Geometry (Railway Maths) (Part – IV)

Total Questions: 50

11. Straight lines l and m are parallel to each other. Points A and B lie on the line l, points C and D lie on the line m, and E is a point that lies between the straight lines l and m, all in such a manner that m∠EAB = 50° and m∠ECD = 70°. Find the measure of ∠AEC if points A and C lie on the same side of point E. [Group D 07/10/2022 (Morning)]

Correct Answer: (d) 120°
Solution:

12. The perimeter of a regular pentagon whose each side is 2a cm long is: [Group D 07/10/2022 (Morning)]

Correct Answer: (d) 10a cm
Solution:

Perimeter of pentagon = 5a = 5 × (2a) = 10a cm

13. Two sides of a triangular field are 41 m and 28 m. If its perimeter is 84 m, then what is the length of the smallest altitude of the triangle? [Give your answer correct to two places of decimal.] [Group D 07/10/2022 (Morning) ]

Correct Answer: (d) 6.15 m
Solution:

14. If ΔABC and ΔDEF are similar and AB = 6 cm, DE = 8 cm , EF = 10 cm and FD = 14 cm, then the perimeter of ΔABC is: [Group D 07/10/2022 (Evening) ]

Correct Answer: (b) 24 cm
Solution:

15. In the given figure, ABCD and APQR are two parallelograms. If <APQ = 100°, find <CDR. [Group D 11/10/2022 (Evening) ]

Correct Answer: (b) 80°
Solution:

16. In the given figure, triangle ABC is similar to triangle ADE. If the area of triangle ADE = 18 cm² , then the area of triangle ABC is : [Group D 11/10/2022 (Evening) ]

Correct Answer: (a) 50cm²
Solution:

17. AB and CD are parallel tangents to a circle with centre O. Points P and Q are on AB and CD, respectively, such that PQ touches the circle at R. Find the measure of ∠POQ. [Level 6 (09/05/2022) Shift 1]

Correct Answer: (b) 90°
Solution:

18. PQRS is a cyclic quadrilateral in a circle with centre O. ∠PQR and ∠PSR are in the ratio 11 : 7. If PQ = QR, then find ∠OPQ. [Level 6 (09/05/2022) Shift 2]

Correct Answer: (a) 55°
Solution:

19. Two chords AB and CD of a circle intersect at a point F outside the circle. If AF = 12 cm, BF = 4 cm and CF = 16 cm, find the length of CD. [Level 5 (12/06/2022) Shift 1]

Correct Answer: (a) 13 cm
Solution:

20. ABCD is a cyclic quadrilateral, AB is a diameter of the circle. If ∠ACD = 35°, find the value of ∠BAD. [Level 5 (12/06/2022) Shift 2]

Correct Answer: (b) 55°
Solution: