Solved geometry Sample paper for NDA exam

Solved geometry Sample paper for NDA exam
NDA exam question papers -
NDA sample papers
National Defence Academy Exam (NDA Exam) Free Online test
1. The angle subtended by an arc of a circle at the centre is K times the angle
subtended by it at any point on the remaining part of the circle, then K is equal to
(a) 1/2
(b) 1
(c) 2
(d) 3
Ans. (c)

2. The angle in a segment greater than a semicircle is
(a) 90°
(b) less than 90°
(c) greater than 90°
(d) not known
Ans. (c)

3. There are two concentric circles of radii 13 cm and 12 cm. Then the length of the
chord of the outer circle which touches the inner circle is
(a) 10 cm
(b) 13 cm
(c) 12 cm
(d) 12.5 cm
Ans. (c)

4. The locus of a point equidistant from two intersecting lines is a
(a) circle
(b) pair of parallel lines
(c) hyperbola
(d) pair of bisectors of angles
Ans. (d)

5. To determine any straight line, at least K points are required. Then K is equal to
(a) 4
(b) 3
(c) 2
(d) 1
Ans. (c)

6. The point of concurrency of three altitudes of a triangle is called its
(a) incentre
(b) circumcentre
(c) centroid
(d) orthocentre
Ans. (d)

7. At 4.24 pm, how many degrees has the hour hand of a clock moved from its position
at noon?
(a) 135°
(b) 134°
(c) 133°
(d) 132°
Ans. (d)

8. If two circles touch each other externally, then the number of common tangents to
the circles is
(a) 4
(b) 3
(c) 2
(d) 1
Ans. (b)

9. A circle is inscribed in a triangle whose sides arc 8 cm, 15 cm and 17 cm then the
radius of the circle is
(a) 3 cm
(b) 4 cm
(c) 5 cm
(d) none of these
Ans. (a)

10. ABCD is a cyclic trapezium and AB CD. If AB be the diameter of the circle and
CAB = 30°, then the value of ADC is
(a) 110°
(b) 115°
(c) 120°
(d) 125°
Ans. (c)

11. The distance of the chord of length 16 cm, from the centre of the circle of diameter
20 cm, is
(a) 3 cm
(b) 4 cm
(c) 5 cm
(d) 6 cm
Ans. (d)

12. The centres of two circles with radii 8 cm and 3 cm are 13 cm apart. A direct
common tangent touches the circles at A and B respectively, then the length of AB
is
(a) 8 cm
(b) 10 cm
(c) 12 cm
(d) none of these
Ans. (c)

13. The maximum number of common tangents drawn to two intersecting circles is
(a) 1
(b) 2
(c) 3
(d) 4
Ans. (b)

14. The length of the tangent from an external point, at a distance of 13 cm from the
centre of the circle of radius 5 cm, is
(a) 10 cm
(b) 12 cm
(c) 13 cm
(d) 14 cm
Ans. (b)

15. The measure of an angle which is five times its supplement is
(a) 36°
(b) 30°
(c) 50°
(d) 180°
Ans. (c)

geometry mcq

geometry mcq
Geometry mcq test Free Online Exams
MCQ(s)::Plane Geometry
1. If AC and BD intersect at O such that AO = CO and BO = DO, then
(a) BC = AD
(b) BC AD and BC = AD
(c) BC AD
(d) none of these
Ans. (b)

2. In any triangle the centroid divides the median in the ratio
(a) 1 : 1
(b) 2: 1
(c) 3: 1
(d) 3: 2
Ans. (b)

3. If D is any point on the side BC of ∆ABC such that ∆ADB and ∆ADC are equal in
area, then
(a) AD is the median
(b) AD is the altitude
(c) AD is an angle bisector
(d) AD is any line
Ans. (a)

4. In a right angled triangle the square of the hypotenuse is twice the product of the
square of the other sides. Then the triangle is
(a) equilateral
(b) isosceles
(c) of s 30°, 60°, 90°
(d) of s 40°, 50°, 90°
Ans. (b)

5. If one angle of ∆ at is equal to the sum of the other two, the triangle is
(a) isosceles
(b) equilateral
(c) right angled
(d) ordinary
Ans. (c)

6. The sum of angles of a quadrilateral is
(a) 180°
(b) 360°
(c) 270°
(d) none of these
Ans. (b)


7. In a right angled triangle ABC, AD is perpendicular to the hypotenuse BC then AD2 is
equal to
(a) AB . BD
(b) AC . DC
(c) BD . DC
(d) AB . AC
Ans. (c)

8. A triangle ABC stands on a rectangle BCDE and AF is a perpendicular from A to
DE. If AB = 6.5 m, CD = 5 m, AF = 7.5 m, then BC can’t be less than
(a) 6m
(b) 5m
(c) 4m
(d) 6.5 m
Ans. (c)



9. A circle has two equal chords AB and AC, chord AD bisects BC in E. If AC = 12 and
AE = 8cm, then the measure of AD is
(a) 24 cm
(b) 18.5 cm
(c) 18 cm
(d) 19 cm
Ans. (c)

10. If G is the centroid of ΔABC and the median AD is 12 cm, then the length of AG is
(a) 7cm
(b) 8cm
(c) 9 cm
(d) 10 cm
Ans. (b)

11. H is the orthocentre of ΔABC and X, Y, Z are the mid points of AH, BH, CH, then
the point H is
(a) centroid of ΔXYZ
(b) orthocentre of ΔXYZ
(c) circumcentre of ΔXYZ
(d) incentre of ΔXYZ
Ans. (b)

12. The direct common tangents of two congruent circles are
(a) equal
(b) parallel
(c) parallel and equal
(d) parallel and unequal
Ans. (c)

13. Sum of the adjacent angles of a parallelogram is equal to
(a) 60°
(b) 90°
(c) 150°
(d) 180°
Ans. (d)



14. The opening between two lines is called
(a) angle
(b) point
(b) line
(d) transversal
Ans. (a)

15. A right angled triangle ABC is right angled at A and D is the mid point of BC. E is a point of trisection of AD, then the orthocentre of the ΔABC is at
(a) D
(b) E
(c) B
(d) A
Ans. (d)

Geometry objective Questions Fully Solved For Exams

Geometry objective Questions Fully Solved For Exams
Geometry objective test Free Online Exams preperation help
Geometry Multiple Choice Practice Questions
1. Two circles are congruent if and only if they have equal
(a) chords
(c) shapes
(b) tangents
(d) radii
Ans. (d)


2. If two medians of a triangle are equal in length, then the triangle is
(a) right angled but not isosceles
(b) isosceles but not right angle
(c) right angled isosceles
(d) equilateral
Ans. (b)

3. The sum of the exterior angles of a hexagon is
(a) 360°
(b) 540°
(c) 720°
(d) none of these
Ans. (a)

4. The sides of a triangle are 5cm, 6cm and 7cm. One more ∆ is formed by joining the
mid points of the sides. The perimeter of the second ∆ is
(a) 18 cm
(b) 12 cm
(c) 9 cm
(d) 6cm
Ans. (c)

5. The sum of all the angles of a pentagon is
(a) 360°
(b) 540°
(c) 720°
(d) none of these
Ans. (b)

6. The angle which is twice its supplement is
(a) 120°
(b) 90°
(c) 60°
(d) 30°
Ans. (a)


7. The sum of the acute angles of an obtuse triangle is 70° and their difference is 10°.
The largest angle is
(a) 110°
(b) 105°
(c) 100°
(d) 95°
Ans. (a)

8. The angle which is one fifth of its complement
(a) 15°
(b) 30°
(c) 45°
(d) 60°
Ans. (a)


9. The angles of a triangle, in ascending order, are x, y, z and y – x = z – y = 100. The
smallest angle is
(a) 40°
(b) 60°
(c) 50°
(d) 70°
Ans. (c)

10. If two parallel lines are intersected by a transverse line, then the bisectors of the
interior angles forms a
(a) square
(b) rectangle
(c) parallelogram
(d) trapezium
Ans. (b)


11. If the angle in a major segment is x and in a minor segment is y, then
(a) x = y
(b) x > y
(c) x + y = 180°
(d) x < y
Ans. (d)

12. In a regular polygon, each exterior angle is twice the interior angle, then the number
of sides will be
(a) 4
(b) 3
(c) 5
(d) 6
Ans. (b)


13. The number of sides of a regular polygon, if each of its interior angles is 135°, is
given by
(a) 4
(b) 6
(c) 8
(d) 10
Ans. (c)


14. The ratio of the sides of two regular polygons is 1: 2 and their interior angles is 3: 4,
then the number of sides in each polygon is
(a) 5, 10
(b) 9, 12
(c) 10, 5
(d) 5, 12
Ans. (a)

15. Any cyclic parallelogram is a
(a) rectangle
(b) rhombus
(c) trapezium
(d) square
Ans. (a)


16. If two medians of a triangle are equal, triangle is
(a) right angled
(b) isosceles
(c) equilateral
(d) scalene
Ans. (b)

17. If the bases of two similar triangles are in the ratio of 2 : 3, then their areas are in the
ratio of
(a) 2: 3
(b) 3 : 2
(c) 4 : 9
(d) 9 : 4
Ans. (c)

18. If the sides of a triangle are in the ratio 4 :6 : 7, then the
(a) triangle is obtuse angled
(b) triangle is acute angled
(c) triangle is right angled
(d) none of these
Ans. (b)

19. In an equilateral triangle, the incentre, the orthocentre and the centroid are
(a) coincident
(b) collinear
(c) concyclic
(d) none of these
Ans. (a)


20. A circle is entirely in another circle. It is possible to draw
(a) only one common tangent
(b) two common tangents
(c) common tangent
(d) infinite number of tangents
Ans. (c)

21. A quadrilateral can be drawn, if the measures of its
(a) four sides are given
(b) three sides and a diagonal are given
(c) four sides and one angle are given
(d) four angles and one side are given
Ans. (c)

22. The orthocentre of an obtuse angled triangle lies
(a) outside the triangle
(b) inside the triangle
(c) on the smallest side of the triangle
(d) on the greatest side of the triangle
Ans. (a)

23. The angles of a pentagon in degrees are x, x +20, x + 40, x + 60 and x + 80, then the
smallest angle of the pentagon is
(a) 50°
(b) 68°
(c) 78°
(d) 85°
Ans. (b)

24. Each interior angle of a regular polygon lies between 136° and 142°, then the number
of sides of the polygon is
(a) 6
(b) 9
(c) 10
(d) 12
Ans. (b)


25. In an equiangular triangle incentre, circumcentre and orthocentre are
(a) collinear
(b) concyclic
(c) coincident
(d) none of these
Ans. (c)