS=2angleRPS`. Find `angleRPS+angleS`A. `60^(@)`B. `45^(@)`C. `72^(@)`D. `54^(@)` |
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Answer» Correct Answer - A `angleQPR+angleQ+angleRPS+angleS=180^(@)` `2angleRPS+2angleS+angleRPS+angleS=180^(@)` `3(angleRPS+angleS)=180^(@)` `angleRPS+angleS=60^(@)` Hence , the correct option is (a). |
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| 222. |
The sum of 3 distinct angles is equal to the sum of 2 right angles and the difference between two pairs of the angles is `10^(@)`. Find the smallest among the angles. |
| Answer» Correct Answer - `50^(@)` | |
| 223. |
In the figure above, PQRS is a trapezium , PQ//SR, QR=RS, and `angleQRS=90^(@)`. If QR=24 cm and PS=25 cm , then find the length of PQ. |
| Answer» Correct Answer - 31 | |
| 224. |
In the above figure, O is the centre of the circle and `AB=CD`. If `/_ APB=110^(@)`, then find the angle made by the chord CD at the centre.A. `220^(@)`B. `110^(@)`C. `120^(@)`D. `140^(@)` |
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Answer» Correct Answer - d (i) Equal chords subtend equal angles at the centre. (ii) JoinAO, OC, OB and OD. (iii) Reflex `/_ AOB =2 /_APB,` use this to find `/_AOB` as `/_ AOB =360^(@) - 2 /_ APB` (iv)` /_AOB = /_ COD` |
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| 225. |
In the following figure, O is the centre of the circle , AC is the diameter and if `angle APB =120^@` , then find `angle BQC` . A. `30^@`B. `150^@`C. `90^@`D. `120^@` |
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Answer» Correct Answer - B (i) APBC is a cyclic quadrilateral. (ii) `angle ABC` is an angle in a semi circle. (iii) ABQC is a cyclic quadrillteral. |
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| 226. |
In the following fiure. O is the centr of the circle and AD is the diameter. If `angle ACB =135^@` , then find `angle DOB`. A. `135^@`B. `60^@`C. `90^@`D. `45^@` |
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Answer» Correct Answer - C (i) ACBD is a cyclic qudrilateral. (ii) `angle ACB and angle ADB` are supplementary angles. (iii) `angle AOB =2angle ADB`. |
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| 227. |
Find the complement of an angle whose supplement is `100^(@)`. |
| Answer» Correct Answer - `10^(@)` | |
| 228. |
State whether the statements are true or false.Angle of 0° is an acute angle |
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Answer» False Measure of acute angle is between 0° and 90°. |
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| 229. |
Angle of 0° is an acute angle. |
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Answer» False [Hint: Measure of acute angle is between 0° and 90°] |
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| 230. |
In Fig. 9.10, if B is the image of the point A with respect to the line l and P is any point lying on l, then the lengths of line segments PA and PB are _______. |
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Answer» Then the lengths of line segments PA and PB are Equal |
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| 231. |
In the figure above (not to scale), AB is the diameter of the circle with centre O. If `/_ ACO=30^(@),` then find `/_ BOC`. |
| Answer» Correct Answer - `60^(@)` | |
| 232. |
In `triangleABC, angleB=90^(@)`, P,Q and R are the mid-points of `bar(AB), bar(BC)` and `bar(AC)` respectively. Then which of the following is true?A. A,P,Q and R are concylic points.B. B,P,R and Q are concylic points.C. C,Q,P and R are concyclic points.D. All of these |
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Answer» Correct Answer - B i) Draw the figure and mark the points P,Q and R on sides AB, BC and AC respectively. ii) Angle B`=90^(@)` and `anglePRQ` is formed by lines PR and RQ, which are parallel to lines BC and AB (mid-point theorem). iii) Since BC and AB are perpendicular, PR and RQ are also perpendicular , i.e., `anglePRQ=90^(@)`. iv) Quadrilateral joining BPRQ is a cyclic quadrilateral. |
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| 233. |
In `triangleABC, AC=BC`, S is the circum-center and `angleASB=150^(@)`. Find `angleCAB`. A. `55 (1/2^(@))`B. `52(1/2)^(@)`C. `90(1/2)^(@)`D. `35(1/2)^(@)` |
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Answer» Correct Answer - B Since, SA=SB=SC, S is the circum-center `angleASB=150^(@)` (given) `rArr angleACB=75^(@)`. Since, AC=BC, `angleCAB=angleCBA=(180^(@)-75^(@))/2` `=521/2^(@)` |
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| 234. |
In the given figure, `bar(AB) || bar(DE)` and area of the parallelogram ABFD is 24 `cm^(2)`. Find the areas of `triangleAFB, triangleAGB` and `triangleAEB`. A. 8 `cm^(2)`B. `12 cm^(2)`C. `10 cm^(2)`D. `14 cm^(2)` |
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Answer» Correct Answer - B Areas of the parallelogram lying on the same base and between same parallel lines are equal. |
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| 235. |
The ratio between the exterior angle and the interior angle of a regular polygon is `1:3`. Find the number of the sides of the polygon.A. 12B. 6C. 8D. 10 |
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Answer» Correct Answer - C Sum of the exteriror and interior angles of a polygon`=180^(@)`. |
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| 236. |
Find each interior and exterior angle of a regular polygon having 30 sides.A. `144^(@), 36^(@)`B. `156^(@), 24^(@)`C. `164^(@), 16^(@)`D. `168^(@),12^(@)` |
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Answer» Correct Answer - D Find one exterior angle. |
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| 237. |
Two complementary angles are in the ratio 2:3. Find the larger angle between them.A. `60^(@)`B. `54^(@)`C. `66^(@)`D. `48^(@)` |
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Answer» Correct Answer - B Let the angle be `2x^(@) and 3x^(@)`. `2x^(@)+3x^(@)=90^(@)` `x^(@)=18^(@)` The larger angle =` (3x)^(@)=54^(@)` Hence, the correct option is (b) |
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| 238. |
In the figure above, `bar(AB)"||"bar(CD)`. Find the value of x.A. `50^(@)`B. `45^(@)`C. `60^(@)`D. `40^(@)` |
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Answer» Correct Answer - D `AB||CD implies (3x-20)^(@)+(x+40)^(@)=180^(@)` `implies x^(@)=40^(@)` Hence, the correct option is (d). |
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| 239. |
An angle is thrice its supplement. Find it.A. `120^(@)`B. `105^(@)`C. `135^(@)`D. `150^(@)` |
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Answer» Correct Answer - C Let the angle be `x^(@)` `:.` Its supplement `=(180-x)^(@)` `x=540^(@)-3x^(@)` `x^(@)=135^(@)`. Hence, the correct option is ( c). |
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| 240. |
In the following figure, O is the centre of the circle. If `angle BAC =60^@` , then `angle OBC=` __________ A. `120^@`B. `30^@`C. `40^@`D. `60^@` |
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Answer» Correct Answer - D `angle BOC=2angle BAC` and proceed. |
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| 241. |
PT and PS are the tangents to the circle with centre O. If `angle TPS=65^@`, then `angle OTS =` __________.A. `32^@`B. `45^@`C. `57(1)/(2)`D. `32(1)/(2)@` |
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Answer» Correct Answer - D Radius of a circle is perpendicular to the tangent at the point of contact and tangents drawn to a circle from an external point are equal. |
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| 242. |
In the adjacent figure, BDE is a triangle in which EB is produced to F and DB is produced to G. If `/_DBE=x^(@)=/_FBG=(x+2)^(@)` and `/_BED=(x+7)^(@)`, then the value of x is |
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Answer» (a) Vertically opposite angles are equal. Sum of the angles of a triangle is `180^(@)`. (b) `/_FBG=/_DBE` as they are vertically opposite angles. (c ) Sum of three angle of `Delta DBE` is `180^(@)` . Use this to find the required angle. |
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| 243. |
if ABCD is a trapezium, `AC and BD` are the diagonals intersecting each other at point Q. then `AC:BD=`A. `AB:CD`B. `AB+AD:DC+BC`C. `AO^2:OB^2`D. `AO-OC:OB-OD` |
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Answer» Correct Answer - D Diagonal of a trapezium divide each other proportionally. |
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| 244. |
In the following figures (not to scale), `overline(PA) and overline(PB) ` are equal chords and ABCD is a cyclic quadrilateral. If `angle DCE=80^@, angle DAP=30^@` then find `angle APB`.A. `40^@`B. `80^@`C. `90^@`D. `160^@` |
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Answer» Correct Answer - B Recall the properties of cyclic qudrilateral. `angle PAB=angle PBA and angle DAB =angle DCE`. |
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| 245. |
In the adjoining figure, O is the centre of the circle. AB and CD are equal chords. If `/_AOB =100^(@)`, then find `/_CED`. |
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Answer» Equal chords subtend equal angles at the centre of the circle. `/_ AOB=100^(@)` `implies /_DOC =100^(@)` (Angle subtended by an arc at the centre of the circle is twice the angle subtended by it anywhere in the remaining part of the circle ) `:. /_CED =(1)/(2)(100^(@))=50^(@)` |
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| 246. |
In the below figure, one part of the line of symmetrcy is given. Recongnise the second part. A. B. C. D. |
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Answer» Correct Answer - b Recall image properties |
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| 247. |
The supplement of an angle and the complement of another have a sum equal to half of a complete angle. If the greater angle is `10^(@)` more than the smaller , find the smaller angle.A. `40^(@)`B. `35^(@)`C. `45^(@)`D. `30^(@)` |
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Answer» Correct Answer - a (i) Consider the angles as x and y `( x gt y)` (ii) Frame the equation according to the given conditions and solve for x. |
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| 248. |
The angles of a triangle are in the ratio `2:3:4` . Find them The following are the steps involved in solving the above problem. Arrange them in sequential order from the first to the last. (A) `2x+3x+4x=180^(@)` `implies 9x= 180^(@)implies x=20^(@)` (B) Let the angles be A,B and C. Given `A:B:C=2:3:4` `implies A=2x,B=3x=C=4x` (C ) We know that the sumf of the angles of a triangle is `180^(@), ie., A+B+C=180^(@)` (D) The angles are `:A=2(20^(@))=40^(@),B=3(20^(@))= 60^(@)` and `C=4(20^(@))=80^(@)`.A. BCADB. CBDAC. BACDD. BDCA |
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Answer» Correct Answer - a (B),(C ) ,(A) and (D) are the sequencital order |
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| 249. |
Observe the diagram and fill the blanks.(i) ‘A’, ‘O’ and ‘B’ are ______ points(ii) ‘A’, ‘O’ and ‘C’ are ______ points(iii) ‘A’ ‘B’ and ‘C’ are _____ points(iv) ______ is the point of concurrency |
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Answer» (i) collinear points Points on a line. (ii) non collinear points Points not on a line (iii) end points/non collinear points (iv) O is the point of concurrency. A points where lines meet |
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| 250. |
The given triangle is _____.(a) a right angled triangle(b) an equilateral triangle(c) a scalene triangle(d) an obtuse angled triangle |
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Answer» (b) an equilateral triangle |
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