QUADRILATERAL AND POLYGON (CDS)

Total Questions: 41

21. If X is any point with in a square ABCD and on AX, a square AXYZ is described. Which of the following is/are correct? [2015 (II) Evening Shift]

1. BX = DZ or BZ = DX
2. ∠ABX = ∠ADZ or ∠ADX = ∠ABZ

Select the correct answer using the codes given below.

Correct Answer: (c) Both 1 and 2
Solution:Here, ∠DAB = ∠XAZ = 90°  ⇒ ∠DAB - ∠XAB = XAZ - ∠XAB

22. In the above figure, ABCD is a parallelogram. P is a point on BC such that PB : PC = 1 : 2 . DP and AB when both produced meet at Q. If area of ∆BPQ is 20 sq units, the area of ∆DCP is [2015 (II) Evening Shift]

Correct Answer: (d) None of these
Solution:Given, PB/PC = 1/2 ...(i)

23. A circle of radius r is inscribed in a regular polygon with n sides (the circle touches all sides of the polygon). If the perimeter of the polygon is p, then the area of the polygon is [2015 (II) Evening Shift]

Correct Answer: (c) pr/2
Solution:We know that, perimeter of polygon

24. The diagonals of a trapezium are at right angles and the slant sides, if produced, form an equilateral triangle with the greater of the two parallel sides. If the area of the trapezium is 16 sq cm, then the distance between the parallel side is [2015 (I) Morning Shift]

Correct Answer: (d) Cannot be determined due to insufficient data
Solution:



25. If each interior angle of a regular polygon is 135°, then the number of diagonals of the polygon is equal to [2015 (I) Morning Shift]

Correct Answer: (c) 20
Solution:Given, each interior angle of a regular polygon = 135°, ∵ Each exterior angle = 180° - Interior angle = 180° - 135° = 45°

26. If a star figure is formed by elongating the sides of a regular pentagon, then the measure of each angle at the angular points of the star figure is [2015 (I) Morning Shift]

Correct Answer: (a) 36°
Solution:∵ Each interior angle of a regular polygon of n sides


27. ABCD is a parallelogram, where AB : AD = 2 : 1. One of the angles of the parallelogram is 60°. The two diagonals are in the ratio [2015 (I) Morning Shift]

Correct Answer: (b) √7 : √3
Solution:


28. Consider the following statements [2015 (I) Morning Shift]

I. If non-parallel sides of a trapezium are equal, then it is cyclic.
II. If the chord of a circle is equal to its radius, then the angle subtended by this chord at a point in major segment is 30°.

Which of the above statement(s) is/are correct?

Correct Answer: (c) Both I and II
Solution:I. ∆ALD and ∆BMC,


29. Let ABCD be a parallelogram. Let X and Y be the mid-points of the sides BC and AD, respectively. Let M and N be the mid-points of the sides AB and CD, respectively. [2014 (II) Evening Shift]

Consider the following statements
1. The straight line MX cannot be parallel to YN.
2. The straight lines AC, BD, XY and MN meet at a point.

Which of the above statement(s) is/are correct?

Correct Answer: (b) Only 2
Solution:1. Given, ABCD is a parallelogram. X and Y are mid-points of BC and AD, respectively. M and N are the mid-points of AB and CD, respectively.

30. (Questions 30-31) Read the following information carefully and answer the given questions that follow. [2014 (II) Evening Shift]

ABCD is a trapezium, in which AB is parallel to CD. Let M be the mid-point of BC.

Consider the following statements
1. ‘Area of ∆ AMD + Area of ∆ DCM’ is equal to three-fourth of the area of trapezium ABCD, if AB CD = .
2. ‘Area of ∆ DCM + Area of ∆ ABM’ is always greater than half of the area of trapezium ABCD.

Which of the above statement(s) is/are correct?

Correct Answer: (c) Both 1 and 2
Solution: