Geometry (Railway Maths) (Part – I)

Total Questions: 50

21. The number of non-overlapping triangles that can be formed in an 11-sided polygon by joining the vertices are: [Group D 22/09/2022 (Morning) ]

Correct Answer: (c) 9
Solution:

non-overlapping triangles can be made in n-gon (polygon having n sides), by joining the vertices = n - 2 Therefore number of triangles
= 11 - 2 = 9

22. In triangle ABC, P. Q, and R are the mid points of its sides BC, CA, and AB, respectively. If the area of triangle PQR is 6 cm², then the area of triangle ABC is : [Group D 22/09/2022 (Evening) ]

Correct Answer: (c) 24 cm²
Solution:

23. In a triangle ABC, if AD is the angle bisector of <BAC, AE 丄 BC, <B = 30° and <C = 50°, then <DAE is: [Group D 28/09/2022 (Evening) ]

Correct Answer: (c) 10°
Solution:

24. In the given figure, AB || CD || EF. The value of x° is : [Group D 29/09/2022 (Afternoon) ]

Correct Answer: (d) 148°
Solution:


In the given figure, AB || CD || EF.
∠ABC = ∠BCD
∠BCD = 65°
∠DCE = 65° − 33° = 32°
∠DCE + ∠CEF = 180°
32° + ∠CEF = 180°
∠CEF = 180° − 32° = 148°
Hence, value of x = 148°

25. Find the area of ABPD if AB = DC = 4 m , AD = BC = 2.5 m , and PC = 1 m. [Group D 06/10/2022 (Evening) ]

Correct Answer: (c) 8.75 m²
Solution:

26. The lengths of two sides of a triangle are 24 cm and 26 cm. Which of the following can be the measure of the third side ? [Group D 06/10/2022 (Evening)]

Correct Answer: (a) 48 cm
Solution:

Two sides of triangle = 24 cm and 26 cm We know, Third side < sum of other two sides So, possible measure of third side = 48 cm

27. The interior angles of an 8-sided polygon are in the ratio 1 : 3 : 4 : 6 : 7 : 11 : 13 : 15. Find the measure of the largest interior angle in this polygon. [Group D 11/10/2022 (Morning)]

Correct Answer: (c) 270°
Solution:

28. In a circle, chords AB and CD are produced to meet at E, outside the circle. If AB = 9 cm and AE = 12 cm and ED = 4 cm, then what is the length of the chord CD ? [NTPC CBT II Level 3 (14/06/2022) Shift 1]

Correct Answer: (b) 5 cm
Solution:


3 × 12 = 4(4 + x) ⇒ 36 = 16 + 4x
4x = 20 ⇒ x = 5
So, length of CD = 5 cm

29. An equilateral triangle ABC is inscribed in a circle with radius 12 cm and centre O. Find the length of each side of the triangle ABC (in cm). [NTPC CBT II Level 5 (15/06/2022) Shift 2]

Correct Answer: (d) 12√3
Solution:

30. Two equal circles, each having a radius of 24 cm, intersect each other, such that each passes through the centre of the other. The length of the common chord is ___ cm. [NTPC CBT II Level 2 (16/06/2022) Shift 3]

Correct Answer: (d) 24√3
Solution:


Length of common chord AB = 2 × AO
= 2 × √(24² − 12²) = 2 × 12√3 = 24√3 cm