Geometry (Railway Maths) (Part – I)

Total Questions: 50

31. In ΔABC, AD is a median of the triangle, intersecting BC at D. The three medians of the triangle meet at a point G. If AG = (7y − 3) cm and DG = 3y cm, then find the length of AD. [NTPC CBT II Level 3 (17/06/2022) Shift 1]

Correct Answer: (d) 27 cm
Solution:

32. From a point Q, the length of the tangent to a circle is 21 cm and the distance of Q from the center ‘O’ of the circle is 29 cm. Find the radius of the circle. [NTPC CBT II Level 3 (17/06/2022) Shift 2]

Correct Answer: (a) 20 cm
Solution:

33. ABC is an equilateral triangle. P, Q and R are the midpoints of sides AB, BC and AC respectively. The length of the side of the triangle is 4 cm. The area of triangle PQR is [NTPC CBT-I 28/12/2020 (Evening)]

Correct Answer: (c) √3 cm²
Solution:

34. In a circle with a radius 10 cm, XY and PQ are two parallel chords 12 cm and 16 cm in length, respectively. The two chords are situated on the opposite sides of the centre. The distance between the chords is [NTPC CBT-I 29/12/2020 (Evening)]

Correct Answer: (b) 14 cm
Solution:

35. In the given figure, <ABD = 55° and <ACD = 30°. If <BAC = y° and non - reflex <BDC = x°, then what is the value of x - y? [NTPC CBT - I 05/01/2021 (Morning) ]

Correct Answer: (c) 85
Solution:

36. The sides of a certain triangle are given below. Identify the one which is a right angled triangle. [NTPC CBT-I 05/01/2021 (Evening)]

Correct Answer: (d) a = 7 cm, b = 24 cm, c = 25 cm
Solution:

37. In which of the following cases is Δ ABC similar to Δ PQR? [NTPC CBT-I 05/01/2021 (Evening)]

Correct Answer: (d) Sides AB = 2.5 cm, BC = 4.5 cm, CA = 3.5 cm, PQ = 5 cm, QR = 9 cm, RP = 7 cm
Solution:

38. A circle touches the side BC of triangle ABC at P. Side AB and AC are produced to touch the circle at points Q and R respectively. The length of AQ is: [NTPC CBT-I 07/01/2021 (Morning)]

Correct Answer: (a) 1/2 (BC + CA + AB)
Solution:

39. In ∆ ABC, <A = 90⁰, AB = 6 cm, AC = 8cm. If AD is prependicular to BC, the AD is equal to [NTPC CBT - I 07/01/2021 (Evening) ]

Correct Answer: (c) 4.8 cm
Solution:

40. Line ABC is a tangent to a circle at B. PQ || AC and ∠QBC = 70°. ∠PBQ is =? [NTPC CBT - I 09/01/2021 (Evening) ]

Correct Answer: (c) 40°
Solution: