Geometry (Railway Maths) (Part – VI)

Total Questions: 50

1. Two adjacent angles form an angle of 100°. The larger angle is 20° less than five times the smaller angle. The larger angle is: [RRB NTPC 11/02/2021 (Morning) ]

Correct Answer: (c) 80°
Solution:

Let the smaller angle = x
Larger angle = 5x - 20
A/Q, x + 5x - 20 = 100°
⇒ 6x = 120° ⇒ x = 20°
Larger angle = 5 × 20 - 20 = 80°

2. When an arm of an angle is extended to double its length then the measure of the angle. [RRB NTPC 11/02/2021 (Morning) ]

Correct Answer: (d) Remains the same
Solution:

The angle does not change with its arm length.

3. What is the sum of all angles of all triangles in the given figure? [RRB NTPC 12/02/2021 (Morning) ]

Correct Answer: (d) 1440⁰
Solution:

Total number of triangle = 8
Sum of the angle in a triangle = 180°
Now, the sum of all angles of all triangles = 8 × 180° = 1440°

4. In a rhombus ABCD, if <ACB = 40⁰, then <ADB = ? [RRB NTPC 15/02/2021 (Evening) ]

Correct Answer: (b) 50⁰
Solution:

5. P is the midpoint of side BC of parallelogram ABCD such that <BAP = <DAP If AD = 10cm, then cd = ? [RRB NTPC 15/02/2021 (Evening) ]

Correct Answer: (c) 5 cm
Solution:

6. If the difference between the areas of the circumcircle and the incircle of an equilateral triangle is 66 cm², then the area of the triangle is: [RRB NTPC 16/02/2021 (Morning) ]

Correct Answer: (c) 21√3 cm²
Solution:

7. The ratio of the areas of two triangles is 4 : 3 and the ratio of their heights is 3 : 4. Find the ratio of their bases. [RRB NTPC 16/02/2021 (Evening) ]

Correct Answer: (c) 16 : 9
Solution:

8. The base and the altitude of a right-angled triangle are 15 cm and 8 cm respectively. What is the altitude from the opposite vertex to its hypotenuse? [RRB NTPC 16/02/2021 (Evening) ]

Correct Answer: (c)
Solution:

9. In a triangle ABC, points D and E are on the sides AB and AC such that DE is parallel to BC and AD / BD = 3 / 5. If AC = 4 cm, Then AE = ? [RRB NTPC 17/02/2021 (Morning)]

Correct Answer: (a) 1.5 cm
Solution:

10. If the side of an equilateral triangle is 2 cm, then find the area and the altitude of the triangle. [RRB NTPC 17/02/2021 (Morning)]

Correct Answer: (b) Area = √3 cm² and altitude = √3 cm
Solution: