Geometry (Railway Maths) (Part – I)

Total Questions: 50

1. Find x if ABCD is a parallelogram as given in figure below, with two diagonals AC and BD intersecting at O and OA = x + 3, OB = y + 2, OC = 2x + y, OD = 3y? [Group D 17/08/2022 (Morning) ]

Correct Answer: (a) 2
Solution:

2. When two transversals intersect three parallel lines, and the ratio of the intercepts formed by the first transversal is 3 : 4, then find the ratio of the intercepts formed by the second transversal. [Group D 17/08/2022 (Afternoon) ]

Correct Answer: (c) 3 : 4
Solution:

3. In the given figure <ABC = <ABD, BC = BD then Δ CAB ≅ Δ.......? [Group D 17/08/2022 (Evening) ]

Correct Answer: (b) DAB
Solution:

4. In the given figure, AB || QP, AB = x, PQ = x + 10, RB = x/2, BP = x + 1. Find PQ [Group D 18/08/2022 (Morning) ]

Correct Answer: (d) 14 units
Solution:

5. Two angles are complementary. The larger angle is 6° less than thrice the measure of the smaller angle. What is the measure of the larger angle? [Group D 18/08/2022 (Afternoon) ]

Correct Answer: (a) 66°
Solution:

6. If AB = x + 3, BC = 2x and AC = 4x − 5, then for what value of ‘x’ does B lie on AC ? [Group D 18/08/2022 (Afternoon)]

Correct Answer: (c) 8
Solution:

7. Which of the following is NOT a true statement ? [Group D 22/08/2022 (Afternoon)]

Correct Answer: (b) Diagonals of a rectangle do not bisect each other.
Solution:

Diagonals of a rectangle bisect each other.

8. In a parallelogram, two adjacent sides are in the ratio 3 : 2 and its perimeter is 65 cm. What is the length of each of the two smaller sides of this parallelogram ? [Group D 23/08/2022 (Evening)]

Correct Answer: (b) 13 cm
Solution:

Let the length and breadth of the parallelogram be 3x and 2x
Perimeter = 2 (length + breadth)
2(3x + 2x) = 65 ⇒ 10x = 65 ⇒ x = 6.5
Smaller side = 2x = 2 × 6.5 = 13 cm

9. The ratio of the sum of all the interior angles to an exterior angle of a regular polygon is 24 : 1. Find the number of sides of the polygon. [Group D 25/08/2022 (Afternoon) ]

Correct Answer: (d) 8
Solution:

10. If Δ ABC ≌ ΔPQR, which of the following need not be NECESSARILY true? [Group D 26/08/2022 (Morning) ]

Correct Answer: (a)
Solution: