**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

**Answer Keys:**

1 | c | 21 | b | 41 | c | 61 | a | 81 | c |

2 | a | 22 | d | 42 | d | 62 | b | 82 | b |

3 | b | 23 | b | 43 | d | 63 | b | 83 | d |

4 | c | 24 | a | 44 | a | 64 | b | 84 | d |

5 | c | 25 | c | 45 | c | 65 | c | 85 | b |

6 | a | 26 | c | 46 | c | 66 | d | 86 | c |

7 | a | 27 | c | 47 | c | 67 | c | 87 | b |

8 | a | 28 | a | 48 | d | 68 | c | 88 | a |

9 | c | 29 | c | 49 | d | 69 | c | 89 | a |

10 | c | 30 | c | 50 | c | 70 | c | 90 | b |

11 | a | 31 | b | 51 | a | 71 | b | 91 | c |

12 | a | 32 | b | 52 | c | 72 | b | 92 | b |

13 | a | 33 | b | 53 | c | 73 | b | 93 | b |

14 | a | 34 | b | 54 | c | 74 | b | 94 | b |

15 | d | 35 | d | 55 | c | 75 | a | 95 | b |

16 | c | 36 | c | 56 | d | 76 | d | 96 | b |

17 | b | 37 | c | 57 | c | 77 | d | 97 | a |

18 | d | 38 | b | 58 | c | 78 | b | ||

19 | d | 39 | c | 59 | b | 79 | c | ||

20 | b | 40 | a | 60 | c | 80 | b |