Geometry (Railway Maths) (Part – VI)

Total Questions: 50

31. The length and breadth of a rectangular field are in the ratio of 6 : 5. If the perimeter of the field is 110 m, then what will be the breadth (in m)? [RRB NTPC 13/03/2021 (Morning)]

Correct Answer: (d) 25
Solution:

32. The sum of two angles ∠A and ∠B of a triangle ∆ABC is equal to its third angle. Find the measure of the third angle? [RRB NTPC 14/03/2021 (Evening)]

Correct Answer: (c) 90°
Solution:

33. Find the number of sides of a regular polygon if each interior angle is 165°. [RRB NTPC 15/03/2021 (Morning)]

Correct Answer: (a) 24
Solution:

34. In the given circle. Diameter AB is extended to meet chord CD extended at P. If the lengths of the line segment AP, CP, and DP are 12 cm, 8 cm, and 6 cm, respectively. What is the length of the radius of the circle? [RRB NTPC 19/03/2021 (Morning) ]

Correct Answer: (d) 4 cm
Solution:

35. In the given circle with center O. the acute angle at the center measures 88°. In the quadrilateral drawn inside the circle, what is the measure of the angle opposite to <0 ? [Figure is not drawn to scale] [RRB NTPC 19/03/2021 (Morning) ]

Correct Answer: (d) 136°
Solution:

Opposite of <O
= (360° - 88°) ÷ 2 = 136°

36. If the largest angle in a triangle is 75°. What is the least possible value of the smallest angle of the triangle? [RRB NTPC 21/03/2021 (Evening)]

Correct Answer: (a) 30°
Solution:

Sum of angles of a triangle = 180°
Sum of remaining two angles
= 180° - 75° = 105°
Sum of two angles must be equal to or greater than 3rd angle Least value of Smallest angle
= 105° - 75° = 30°

37. What is the sum of the measures of the interior angles of a hexagon? [RRB NTPC 27/03/2021 (Morning)]

Correct Answer: (a) 720°
Solution:

Sum of interior angles of hexagon = 180 × (6 - 2)
= 180 × 4 = 720°

38. The circumradius of a triangle is 9 cm while the inradius is 4 cm. What is the distance between the circumcentre and the incentre of the triangle? [RRB NTPC 27/03/2021 (Evening)]

Correct Answer: (c) 3 cm
Solution:

39. If AB / AC = BD / DC then <ABC is: [RRB NTPC 01/04/2021 (Morning) ]

Correct Answer: (c) 64°
Solution:

40. Find the area of ∆ABC. [RRB NTPC 01/04/2021 (Morning) ]

Correct Answer: (b) 160 cm²
Solution:

ABC is a right angled triangle because angle A is the angle formed by diameter. Area of ∆ABC
= 1/2 × 16 × 20 = 160 cm²