Geometry (Railway Maths) (Part – VII)

Total Questions: 47

21. What is the maximum number of parallel tangents a circle can have? [ALP Tier II 21/01/2019 (Afternoon) ]

Correct Answer: (b) two
Solution:

The Maximum number of parallel tangents that can be drawn on a circle is two.

22. The sides of a triangle are 4 cm, 6 cm and 8 cm respectively. Find the radius of the incircle of the Triangle? [ALP Tier II 21/01/2019 (Afternoon) ]

Correct Answer: (d) √15/3 cm
Solution:

23. If the triangles A₁B₁C₁ and A₂B₂C₂ are similar, then which of the following option will be correct? [ALP Tier II 21/01/2019 (Afternoon) ]

Correct Answer: (d)
Solution:

24. If in triangle ABC, AB = 4 cm, BC = 6 cm and AC = 7 cm and in triangle PQR, QR = 12 cm and <A = ∠P, ∠B = ∠Q, then Find out the length of PQ? [ALP Tier II 21/01/2019 (Afternoon)]

Correct Answer: (a) 8 cm
Solution:

25. If a, b and c are the three sides of a triangle and if a² + b² = c², then which triangle is it? [ALP Tier II 21/01/2019 (Afternoon)]

Correct Answer: (d) right angled triangle
Solution:

Let a triangle of sides a , b and c.
a² + b² = c² This relation shows pythagoras theorem. So, ABC is a right angled triangle

26. The sides of some triangles are given below. Can you tell which of these are right triangles? [ALP Tier II 21/01/2019 (Afternoon)]

1.  7 cm, 24 cm, 25 cm
2.  3 cm, 8 cm, 6 cm
3.  50 cm, 80 cm, 100 cm
4. 17 cm, 15 cm, 8 cm

Correct Answer: (c) 2 and 3
Solution:

As we know, (7, 24, 25) and (17, 15, 8) are triplets. Only option 1 and 4 have sides of the right angle triangle.

27. A tangent drawn from a point P to a circle meets it at point A. Chord AB subtends an angle of 40° at a point on the circumference on the other side of P. Angle PAB will be: [ALP Tier II 21/01/2019 (Afternoon)]

Correct Answer: (b) 40°
Solution:

28. What is the use of 'Parker (Compass)' to make? [ALP Tier II 21/01/2019 (Evening)]

Correct Answer: (c) circle
Solution:

Compass is used to draw circles.

29. ∆DEF is the same as ∆PQR. If the ratio of the semi-perimeters of ∆DEF and ∆PQR is 4 : 5 and if PQ = 15 cm, then the length of DE is: [ALP Tier II 21/01/2019 (Evening)]

Correct Answer: (a) 12 cm
Solution:

30. If the radius of a circle is increased by 7 times, its circumference will be how many times of its former circumference? [RPF S.I. 19/12/2018 (Evening) ]

Correct Answer: (b) 7
Solution:

Circumference of circle = 2πr As, we know that circumference is directly proportional to the radius of circle
if radius is increased 7 times then circumference is also increased by 7 times.