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Exam  >   Tests  >  Vector Test (13-11-2016) - MCQ

Vector Test (13-11-2016) - MCQ


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30 Questions MCQ Test - Vector Test (13-11-2016)

Vector Test (13-11-2016) - Question 1
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Which of the following statements is correct?
A.    Force is vector because it obeys laws of vector algebra
B.    Force obeys laws of vector algebra because force is a vector.

Detailed Solution for Vector Test (13-11-2016) - Question 1

Ans:-  b

If any quantity obeys laws of vector algebra only then it is considered as a vector. So statement A is correct.

Vector Test (13-11-2016) - Question 2
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Can we add two  quantities having same units and dimensions

Detailed Solution for Vector Test (13-11-2016) - Question 2

Ans:- c 
In order to add two quantities it is necessary that both are either scalars or vectors. Since we don’t  know about the nature of the quantities here so we cannot tell. For example speed and velocity has same unit and dimension but they cannot be added.

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Vector Test (13-11-2016) - Question 3
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Which of the following operations is  possible if vectors A and B are of same nature and vector C  is of different nature (here all symbols have usual meanings )

Detailed Solution for Vector Test (13-11-2016) - Question 3

Ans:-  d

We cannot add or subtract vectors of different nature together so option a is not possible. We cannot add a scalar to a vector so b is also not possible. In option c again the nature of three vectors are different so they cannot be added. In option  d we are multiplying a scalar with a vector which is a valid process.

Vector Test (13-11-2016) - Question 4
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A vector is rotated by an angle θ  then, here θ is less than 180°.
Detailed Solution for Vector Test (13-11-2016) - Question 4

Ans :- b

When we rotate a vector its magnitude does not change so change in magnitude is zero , but if we talk about magnitude of change in that case its value is 2V sin θ/2 , which is non zero in this case.

Vector Test (13-11-2016) - Question 5
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The vector sum is smaller than the vector difference then
Detailed Solution for Vector Test (13-11-2016) - Question 5

Ans:- b

It is clear that the angle between the vectors is more than 90° so the minor diagonal will represent the sum.

Vector Test (13-11-2016) - Question 6
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If position vector is given by  a sin ωt + a cosωt then the kinetic energy of the body is
Detailed Solution for Vector Test (13-11-2016) - Question 6

Ans:- c

If we differentiate the position vector it gives us the velocity vector. When we find its dot product with the position vector it turns out to be zero, this means velocity is perpendicular to displacement. When we differentiate velocity vector we get acceleration which again comes out to be perpendicular to velocity. The force being perpendicular to velocity will not do any work so the KE is constant

Vector Test (13-11-2016) - Question 7
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A body of weight mg is thrown horizontally in air. An additional force AXB where A and B are vectors is acting on it , if A is acting towards east and its given that the body is moving with constant velocity then vector B
Detailed Solution for Vector Test (13-11-2016) - Question 7

Ans :-b

As the net force is zero

Mg=AB sin θ

B= mg/ A sin θ

B will be minimum when sin θ is maximum , which is 1

 So,  B (min) = mg /A

Moreover the direction of A x B should be upwards to cancel the weight  , so B should be in the North direction.

Vector Test (13-11-2016) - Question 8
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The two diagonals of the parallelogram are 2i  and 2j  then the area of the parallelogram is
Detailed Solution for Vector Test (13-11-2016) - Question 8

Ans :- b

The area of parallelogram is half of cross product of the diagonals of the parallelogram

A = ½ 2x2 sin 90°

Vector Test (13-11-2016) - Question 9
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If  the dot product of vector sum and vector difference of two non-zero vectors is zero then
Detailed Solution for Vector Test (13-11-2016) - Question 9

Ans:-  d

vector sum is perpendicular to vector difference only when we add vectors of equal magnitude

Vector Test (13-11-2016) - Question 10
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For vectors A and B the value of ?

Then the value of n is:
Detailed Solution for Vector Test (13-11-2016) - Question 10

Ans :- c

Vector Test (13-11-2016) - Question 11
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The forces whose magnitudes are in the ratio 3:5 give a resultant of 28 . If the angle between them is 60 , then the individual forces are
Detailed Solution for Vector Test (13-11-2016) - Question 11

Ans:- d

 A= 3x , B = 5x , R = 28 N

R=( A2 + B2 + 2AB cos θ) 1/2

28 =( (3x)2 + (5x)2 + 2(3x)(5x) cos 60°) ½ 

                  = (9x2 + 25x2 + 15x2 )1/2 = 7x

                        7x =28

                        x=7    

so, A = 12 and B = 20

Vector Test (13-11-2016) - Question 12
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Seven equal forces F acting at equal angles keep a body of mass m at rest now one force is removed then the acceleration of the body is
Detailed Solution for Vector Test (13-11-2016) - Question 12

Ans:- c

 F1 + F2 + F3 + F4 +F5 + F6 + F7 = 0

 F1 + F2 + F3 + F4 +F5 + F6 =- F7

As, F7  =  F

 So,     a=F/m

Vector Test (13-11-2016) - Question 13
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Sin 0° + sin 60° + sin 120° + sin 180° + sin 240° =
Detailed Solution for Vector Test (13-11-2016) - Question 13

Ans:-c

Let us consider 6 equal vectors making a closed polygon , sum of all y components

Sin 0° + sin 60° + sin 120° + sin 180° + sin 240° + Sin 300° = 0

Sin 0° + sin 60° + sin 120° + sin 180° + sin 240° = – sin 300°

 

Vector Test (13-11-2016) - Question 14
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The maximum and minimum value of vector sum of two vectors  is 6 and 10 then the maximum value of their cross product is
Detailed Solution for Vector Test (13-11-2016) - Question 14

Ans:- b

A+B = 10  , A-B = 6   so A=8  and B = 2

AXB= AB sin θ

So maximum value will be 16

Vector Test (13-11-2016) - Question 15
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Which of the following operations will definitely change a vector
Detailed Solution for Vector Test (13-11-2016) - Question 15

Ans:- d

This operation will change the direction of the vector

Vector Test (13-11-2016) - Question 16
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If A and B are two vectors then the angle which vector sum of A+B and A – B makes with A is
Detailed Solution for Vector Test (13-11-2016) - Question 16

Ans :- d

The diagonal of the parallelogram will lie along the vector A so the angle will be zero

Vector Test (13-11-2016) - Question 17
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For three coplanar vectors A,B and C which of the following is definitely zero
Detailed Solution for Vector Test (13-11-2016) - Question 17

Ans:-c

As the vectors are coplanar the volume of the parallelepiped formed will be zero.

Vector Test (13-11-2016) - Question 18
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Magnitude of three vectors A, B and C are equal. In first case Vectors  A and B when added gives vector C,  where C makes an angle θ1 with A and in second case vectors  A,B and C add up to zero in this condition angle between A and C is θ2  , then
Detailed Solution for Vector Test (13-11-2016) - Question 18

Ans:- b

In case 1 the angle is 60 where as in 2nd case the angle is 120

Vector Test (13-11-2016) - Question 19
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If vectors  add to zero then is equal to
Detailed Solution for Vector Test (13-11-2016) - Question 19

Ans:-b

C  is equal and opposite to the vector sum of A and B  but when we reverse the direction of C it will double the value of the vector sum

Vector Test (13-11-2016) - Question 20
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If the coordinate axis is rotated then which of the followings may change
Detailed Solution for Vector Test (13-11-2016) - Question 20

Ans:- d

The vector , its magnitude and direction do not change but the component might change due to change of angle with the axis.

Vector Test (13-11-2016) - Question 21
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Fifty equal forces making an angle 7° with the successive vector are  acting on a body of mass 'm' the  body
Detailed Solution for Vector Test (13-11-2016) - Question 21

Ans :- c

The vector sum is non-zero here so the body accelerates

Vector Test (13-11-2016) - Question 22
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In the previous problem the angles between the vectors are adjusted to keep the body under equilibrium then the angle are
Detailed Solution for Vector Test (13-11-2016) - Question 22

Ans:- a

The angle should be equal to 2π/N for the resultant to be zero

360/50 = 7.2 so we have to increase by 0.2

Vector Test (13-11-2016) - Question 23
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A non-zero vector may have
Detailed Solution for Vector Test (13-11-2016) - Question 23

Ans:- d

 A vector along the axis will have two of the components zero and a vector in plane may have one component zero.

Vector Test (13-11-2016) - Question 24
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Small angle is
Detailed Solution for Vector Test (13-11-2016) - Question 24

Ans:-  a

small angle obeys laws of vector algebra so it’s a vector.

Vector Test (13-11-2016) - Question 25
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Vector  is equal to
Detailed Solution for Vector Test (13-11-2016) - Question 25

Ans:- c

Cross product is normal to A so its dot product is zero.

Vector Test (13-11-2016) - Question 26
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Out of the given sets which of the following will never produce a null vector
Detailed Solution for Vector Test (13-11-2016) - Question 26

Ans:- d

Sum of any three should be larger than the 4th

Vector Test (13-11-2016) - Question 27
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Which operations obey commutative law

  1. Vector addition
  2. Vector subtraction
  3. Dot product
  4. Cross product
Detailed Solution for Vector Test (13-11-2016) - Question 27

Ans:- d

Only addition and dot product obey the law.

Vector Test (13-11-2016) - Question 28
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If  and  then find the vector which has magnitude equal to  but its direction is normal to both A and B
Detailed Solution for Vector Test (13-11-2016) - Question 28

Ans:- d

We will have to add the vectors and take its magnitude, then we will have to find the unit vector  in the direction of the cross product and multiply the magnitude to it.

Vector Test (13-11-2016) - Question 29
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Vectors of magnitude 3,4 and  5 add to zero then the angles between them are
Detailed Solution for Vector Test (13-11-2016) - Question 29

Ans:- c

 Angle between the vectors is taken by joining the tails or heads.

Vector Test (13-11-2016) - Question 30
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A car moving in rain finds the rain falling vertically downwards, then the wind may be
Detailed Solution for Vector Test (13-11-2016) - Question 30

Ans:- b

The resultant of rain and wind should be at any angle more than 90° to the negative of velocity of car.

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