# AFFINE AND EUCLIDEAN GEOMETRY Mcqs

1.How many conditions are to be satisfied for an affine space

a. 4

b. 5

c. 3

d. 2

2.An affine subspace is also called a

a. flat

b. berycenter

c. affine space

d. none

3.For any subspace  V of E , for any a that belongs to E, the set V  is an affine subspace if

a. all

b. V=a+V

c. V=a-V

d. V=V-a

4.The distance between two points (8,2,6) and (3,5,7) is

a. 5.4

b. 5.3

c. 5.9

d. 5.6

5.If three points A, B and C lie on the circumference of a circle, whereby the line AC is the diameter of the of the circle, if  the angle CAB  is 500  what is the measure of  angle ACB

a. 60

b. 90

c. 40

d. 50

6.Distributive property over vector addition is :

a. a.(b+c)=a.b+a.c

b. a.(b-c)=a.b+a.c

c. a.(b+c)=a.b-a.c

d. none

7.Two non-zero vectors a and b are orthogonal if and only if

a. a . b = 0

b. a+b=0

c. a-b=0

d. none

8.If the angle between the other sides is a right angle, the law of cosines reduces to the

a. Pythagorean equation

b. law of sine

c. ceva’s theorem

d. norm

9.|<x,y>|≤

a. ||x||-||y||

b. ||x||y

c. ||x||.||y||

d. ||x||+||y||

10.<0,z>=

a. <z>

b. 1

c. 0

d. z

11.If two triangles have two sides of the one equal to two sides of the other then it is called.

a. iossceles

b. right angled

c. congurent

d. none

12.A function from a vector space over the real or complex numbers to the nonnegative real numbers takes zero value if input vector is zero is called

a. norm

b. law of sine

c. ceva’s theorem

d. none

13.All norms are.

a. semi-norms

b. vectors

c. loci

d. none

14.Are (3,2.5) , (5,2,3) and (4,3,7) collinear?

a. no

b. yes

c.

d.

15.It states that the sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals is called

a. ceva’s theorem

b. law of sine

c. pythagorean theorem

d. parallelogram law

16.Find the norm of 4i-3j+5k

a. 9.09

b. 10

c. 7.07

d. 8.08

17.Shifting the plan one inch to right is an example of

a. movement

b. translation

c. rotation

d. reflection

18.Turning the sheet over is an example of

a. glide reflection

b. translation

c. rotation

d. reflection

19.The set of point equidistant from two points is an example of

a. rotation

b. reflection

c. translation

d. loci

20.The set of points for which the distance from a single point is constant is called

a. loci

b. circle

c. parabola

d. hyperbola

21.Adding a fixed vector to the elements of a linear vector space produces an

a. eculidean subspace

b. vector subspace

c. affine subspace

d. affine space

22.A triangle that has no equal sides and no equal angles is known as

a. isosceles triangle

b. equilateral triangle

c. right angle

d. scalene triangle

23.____ points are points that lie on the same line.

a. eculidean

b. collinear

c. coline

d. non-colinear

24.are the points (1, – 1), (5, 5) and (- 3, – 7) collinear?

a. yes

b. no

c.

d.

25.How many substrings (of all lengths inclusive) can be formed from a character string of length 8? (Assume all characters to be distinct)

a. 47

b. 63

c. 37

d. 54

26.In how many ways can 10 boys be seated in a row having 28 seats such that no two friends occupy adjacent seats?

a. 13P5

b. 15P7

c. 19P10

d. 9P29

27.How many ways can 8 prizes be given away to 7 students, if each student is eligible for all the prizes?

a. 40520

b. 40720

c. 40320

d. 40325

28.In △ABC, AB = 3 and, AC = 4 cm and AD is the bisector of ∠A. Then, BD : DC is

a. 0.12777777778

b.

c.

d.

29.If the distance between the top of two trees 20 m and 28 m tall is 17 m, then the horizontal distance between the trees is :

a. 12m

b. 14m

c. 15m

d. 11m

30.For two vectors A and B, what is A.B (if they have angle α between them)?

a. √(|A||B|) cosα

b. |A||B| sinα

c. |A||B| cosα

d. |A||B|

31.Parallelograms on equal bases and having the same altitude are equal in

a. height

b. area

c. volume

d. angles

32.What is Distributive law?

a. a(A.B) = AxB

b. A.(B+D) = (A.B) + (A.D)

c. A.B =B.A

d. a(A.B) = A.(aB)

33.What is multiplication law?

a. a(A.B) = AxB

b. a(A.B) = A.(aB)

c. A.B =B.A

d. A.(B+D) = (A.B) + (A.D)

34.What is k.i?

a. infinity

b. 0

c. 1

d. -1

35.If A is any vector with Ai + Bj + Ck then what is the y-axis component of the vector?

a. A units

b. C units

c. Square root of a sum of squares of the three, i.e. A, B and C

d. B units

36.What is cosα for force vector F = Ax + By +Cz (Given α, β and γ are the angles made by the vector with x, y and z axis respectively)?

a. C/F

b. 1

c. A/F

d. B/F

37.The locus of a point P about another point O such that its distance from O is constant is ________

a. two parallel lines equidistant from O

b. a curve with O in it

c. a circle with center O

d. a line passing through O

38.The locus of point P whose perpendicular distance from a fixed line and distance from a point T is equal is _______________

a. a hyperbola

b. a parabola

c. an ellipse

d. a circle

39.The lengths of sides of triangle are x cm,(x + 1) cm and (x + 2) cm, the value of x when triangle is right angled is

a. 5 cm

b. 7 cm

c. 3 cm

d. 4 cm

40.In a triangle with sides a,b and c, if a² = b² + c², then angle facing a is

a. right angle

b. abtuse

c. obtuse angle

d. none

41.Each side of square field ABCD is 50m long, the length of diagonal field is

a. 23m

b. 45m

c. 70.7m

d. 50.5m

42.Cable subjected to its own weight takes a shape of a ____________ when is subjected to loadings

a. helix

b. spring

c. parabola

d. line

43.The loading in the cable subjected to its own weight doesn’t change the ___________ of the cables

a. Colour

b. Bending moment

c. Point at which the shear stress is zero

d. Geometry

44.Which of the following is true for two figures having equal area?

a. may are may not congurent

b. are never congruent

c. congurent

d.

45.The sine rule for a triangle states that

a. a/sinA+b/sinB+c/sin C

b. 2a/sin A = 2b/sin B = 2c/sin C

c. sin A/a = sin B/b = sin C/c

d. a/sinA=b/sinB=c/sinC

46.In the triangle ABC, if angle B = 60°, b = 11 cm and c = 8.7 cm then angle A and length of ‘a’ is

a. 46°

b. 49°

c. 43.23°

d. 52°

47.The angle between the isometric axes is __________

a. 90 degree

b. 270 degree

c. 120 degrees

d. 180 degrees

48.The lines parallel to isometric axes are called ________ lines.

a. parallel

b. auxiliary

c. oblique

d. isometric

49.The three lines meeting at a point and making an angle of 120 with each other is called________

a. axonometric

b. orthographic axes

c. oblique axes

d. isometric axes

50.The shape of the base of a Pyramid is:

a. Square

b. Rectangle

c. Any polygon

d. Triangle

51.The edges of the surface are :

a. line

b. point

c. curve

d. none

52.There are ________ number of Euclid’s Postulates

a. 4

b. 3

c. 6

d. 5

53.A solid has ———– dimensions.

a. one

b. zero

c. Three

d. Two

54.The edges of the surface are

a. points

b. None

c. Lines

d. curves

55.An affine space of dimension two is called——-.

a. Affine Space

b. None

c. Affine Plane

d. Affine Line

56.Which of the following is not isometry?

a. Translations

b. Reflections

c. Rotations

d. Dilations

57.Two vectors  are said to be orthogonal if angle between them is

a. 45

b. 30

c. 90

d. 60

58.The dot product of two vectors i and j is equal to

a. -1

b. 3

c. zero

d. 1

59.A single vector is always —–

a. complete

b. Independent

c. Dependent

d. Null

60.Number of elements of basis is ——- the dimension of vector space.

a. ≥

b. >

c. ≤

d. b) =

61.d(x,y)=0 iff

a. x=y

b. x≤y

c. x≠y

d. xy

62.If there is no crossing in a graph then graph is said to be ——-

a. Loop

b. Planar

c. Nonplanar

d. Isolated

63.The number of edges incidency on a vertex is called —— of vertex.

