Geometry (Railway Maths) (Part – II)

Total Questions: 50

1. The earth takes 24 h to rotate about its own axis. Through what angle will it turn in 5 h and 24 min? [NTPC CBT-I 09/02/2021 (Evening)]

Correct Answer: (b) 81°
Solution:

2. Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm. [NTPC CBT-I 11/02/2021 (Morning)]

Correct Answer: (c) 12° 36′
Solution:

3. If a, b and c are the sides of a triangle and a² + b² + c² = ab + bc + ca, then the triangle is: [NTPC CBT-I 16/02/2021 (Morning)]

Correct Answer: (a) equilateral
Solution:

It's possible in equilateral triangle In an equilateral triangle , all sides are equal to each other., (a = b = c)

4. Two sides of a triangle are of lengths 4 cm and 10 cm. If the length of the third side is a cm, then … [NTPC CBT-I 17/02/2021 (Morning)]

Correct Answer: (c) 6 < a < 14
Solution:

Let the 3rd side = a Third side of the triangle lies
10 - 4 < a < 10 + 4 ⇒ 6 < a < 14

5. A boy walks along two adjacent sides of a rectangular field. If he walks along its diagonal, then he saves a distance equal to one-third of the larger side. Find the ratio of the larger side to the smaller side. [NTPC CBT-I 01/03/2021 (Evening)]

Correct Answer: (d) 12 : 5
Solution:

6. The angle between two circles x² + y² − 12x − 6y + 41 = 0 and x² + y² + kx + 6y − 59 = 0 is 45°. Find the value of k. [NTPC CBT-I 09/03/2021 (Evening)]

Correct Answer: (b) ±4
Solution:

7. In the figure, if the area of the shaded sector is 70% of the area of the entire circle, then the measure of x° is________. [NTPC CBT - I 01/04/2021 (Evening) ]

Correct Answer: (a) 108°
Solution:

100% = 360°
100 - 70% = 30% = 30 × 360°/ 100 = 108°

8. A circle having centre C₁, radius r₁ = 5 cm is placed against a right angle. Another smaller circle having centre c₂, radius r₂ is also placed touching the sides of the angle and the bigger circle as shown in the figure. Find the radius, r₂ in cm, of the smaller circle. [NTPC CBT - I 03/04/2021 (Morning) ]

Correct Answer: (c) 5(3 - 2√2)
Solution:

9. The perimeters of two similar triangles Δ PQR and Δ XYZ are 48 cm and 24 cm respectively. If XY = 12 cm, then PQ is [NTPC CBT - I 03/04/2021 (Evening) ]

Correct Answer: (c) 24 cm
Solution:

10. The length of the tangent drawn from a point Q to a circle is 40 cm and the distance of point Q from the center is 41 cm, then The radius of the circle will be_____cm. [ALP Tier II 21/01/2019 (Afternoon) ]

Correct Answer: (c) 9
Solution: