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This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Thales belongs to the country : (A) Babylonia (B) Egypt (C) Greece (D) Rome |
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Answer» (C) Greece Thales belongs to the country Greece. |
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| 2. |
Euclid belongs to the country(a) Babylonia(b) Egypt(c) Greece(d) India |
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Answer» (c) Greece Euclid belongs to the country Greece. |
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| 3. |
In ancient India, altars with combination of shapes like rectangles, triangles and trapeziums were used for(a) public worship(b) household rituals(c) Both (a) and (b)(d) None of these |
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Answer» (a) public worship In ancient India altars whose shapes were combinations of rectangles, triangles and trapeziums were used for public worship. |
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| 4. |
The number of interwoven isosceles triangles in Sriyantra (in the Atharvaveda) is: (A) Seven (B) Eight (C) Nine (D) Eleven |
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Answer» (C) Nine The Sriyantra (in the Atharvaveda) consists of nine interwoven isosceles triangles. |
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| 5. |
Write whether the following statements are True or False? Justify your answer.(i) Pyramid is a solid figure, the base of which is a triangle or square or some other polygon and its side faces are equilateral triangles that converges to a point at the top. (ii) In Vedic period, squares and circular shaped altars were used for household rituals, while altars whose shapes were combination of rectangles, triangles and trapeziums were used for public worship. (iii) In geometry, we take a point, a line and a plane as undefined terms. (iv) If the area of a triangle equals the area of a rectangle and the area of the rectangle equals that of a square, then the area of the triangle also equals the area of the square. (v) Euclid’s fourth axiom says that everything equals itself. (vi) The Euclidean geometry is valid only for figures in the plane. |
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Answer» (i) False. The side faces of a pyramid are triangles not necessarily equilateral triangles. (ii) True. The geometry of Vedic period originated with the construction of vedis and fireplaces for performing vedic rites. The location of the sacred fires had to be in accordance to the clearly laid down instructions about their shapes and area. (iii) True. To define a point, a line and a plane in geometry we need to define many other things that give a long chain of definitions without an end. For such reasons, mathematicians agree to leave these geometric terms undefined. (iv) True. Things equal to the same thing are equal. (v) True. It is the justification of the principle of superposition. (vi) True. It fails on the curved surfaces. For example on curved surfaces, the sum of angles of a triangle may be more than 180°. |
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| 6. |
Write whether True or False and justify your answer.Euclidean geometry is valid only for curved surfaces. |
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Answer» False Because Euclidean geometry is valid only for the figures in the plane but on the curved surfaces, it fails. |
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| 7. |
‘Lines are parallel if they do not intersect’ is stated in the form of (A) an axiom (B) a definition (C) a postulate (D) a proof |
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Answer» (B) a definition ‘Lines are parallel, if they do not intersect’ is the definition of parallel lines. |
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| 8. |
Look at the Fig. Show that length AH > sum of lengths of AB + BC + CD. |
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Answer» According to the given figure, we have, AB+BC+CD =AD Here, AD is a part of AH. According to Euclid’s axiom, “The whole is greater than the part” i.e., AH > AD Therefore, length AH > sum of the lengths of AB+BC+CD. |
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| 9. |
Two salesmen make equal sales during the month of August. In September, each salesman doubles his sale of the month of August. Compare their sales in September. |
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Answer» Let the equal sale of two salesmen in August be x. In September each salesman doubles his sale of August. Thus, sale of first salesman is 2x and sale of second salesman is 2x. According to Euclid’s axioms, things which are double of the same things are equal to one another. So, in September their sales are again equal. |
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| 10. |
Ram and Ravi have the same weight. If they each gain weight by 2 kg, how will their new weights be compared ? |
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Answer» Let x kg be the weight each of Ram and Ravi. On gaining 2 kg, weight of Ram and Ravi will be (x + 2) each. According to Euclid’s second axiom, when equals are added to equals, the wholes are equal. So, weight of Ram and Ravi are again equal. |
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| 11. |
It is known that x + y = 10 and that x = z. Show that z + y = 10? |
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Answer» According to the question, We have, x+y=10 …(i) And, x=z …(ii) Applying the Euclid’s axiom, “if equals are added to equals, the wholes are equal” We get, From Eqs. (i) and (ii) x+y=z+y ….(iii) From Eqs. (i) and (iii) z+y=10 |
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| 12. |
In the adjoining figure, we have X and Y are the mid-points of AC and BC and AX = CY. Show that AC = BC. |
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Answer» Given, X is the mid-point of AC AX = CX= ½ AC ⇒ 2AX =2CX = AC …(i) Y is the mid-point of BC. BY = CY = ½ BC ⇒ 2BY = 2CY= BC …(ii) According to the question, We also have, AX=CY …(iii) Applying the Euclid’s axiom, “Things which are double of the same things are equal to one another”. We get, From Eq. (iii), 2AX = 2CY Using Eqs. (i) and (ii), we get, AC=BC Hence Proved. |
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| 13. |
In the adjoining figure, if AB = BC and BX = BY, then show that AX = CY |
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Answer» According to the question, We have, AB =BC …(i) and BX=BY …(ii) According to Euclid’s axiom, “If equals are subtracted from equals, the remainders are equal.” Subtracting Eq.(ii) from (i), We get, AB-BX = BC-BY ⇒ AX = CY [from the given figure] |
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| 14. |
In the Fig., if ∠1 = ∠3, ∠2 = ∠4 and ∠3 = ∠4, write the relation between ∠1 and ∠2, using an Euclid’s axiom. |
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Answer» Here, ∠3 = ∠4, ∠1 = ∠3 and ∠2 = ∠4. Euclid’s first axiom says, the things which are equal to equal thing are equal to one another. So, ∠1 = ∠2. |
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| 15. |
In the adjoining figure, we have ∠1 =∠3 and ∠2 = ∠4. Show that ∠A = ∠C. |
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Answer» Given,∠1 = ∠3 …(i) and ∠2 = ∠4 …(ii) According to Euclid’s axiom, if equals are added to equals, then wholes are also equal. On adding Eqs. (i) and (ii), we get ∠1 + ∠2 = ∠3 +∠4 => ∠A = ∠C |
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| 16. |
In the adjoining figure, we have ∠1 = ∠2 and ∠2= ∠3. Show that ∠1 = ∠3. |
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Answer» Given, ∠1 =∠2 …(i) and ∠2 = ∠3 …(ii) According to Euclid’s axiom, things which are equal to the same thing are equal to one another. From Eqs. (i) and (ii), ∠1 = ∠3 |
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| 17. |
In Fig., we have : AC = XD, C is the mid-point of AB and D is the mid-point of XY. Using an Euclid’s axiom, show that AB = XY. |
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Answer» AB = 2AC (C is the mid-point of AB) XY = 2XD (D is the mid-point of XY) Also, AC = XD (Given) Therefore, AB = XY, because things which are double of the same things are equal to one another. |
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| 18. |
Solve the equation a – 15 = 25 and state which axiom do you use here. |
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Answer» a – 15 = 25. On adding 15 to both sides, we have a – 15 + 15 = 25 + 15 = 40 (using Euclid’s second axiom). or a = 40 |
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| 19. |
In the adjoining figure, if BX = ½ AB, BY = ½ BC and AB = BC, then show that BX = BY. |
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Answer» According to the question, We have, BX = ½ AB and BY = ½ BC ⇒ 2BX = AB ….(i) ⇒ 2BY = BC ….(ii) It is also given that, AB = BC …(iii) Substituting the values from Eqs. (i) and (ii) in eq. (iii), we get, 2BX = 2BY Applying the Euclid’s axiom, “things which are double of same things are equal to one another”. BX = BY |
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| 20. |
It is known that if x + y = 10 then x + y + z = 10 + z. The Euclid’s axiom that illustrates this statement is :(A) First Axiom (B) Second Axiom (C) Third Axiom (D) Fourth Axiom |
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Answer» (B) Second Axiom The Euclid’s axiom that illustrates the given statement is second axiom, according to |
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| 21. |
Write whether True or False and justify your answer.Attempt to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries. |
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Answer» True All attempts to prove the fifth postulate as a theorem led to a great achievement in the creation of several other geometries. These geometries are quite different from Euclidean geometry and called non-Euclidean geometry. |
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| 22. |
Which of the following needs a proof ? (A) Theorem (B) Axiom (C) Definition (D) Postulate |
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Answer» (A) Theorem The statements that were proved are called propositions or theorems. |
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