a. isolated

b. degree

c. order

d. loop

64.If all the vertices are connected to each other then graph is

a. non planar

b. Complete

c. Simple

d. planar

65.If v, r and  e are vertices, regions, and edges then v+r-e=

a. 3

b. 5

c. 4

d. 2

66.Lp space is inner product space?

a. Yes

b. Complete

c. Sequence

d. No

67.|x+y| ≤

a. |x|-|y|

b. None

c. |x|+|y|

d. |x|-||y||

68.||αx||=

a. ||x||α

b. ||x||

c. |α| ||x||

d. ||α|| |x|

69.<ax+by,z>=

a. a<x,z>-b<y,z>

b. <x,y>

c. a<x,z>+b<y,z>

d. <ax,z>+b<y,z>

70.<x,αy>=

a. α <x+y>

b. <x,y>

c. α͞   <x,y>

d. α<x,y>

71.Let F=R and V=Z with multiplication is a vector space?

a. Independent

b. not

c. yes

d. Dependent

72.W={(x,y,z): x+y+z=0}is ——- of R3.

a. complete

b. Subspace

c. combination

d. Not Subspace

73.The vectors  x,cosx are

a. Euler

b. Independent

c. dependent

d. Cauchy

74.Every norm is:

a. integrable function

b. Uniformly continuous function

c. continuous function

d. differentiable function

75.A norm on X defines a metric d on X which is given by for all x, y Є X

a. d(x, y) = ||x – y||

b. d(x, y) = ||x + y||

c. d(x, y) = ||x .y||

d. x+y

76.A vector space V over a field F is called linear space if F is either

a. Z

b. E

c. Q

d. R or C

77.Scalar product is also called ——

a. Cross Product

b. both

c. Product

d. Dot product

78.The vectors sinx, cosx, sinhx, coshx are

a. Complete

b. Independent

c. Convex

d. dependent

79.T(αu)=

a. T(u)

b. ||T||

c. αT(u)

d. αT||u||

80.d(x,y) is always

a. constant

b. Non Negative

c. negative

d. zero

81.Two vectors  are said to be orthogonal if

a. <x,y>≠0

b. <x,y>≤0

c. <x,y>=0

d. <x,y>=1

82.If any function preserves distance then it is

a. Collinear

b. Isometry

c. not isometry

d. Dependent

83.A vertex whose degree is zero called

a. Edge

b. Loop

c. Parallel edges

d. Isolated

84.The number of vertices of graph G  are called —— of G.

a. degree

b. loop

c. size

d. order

85.If crossing number of a graph is zero then graph is

a. incomplete

b. Planar

c. Non Planar

d. Complete

86.If e=6, v=4 then number of regions will b

a. 5

b. 9

c. 4

d. 3

87.A hyperplane is a subspace of dimension

a. m

b. m-1

c. m-2

d. m+1

88.If a space is 2D, then its hyperplanes are

a. one-dimensional lines

b. two-dimensional planes

c. three-dimensional space

d. None

89.A map f:A→B is an affine map if f(λa+μb)=λf(a)+μf(b)for a,bεA and

a. λ+μ=1

b. λ-μ=1

c. λμ=1

d. None

90.In face Isometries are

a. Basis

b. Affine maps

c. Affine hyperplane

d. affine dependent

91.An angle of polyhedron must measure less than

a. 45

b. 90

c. 360

d. 180

92.In all the Polyhedron ———— theorem is satisfied.

a. Desargues

b. Euler

c. Ceva’s

d. Menelaus

93.A closed plane figure bounded by straight lines called

a. Loop

b. Polygon

c. Polyhedron

d. Vertex

94.If a,bεA and A is an affine subspace then A-a=

a. AA

b. A-b

c. A+b

d. Ab

95.Linear subspaces  always contain the

a. hyperplane

b. origin

c. line

d. plane

96.For any two elements in inner product space then |<x,y>|≤||x||.||y|| is

a. Ceva’s Law

b. Cauchy Schwarz Inequality

c. Parallelogram Law

d. Pythagoran Theorem

97.Scalar product is

a. Commutative

b. Not Commutative

c. Cross Product

d. None