Geometry (Railway Maths) (Part – III)

Total Questions: 50

31. The length of each of the two equal sides of an isosceles triangle is 5 cm each and the length of its base is 8 cm. The area (in cm²) of the triangle is: [Group D 13/09/2022 (Afternoon)]

Correct Answer: (d) 12
Solution:

32. In a triangle, if one angle measures twice the smallest angle and the third one measures three times the smallest angle, then the measure of the greatest angle is: [Group D 14/09/2022 (Morning)]

Correct Answer: (a) 90°
Solution:

33. m and n are two parallel lines. If l is a transversal intersecting m and n, then the sum of the interior angles formed on the same side of l is equal to: [Group D 14/09/2022 (Afternoon)]

Correct Answer: (c) 180°
Solution:

From the properties of parallel lines, When two parallel lines are intersected by a transversal then sum of the interior angles formed on the same side of the transversal = 180°

34. If the lengths of the sides of a triangle are x+1, 7-x and 4x-2, then the value of x for which the triangle represents an isosceles triangle is_________. [Group D 14/09/2022 (Afternoon) ]

Correct Answer: (a) 1.8
Solution:

In an isosceles triangle, two sides are equal in length.
4x - 2 = 7 - x
⇒ 4x + x = 7 + 2 ⇒ 5x = 9 ⇒ x = 1.8

35. In an isosceles triangle, the vertex angle measures 80°. What is the measure of each of the base angles? [Group D 14/09/2022 (Evening) ]

Correct Answer: (a) 50° and 50°
Solution:

36. As per the figure given below ∆ QRS ≅ _______.[Note: Diagram is not drawn to scale or measurements indicated.] [Group D 15/09/2022 (Morning) ]

Correct Answer: (b) 🛆QPT
Solution:

37. In a triangle PQR, <P = 30° and the straigth line UV is drawn parallel to QR, intersecting PQ at S and PR at T. Which of the following is always true? [Group D 17/09/2022 (Morning) ]

(1) PS / PQ = PT / PR
(2) ST = QR/2
(3) The triangle PST is similar to the triangle PQR.

Correct Answer: (a) Only 1 and 3
Solution:

38. AD is the altitude of an isosceles triangle ABC in which AB = AC. Which of the following is true for AD? [Group D 17/09/2022 (Morning) ]

Correct Answer: (a) AD bisects <A
Solution:

39. In the given figure, AB is parallel to CD. What is the value of x° ? [Group D 17/09/2022 (Afternoon) ]

Correct Answer: (c) 80°
Solution:

40. In triangle DEF, side EF is produced to G. If <DFG = 110° and EF = DF, then <DEF measures: [Group D 18/09/2022 (Morning) ]

Correct Answer: (c) 55°
Solution: