QUADILATERAL

QUADRILATERAL

1.       If a regular polygon has each of its angles equal to  times of two right angles, then the number of sides is

(1) 3                              (2) 5                          (3) 6                             (4) 8

2.       If the length of the side PQ of the rhombus PQRS is 6cm and angle PQR = 120⁰. Then the length of QS, in cm is

(1) 4                               (2) 6                          (3) 3                             (4) 5

3.       Side AB of rectangle of ABCD is divided into four equal parts by points x, y, z. The ratio of the  is

(1)                               (2)                             (3)                             (4)

4.       ABCD is a quadrilateral in which diagonal BD = 64cm. AL perpendicular BD and CM perpendicular BD, such that AL = 13.2cm and CM = 16.8cm. The area of the quadrilateral ABCD in square cm is

(1) 422.4                       (2) 690.0                     (3) 537.6                   (4) 960.0

5.       ABCD is a square. M is the mid-point of AB and N is the mid-point of BC. DM and AN are joined and they meet at O. Then which of the following is correct?

(1) OA : OM = 1 : 2         (2) AN = MD       (3) ∠ ADM = ∠ ANB  (4) ∠ AMD = ∠ BAN

6.       The side AB of a parallelogram ABCD is produced to E in such a way that BE = AB. DE intersects BC at Q. The point Q divides BC in the ratio

(1)                               (2)                             (3)                                (4)

7.       The length of the diagonal BD of the parallelogram ABCD is 18cm. If P and Q are the centroid of the  and respectively then the length of the line segment PQ is

(1) 4cm                         (2) 6cm                         (3) 9cm                         (4) 12cm

8.       ABCD is a cyclic trapezium whose sides AD and BC are parallel to each other. If angle ABC = 72⁰, then the measure of the angle BCD is

(1) 162⁰                         (2) 18⁰                            (3) 108⁰                         (4) 72⁰

9.       In a quadrilateral ABCD with unequal sides if the diagonals AC and BD intersect at right angles, then

(1) AB² + BC² = CD² + DA²

(2) AB² + CD² = BC² + DA²

(3)  AB² + AD² = BC² + CD²

(4)  AB² + BC² = 2(CD² + DA²)

10.   If an exterior angle of a cyclic quadrilateral be 50⁰, then the interior opposite angle is

(1) 130⁰                         (2) 40⁰                               (3) 50⁰                          (4) 90⁰

11.   ABCD is a rhombus whose side AB = 4 and angle ABC = 120⁰, then the length of diagonal BD is equal to

(1) 1 cm                         (2) 2 cm                             (3) 3 cm                       (4) 4 cm

12.   The ratio between the number of sides of two regular polygons is 1 : 2 and the ratio between their interior angles is 2 : 3. The number of sides of these polygons is respectively

(1) 6, 12                        (2) 5, 10                              (3) 4, 8                         (4) 7, 14

13.   ABCD is a quadrilateral inscribed in a circle with centre O. If angle COD = 120⁰ and angle BAC = 30⁰, then angle BCD is

(1) 75⁰                           (2) 90⁰                                 (3) 120⁰                        (4) 60

14.   ABCD is a trapezium whose side AD is parallel to BC. Diagonals AC and BD intersect at O. If AO = 3, CO = x – 3, BO = 3x – 19 and DO = x - 5, the valus of x will be

(1) 7,6                          (2) 12,6                                  (3) 7,10                        (4) 8,9

15.   Two circles with centres A and B and radius 2 units touch each other externally at ‘C’. A third circle with centre ‘C’ and radius 2 units meets other two at D and E. Then the area of the quadrilateral ABDE is

(1) 2 sq. unit       (2)  3 sq. unit             (3) 3 sq. unit       (4)  2 sq. unit

16.   ABCD is a cyclic quadrilateral and O is the centre of the circle. If angle COD = 140⁰ and angle BAC = 40⁰, then the value of angle BCD is equal to

(1) 70⁰                        (2) 90⁰                              (3) 60⁰                         (4) 80⁰

17.   Q is a point in the interior of a rectangle ABCD. If QA = 3cm, QB = 4cm and QC = 5cm, then the length of QD (in cm) is

(1)  3                    (2) 5                           (3)                           (4)

18.   There are two regular polygons with number of sides equal to (n - 1) and (n + 2). Their exterior angles differ by 6⁰. The value of n is

(1) 14                          (2) 12                              (3) 13                              (4) 11

19.   In a regular polygon if one of its internal angle is greater than the external angle by 132⁰, then the number of sides of the polygon is

(1) 14                          (2) 12                                (3) 15                          (4) 16

20.   A quadrilateral ABCD circumscribes a circle and AB = 6cm, CD = 5cm and AD = 7cm. The length of side BC is

(1) 4cm                        (2) 5cm                           (3) 3cm                        (4) 6cm

21.   ABCD is a rhombus. A straight line through C cuts AD produced at P and AB produced at Q. If DP =  AB, then the ratio of the length of BQ and AB is

(1) 2 : 1                        (2) 1 : 2                             (3) 1 : 1                           (4) 3 : 1

22.   ABCD is a rhombus. AB is produced to F and BA is produced to E such that AB = AE = BF. Then

(1) ED ˃ CF               (2) ED perpendicular CF         (3) ED² + CF² = EF²          (4) ED || CF

23.   If the ratio of the angles of a quadrilateral is 2 : 7 : 2 :7, then it is a

(1) trapezium              (2) parallelogram       (3) square      4.rhombus

24.   In a rhombus ABCD, angle A = 60⁰ and AB = 12cm. Then the diagonal BD is

(1) 10cm                       (2) 2cm                        (3) 6cm                         (4) 12cm

25.   If D, E and F are the mid-points of BC, CA and AB respectively of the ABC then the ratio of area of the parallelogram DEFB and area of the trapezium CAFD is

(1) 2 : 3                          (2) 3 : 4                             (3) 1 :2                         (4) 1 : 3

26.   PQRST is a cyclic pentagon and PT is a diameter, then angle PQR + angle RST is equal to

(1) 180⁰                         (2) 270⁰                             (3) 216⁰                         (4) 144⁰