LINES AND ANGLES (CDS)

Total Questions: 16

1. Three parallel lines x, y and z are cut by two transversals m and n. Transversal m cuts the lines x, y, z at P, Q, R, respectively and transversal n cuts the lines x, y, z at L, M, N, respectively. If PQ = 3 cm, QR = 9 cm and MN = 10.5 cm, then what is the length of LM? [2019 (II) Evening Shift]

Correct Answer: (b) 3.5 cm
Solution:


2. Let the bisector of the angle BAC of a triangle ABC meet BC in X. Which one of the following is correct? [2019 (II) Evening Shift]

Correct Answer: (b) AB < BX
Solution:

3. If two lines AB and CD intersect at O such that = ∠AOC = 5 ∠AOD, then the four angles at O are [2018 (II) Evening Shift]

Correct Answer: (b) 30° 30° 150° 150°
Solution:We have,


4. The length of a line segment AB is 2 cm. It is divided into two parts at a point C such that AC² = AB × CB. What is the length of CB? [2018 (I) Morning Shift]

Correct Answer: (b) 3 - √5 cm
Solution:

5. The locus of a point equidistant from two intersecting lines is [2018 (I) Morning Shift]

Correct Answer: (a) A straight line
Solution:The locus of point equidistant

6. In the figure given below, p, q, r are parallel lines; l and m are two transversals [2018 (I) Morning Shift]

Consider the following
1. AB  : AC = DE : DF
2. AB × EF = BC × DE

Which of the above is/are correct?

Correct Answer: (c) Both 1 and 2
Solution:AB/BC = DE/EF, Because p || q || r and l and m are transversal. (By BPT Theorem)

7. Consider the following statements in respect of three straight lines A B, and C on a plane [2017 (II) Evening Shift]

1. If A and C are parallel and B and C are parallel; then A and B are parallel.
2. If A is perpendicular to C and B is perpendicular to C; then A and B are parallel.
3. If the acute angle between A and C is equal to the acute angle between B and C; then A and B are parallel.

Which of the above statements are correct?

Correct Answer: (a) 1, 2 and 3
Solution:1. If A andC parallel and B andC are parallel


8. There are 8 lines in a plane, no two of which are parallel. What is the maximum number of points at which they can intersects? [2017 (II) Evening Shift]

Correct Answer: (c) 28
Solution:We know that, two non-parallel, lines always intersect at a point.

9. In the figure given below, PQ is parallel to RS and PR is parallel to QS. If ∠LPR = 35º And ∠UST = 70º then what is ∠MPQ equal to? [2017 (I) Morning Shift]

Correct Answer: (c) 75°
Solution:We have,

10. If a transversal intersects four parallel straight lines, then the number of distinct values of the angles formed will be [2016 (I) Morning Shift]

Correct Answer: (a) 2
Solution:If line P intersects four parallel lines l, m, n and o, then 16 angles will be formed.