NDA exam Sample questions Geometry maths

NDA exam Sample questions Geometry maths
NDA Entrance Exam Solved Question Paper
1. The point O lies inside a triangle PQR such that ?OPQ, ?OQR and ?ORP are
equal in area. Then, the point O is called as
(a) incentre
(b) centroid
(c) circumcentre
(d) orthocentre
Ans. (b)


2. In ?ABC, O is the orthocentre and BOC = 2 A, then the magnitude of BOC is
equal to
(a) 120°
(b) 100°
(c) 80°
(d) 60°
Ans. (a)

3. ABC is a triangle whose sides BC and CA ate produced to D and E respectively. If
DCA = 108°, EAB = 124°, then the value of ABC is
(a) 72°
(b) 56°
(d) 1500
Ans. (c)

4. ABCD is a cyclic quadrilateral in which AD is the diameter and BCD = 125°, then
the measure of ADB is
(a) 72°
(b) 45°
(c) 55°
(d) 65°
Ans. (a)

5. AD is the bisector of A of ?ABC, AC = 4.2 cm, DC = 6 cm, BC = 10 cm, then AB is
(a) 2.8 cm
(b) 3 cm
(c) 3.5 cm
(d) none of these
Ans. (a)

6. If O is the orthocentre of the ?ABC, then
(a) BOC = 2 BAC
(b) BOC and BAC are supplementary
(c) BOC= BAC
(d) none of these
Ans. (b)

7. In ?ABC, D, E and F are the mid points of the sides BC, CA and AB respectively.
The area of ?ABC is 24 cm2, then the area of ?DEF is
(a) 7 cm2
(b) 6 cm2
(c) 18 cm2
(d) 16 cm2
Ans. (b)

8. In a parallelogram PQRS, PQ = 4.5 cm, PR =6 cm, QS = 7.8 cm and the diagonals
PR and QS intersect each other at O, then to draw a parallelogram we have to draw
first
(a) ?PQR
(b) ?ROS
(c) ?QOR
(d) ?PRS
Ans. (b)


9. In the trapezium PQRS, PQ is parallel to RS and the diagonals intersect at O. If OP .
SR = m(OR . PQ), then the value of m is
(a) 1/4
(b) 1/3
(c) 1
(d) 1/2
Ans. (c)

10. In a parallelogram PQRS, X is the mid point of PS and Y is the mid point of QR,
then XY divides QS in the ratio of
(a) 1 : 4
(b) 1 : 1
(c) 1 : 2
(d) 1 : 3
Ans. (b)

11. The minimum number of dimensions needed to construct a rectangle is
(a) 2
(b) 3
(c) 4
(d) 5
Ans. (a)


12. ABC is right angled triangle with BP as the perpendicular to the hypotenuse. The
ratio AB : AC is equal to
(a) 2 : 3
(b) BP : BC
(c) BP2 : BC2
(d) none of these
Ans. (b)

13. The triangle ABC has AB = 5 cm, AC = 8 cm and BC = 9 cm, then ?ABC is
(a) obtuse angled
(b) not obtuse angled
(c) right angled
(d) none of these
Ans. (b)

14. A rectangle PQRS is inscribed in a quadrant of a circle, with P at the centre and R
on the circumference. If PS is 12 cm and PQ is 5 cm, then the diameter of the circle
is
(a) 26 cm
(b) 29 cm
(c) 28 cm
(d) none of these
Ans. (a)

15. In a right angled triangle, if one angle is 30 then the side opposite to it is
(a) one third of the base
(b) half of the hypotenuse
(c) one fourth of the hypotenuse
(d) one sixth of the hypotenuse
Ans. (b)

16. A circle is divided into 12 equal parts. The number of degrees in each arc is
(a) 60°
(b) 30°
(c) 45°
(d) none of these
Ans. (b)

17. The figure formed by joining the mid points of the sides of a quadrilateral is a
(a) trapezium
(b) rhombus
(c) parallelogram
(d) rectangle
Ans. (c)

18. If a pair of opposite angles of a quadrilateral are supplementary, the quadrilateral is
a
(a) cyclic
(b) parallelogram
(c) rectangle
(d) rhombus
Ans. (a)


19. A pair of opposite sides of a cyclic quadrilateral are equal. Which one is true?
(a) Its diagonals are equal.
(b) It is a rhombus
(c) It is a parallelogram.
(d) All of these
Ans. (a)

20. The sum of the angles in four segments exterior to a cyclic quadrilateral is equal to
(a) 350°
(b) 450°
(c) 540°
(d) 180°
Ans. (c)