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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.
| 251. |
I am a closed figure with each of my three angles is 60°. Who am I? |
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Answer» Equilateral Triangle. |
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| 252. |
Two angles of the triangles are given. Find the third angle.(i) 80°, 60°(ii) 52°, 68°(iii) 75°, 35°(iv) 50°, 90°(v) 120°, 30°(vi) 55°, 85° |
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Answer» (i) 80°, 60° Let the third angle be x. Sum of the angles = 180° 80° + 60° + x = 180° 140 + x = 180° x = 180°- 140° x = 40° Third angle = 40° (ii) 52°, 68° Let the third angle be x. Sum of the angles = 180° 52° + 68° + x = 180° 120 + x = 180° 180° – 120° x = 60° Third angle = 60° (iii) 75°, 35° Let the third angle be x. Sum of the angles 180° 75° + 35° + x = 180° 110 + x = 180° x = 180° – 110° x = 70° Third angle = 70° (iv) 50°, 90° Let the third angle be x. Sum of the angles = 180° 50° + 90° + x = 180° 140 + x = 180° x = 180° – 140° x = 40° Third angle = 40° (v) 120°, 30° Let the third angle be x. Sum of the angles = 180° 120° + 30° + x = 180° 150 + x = 180° x = 180° – 150° x = 30° Third angle = 30° (vi) 55°, 85° Let the third angle be x. Sum of the angles = 180° 55° + 85° + x = 180° 140 + x = 180° x = 180° – 140° x = 40° Third angle = 40° |
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| 253. |
Study the given figure and identify the following triangles.(a) equilateral triangle(b) isosceles triangles(c) scalene triangles(d) acute triangles(e) obtuse triangles(f) right triangles |
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Answer» (a) BC = 1 + 1 + 1 + 1 = 4 cm AB = AC = 4 cm ∆ABC is an equilateral triangle. (b) ∆ABC and ∆AEF are isosceles triangles. Since AB = AC = 4 cm Also AE = AF. (c) In a scalene triangle, no two sides are equal. ∆AEB, ∆AED, ∆ADF, ∆AFC, ∆ABD, ∆ADC, ∆ABF and ∆AEC are scalene triangles. (d) In an acute-angled triangle all the three angles are less than 90°. ∆ABC, ∆AEF, ∆ABF and ∆AEC are acute-angled triangles. (e) In an obtuse-angled triangle any one of the angles is greater than 90°. ∆AEB and ∆AFC are obtuse angled triangles. (f) In a right triangle, one of the angles is 90°. ∆ADB, ∆ADC, ∆ADE and ∆ADF are right-angled triangles. |
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| 254. |
Find the value of ∠ABD = ? |
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Answer» On Sum of complementary angles = 90° ∠ABC = 90° ∠CBD = 30° ∠ABD = ∠ABC – ∠DBC = 90° – 30° = 60° ∠ABD = 60° Complementary angle of 30° = 60° |
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| 255. |
In the following figure, name the angles. |
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Answer» ∠AOB, ∠BOZ, ∠AOZ |
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| 256. |
Write the alternate name of the angle ∠XYZ in the given figure. |
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Answer» the alternate name of the angle ∠XYZ is ∠Y or ∠ZYX. |
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| 257. |
Draw the diagram of two angles having only one common point. |
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Answer» ∠COD and ∠AOB have the point ‘O’ in common. |
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| 258. |
Which direction will you face if you start facing North and take two right turns anticlockwise? |
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Answer» Will be facing South. |
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| 259. |
1. Name the rays in the given figure.2. What is the common point of all these rays? |
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Answer» 1. TA, TB, TC and TD are the rays given. 2. Point T is the common point of all these rays. |
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| 260. |
Which direction will you face if you start facing West and take three right turns clockwise? |
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Answer» Will be facing South. |
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| 261. |
state whether the statements are true (T) or false (F).(A) A regular octagon has 10 lines of symmetry.(B) Infinitely many perpendiculars can be drawn to a given ray.(C) Infinitely many perpendicular bisectors can be drawn to a given ray. |
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Answer» (A) False (B) True (C) False |
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| 262. |
Which of the following is the length of the sides of a triangle?A. 3 cm, 7 cm, 10 cmB. 2 cm, 5 cm, 7 cmC. 6 cm, 12 cm, 19 cmD. 7 cm, 24 cm, 25 cm |
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Answer» Correct Answer - D 7, 24, 25 can be the sides of the triangle. |
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| 263. |
A quadrant of a circle has ___________line of symmetry. |
| Answer» Correct Answer - one | |
| 264. |
The letter I has __________ lines of symmetry. |
| Answer» Correct Answer - two | |
| 265. |
A letter X has __________ lines of symmetry. |
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Answer» Correct Answer - two X has two lines of symmetry. `larroverset(uarr)underset(darr)"X"rarr` |
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| 266. |
Identify the shapes on the basis of description. (i) A three-sided polygon with all sides equal (ii) The longest side of a right-angled triangle. |
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Answer» (i) Equilateral triangle (ii) Hypotenuse |
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| 267. |
In the following figure, AQ is a tangent to the circular at A. If `angle ACB=60^@` , then `angle BAQ=` _______ A. `30^@`B. `60^@`C. `120^@`D. `45^@` |
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Answer» Correct Answer - B Apply alternate segment theorem. |
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| 268. |
The region bounded by the line segment AB and the part of the circle ATB is called ________ of the circle. |
| Answer» Correct Answer - segment | |
| 269. |
The tangent AB touches a circle, with centre O, at the point P, if the radius of the circle is 5 cm. `OB =10 cm` and `OB=AB`. Then find AP.A. `5sqrt(5)cm `B. `10sqrt(5) cm`C. `(10-5sqrt(3))cm`D. `(10-(5)/(sqrt3))cm` |
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Answer» Correct Answer - C Apply Pythagoras theorem. |
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| 270. |
Write the letters of the word ‘MATHEMATICS’ which have no line of symmetry. |
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Answer» The correct answer is S |
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| 271. |
The line RS which touches the circle at T is called _______ to the circle. |
| Answer» Correct Answer - tangent | |
| 272. |
Construct a quadrilateral ABCD in which AB =4.6 cm , BC=2.6 cm, CD=3.5 cm, AD=2.6 cm , and the diagonal AC=4.9 cm. |
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Answer» Steps: 1. Draw a line segment AB=4.6 cm. 2. With A and B as centres, draw two arcs of radii 4.9 cm and 2.6 cm, respectively , to intersect each other at C. 3. With C and A as centre, draw two arcs of radii 3.5 cm and 2.6 cm, respectively, to intersect at D. 4. Join BC, CD and , AD to form quadrilateral ABCD. ABCD is the required quadrilateral . |
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| 273. |
The line intersecting the circle at M and N is called _______ of the circle. |
| Answer» Correct Answer - secant | |
| 274. |
P is an interior point of quadrilateral ABCD and `AB =3.5`cm, `BC =4 cm, CD=4.8 cm ` and `AD =3.7 ` cm . Then which of the following can be the possible value of `(AP+BP+CP+DP)` ?A. 7.9 cmB. 8 cmC. 8.1 cmD. 6.4 cm |
| Answer» Correct Answer - C | |
| 275. |
`{:("Across","Down"),("1. Angle P is 30 degrees and angle Q is 60 degrees","1. The two non-adjacent angles which are not alternate is"),("2. The line intersecting two or more lines at different points is","3. Union of two rays"),("6. Straight lines intersecting at right angles","4. Sum of these angles is 180 degrees"),("8. Non-intersecting lines","5. Geometrical instrument"),("10.The two interior non-adjacent angles which lie on either side of the transversal is ","7. Unit for measuring angles"),("11.The rays which form the angle are","9. The common point of the arms of an angle"):}` |
| Answer» Correct Answer - `{:("Across","Down"),("1. Complementary","1. Corresponding"),("2. Transversal","3. Angle"),("6. Perpendicular","4. Supplementary"),("8. Parallel","5. Protractor"),("10.Alternate","7. Degrees"),("11.Arms","9. Vertex"):}` | |
| 276. |
In the following figures, the figure that is not symmetric with respect to any line is:(A) (i) (B) (ii) (C) (iii) (D) (iv) |
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Answer» The correct answer is (B) (ii) |
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| 277. |
State whether the statement are true (T) or false (F):A horizontal line and a vertical line always intersect at right angles. |
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Answer» True. A horizontal line and a vertical line always intersect at right angles. |
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| 278. |
Fill in the blanks to make the statements true:The common part between the two angles BAC and DAB in Fig. is ______. |
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Answer» The common part between the two angles BAC and DAB in Fig. is ray AB. |
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| 279. |
Fill in the blanks to make the statements true:The number of common points in the two angles marked in Fig. is ______. |
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Answer» One The two angles marked; ∠CAB and ∠DAE. ∴ The number of common point is 1 and that is A. |
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| 280. |
Fill in the blanks to make the statements true:The number of common points in the two angles marked in Fig. ______ . |
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Answer» Three There are 3 common points in the two angles marked in the given figure and these are P, Q and R. |
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| 281. |
The sum of an angle and half of its complementary angle is `75^(@)`. Find the angle .A. `40^(@)`B. `50^(@)`C. `60^(@)`D. `80^(@)` |
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Answer» Correct Answer - C Let the required angle be x. `:.` Complement of x is `90^(@)-x` `implies x+((90^(@)-x))/(2)=75^(@)` `implies 2x+90^(@)-x=150^(@)` `implies x=60^(@)` Hence, the correct option is (c ). |
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| 282. |
Which of the following is/are point symmetric ?A. RectangleB. SquareC. ParallelogramD. All of these |
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Answer» Correct Answer - D All the given figure are point symmetric. The point of symmetry is the point of intersection of their diagonals. Hence, the correct option is (d). |
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| 283. |
Find the diameter of a circle whose circumference is 39.6 cm. |
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Answer» Correct Answer - 12.6 cm Given, the circumference of the circle = 39.6 cm `2pir=39.6cm` `2xx(22)/(7)xxr=39.6` `2r=39.6xx(7)/(22)` `2r=1.8xx7` `2r=12.6cm` `therefore"Diameter of the circle"=12.6 cm` |
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| 284. |
Find the perimeter of the quadrant of a circle of radius 14 cm. |
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Answer» Correct Answer - 50 cm `"Perimeter of quadrant"=2r+(1)/(4)xx2pir` Given r = 14 cm. `"Perimeter"=2xx14+(1)/(2)xx(22)/(7)xx14` `=28+22` `= 50 cm` |
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| 285. |
Which of the following cannot be the measures of an isosceles triangle ABC?A. Angle A is `50^(@)` and angle B is `80^(@)`B. Angle A is `65^(@)` and angle B is `50^(@)`C. Angle A is `60^(@)` and angle B is `70^(@)`D. All of these |
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Answer» Correct Answer - C If any two angles of a triangle are equal, then the triangle is isosceles. The sum of all angles of a triangle is `180^(@)`. Choice (a) : Angle A is `50^(@)` and angle B is `80^(@)`. Angle C = `180^(@)-50^(@)-80^(@)=50^(@). rArrABC` is an isosceles triangle. Choice (b) : Angle A is `65^(@)` and angle B is `50^(@)`. Angle ` C= 180^(@)-65^(@)-50^(@)=65^(@).rArrABC` is an isosceles triangle. Choice (c) Angle A is `60^(@)` and angle B is `70^(@)`. Angle `C=180^(@)-60^(@)-70^(@)=50^(@)rArrABC` is not an isosceles triangle. Hence, choice (c) follows. Hence, the correct option is (c). |
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| 286. |
The perimeter of the quadrant of a circle is 37.5 cm. Find the circle (in `cm^(2)`).A. 346.5B. 325.5C. 275.25D. 173.25 |
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Answer» Correct Answer - A Given that the perimeter of the quadrant of a circle is 37.5 cm. `rArr (2pi//4)+2r=37.5` `rArr(11r//7)+2r=37.5` `rArr(11//7+2)r=37.5` `rArr(25//7)r=37.5` `rArrr = 10.5` The area of the circle (in `cm^(2)`) = `pir^(2)` `=(22//7)(10.5)2` `=(22)(1.5)(10.5)` `=(33)(10.5)` `=(33)(10.5)` `=346.5` Hence, the correct option is (a). |
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| 287. |
Fill in the blanks to make the statements true:The number of right angles in a straight angle is ______ and that in a complete angle is ______. |
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Answer» The number of right angles in a straight angle is two and that in a complete angle is four. We know that, angle formed by straight angle = 180o and angle formed by right angle = 90o So, number of right angles = 180o/90o= 2 We know that, complete angle = 360o So, number of right angles = 360o/90o= 4 |
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| 288. |
State the mid points of all the sides of Fig. |
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Answer» X is a mid-point of AC, Y is a mid-point of BC and Z is a mid-point of AB. |
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| 289. |
Name the vertices and the line segments in Fig.. |
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Answer» The vertices are : A, B, C, D and E. The line segments are : AB, BC, CD, DE, EA, AC and AD. |
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| 290. |
A line which intersects a circle at two distinct point is called a ______ of the circle. |
| Answer» Correct Answer - secant | |
| 291. |
Name the line segments shown in Fig. |
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Answer» The line segments are AB, BC, CD, DE and EA. |
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| 292. |
state whether the statements are true (T) or false (F).(A) If a rectangle has more than two lines of symmetry, then it must be a square.(B) With ruler and compasses, we can bisect any given line segment.(C) Only one perpendicular bisector can be drawn to a given line segment. |
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Answer» (A) True (B) True (C) True |
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| 293. |
The sum an angle and one-third of its supplementary angle is `90^(@)`. Find the angle.A. `135^(@)`B. `120^(@)`C. `60^(@)`D. `45^(@)` |
| Answer» Correct Answer - D | |
| 294. |
State whether the statement are true (T) or false (F):Two angles can have exactly five points in common. |
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Answer» False. Two angles can have either one or two five points in common. |
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| 295. |
Fill in the blanks to make the statements true.(A) The distance of the image of a point (or an object) from the line of symmetry (mirror) is ________ as that of the point (object) from the line (mirror).(B) The number of lines of symmetry in a picture of Taj Mahal is _______.(C) The number of lines of symmetry in a rectangle and a rhombus are ______ (equal/unequal). |
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Answer» (A) The distance of the image of a point (or an object) from the line of symmetry (mirror) is same as that of the point (object) from the line (mirror). (B) The number of lines of symmetry in a picture of Taj Mahal is One. (C) The number of lines of symmetry in a rectangle and a rhombus are Equal (equal/unequal). |
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| 296. |
Fill in the blank,If an angle of measure 80o is reflected in a line of symmetry, then the reflection is an ______ of measure _______. |
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Answer» If an angle of measure 80o is reflected in a line of symmetry, then the reflection is an Angle of measure 80°. |
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| 297. |
Fill in the blank(A) A rhombus is symmetrical about _________.(B) A rectangle is symmetrical about the lines joining the _________ of the opposite sides. |
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Answer» (A) A rhombus is symmetrical about diagonals (B) A rectangle is symmetrical about the lines joining the mid point of the opposite sides. |
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| 298. |
Fill int the blank to make the statements true.(A)The common properties in the two set-squares of a geometry box are that they have a __________ angle and they are of the shape of a __________.(B) The digits having only two lines of symmetry are_________ and __________.(C) The digit having only one line of symmetry is __________. |
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Answer» (A)The common properties in the two set-squares of a geometry box are that they have a right angle and they are of the shape of a triangle. (B) The digits having only two lines of symmetry are o and 8. (C) The digit having only one line of symmetry is 3. |
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| 299. |
How many excircles can be drawn for a triangle ?A. 3B. 2C. 4D. 1 |
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Answer» Correct Answer - A 3 Hence, the correct option is (a) |
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| 300. |
Which of the following angle cannot be an interior angle of any convex polygon ? |
| Answer» Interior angle of any convex polygon cnnot be more than `180^(@)`. | |