Free Objective Test 02 Practice Test - 11th and 12th

Question 1

Two vectors of the same physical quantity are unequal if

A. they have the same magnitude and the same direction

B. they have different magnitudes but the same direction

C. they have the same magnitude but different directions

D. they have different magnitudes and different directions.

SOLUTION

Solution : B, C, and D

For many purposes, two vectors $⃗ A a n d ⃗ B$ may be defined to be equal if they have the same magnitude and point in the same direction.

Question 2

What happens if a vector is multiplied by a number 2?

A. The magnitude of the vector is doubled but its direction remains the same

B. The magnitude of the vector remains the same but its direction is reversed

C. The magnitude of the vector id doubled and its direction is reversed

D. Neither the magnitude nor the direction of the vector undergo any change

SOLUTION

Solution : A

Multiplication of a vector by a real positive number n makes its magnitude n times but does not change the direction of the vector.
Hence the correct choice is (a).

Question 3

A null vector has

A. zero magnitude and a specific direction

B. a finite magnitude and no specific direction

C. a finite magnitude and a specific direction

D. zero magnitude and no specific direction

SOLUTION

Solution : D

If vectors A and B are equal, i.e. A = B, then their difference (A – B) is defined as a null vector. It has a zero magnitude and no specific direction.
Hence the correct choice is (d).

Question 4

The magnitude of the resultant of two vectors of magnitudes 3 units and 4 units in 5 units. What is the angle between two vectors?

\frac{π}{4}

\frac{π}{2}

\frac{3 π}{4}

π

SOLUTION

Solution : B

The magnitude R of the resultant vector R of two vectors A and B inclined at an angle $θ$ is given by
$R^{2} = A^{2} + B^{2} + 2 A B cos θ$
$cos θ = \frac{R^{2} - A^{2} - B^{2}}{2 A B} = \frac{(5)^{2} - (3)^{2} - (4)^{2}}{2 \times 3 \times 4} = 0$
$∴$ $θ = \frac{π}{2} .$
Hence the correct choice is (b)

Question 5

The magnitude of the resultant of two equal vectors is equal to the magnitude of either vector. The angle between the resultant and either vector will be

60^{\circ}

90^{\circ}

120^{\circ}

150^{\circ}

SOLUTION

Solution : A

From the triangle law of vector addition, it is clear that the vectors R, A and B must be represented by the three sides of an equilateral triangle because the magnitudes of the three vectors are equal. Hence the angle $α$ between vectors R and A is $60^{\circ}$ . Alternatively, the value of $α$ is given by
$tan α = \frac{B sin θ}{A + B cos θ} = \frac{sin θ}{1 + cos θ} (∵ A = B)$
$= \frac{sin 120^{\circ}}{1 + cos 120^{\circ}} = 1.732$
Which gives $α = 60^{\circ} .$
Hence the correct choice is (a)

Question 6

The magnitudes of four pairs of displacement vectors are given. Which pair of displacement vectors cannot be added to give a resultant vector of magnitude 4 cm?

A. 1 cm, 1 cm

B. 1 cm, 3 cm

C. 1 cm, 5 cm

D. 1 cm, 7 cm

SOLUTION

Solution : A and D

The magnitude R of the resultant of two vectors A and B depends upon the magnitudes of A and B and the angle $θ$ between them and is given by
$R^{2} = A^{2} + B^{2} + 2 A B c o s θ$
When $θ = 0$ , R is maximum given by
$R_{m a x}^{2} = A^{2} + B^{2} + 2 A B$
or, $R_{m a x} = A + B$
When $θ = 180^{0}$ , R is minimum given by
$R_{m a x}^{2} = A^{2} + B^{2} - 2 A B$
or, $R_{m i n} = A - B$
Thus, the magnitude of resultant will lie between A – B and A + B.
Hence the correct choices are (a) and (d).

Question 7

Which of the given 2 vectors are negative of each other?

(E) & (D)

(A) & (D)

both option a & b

None of these

SOLUTION

Solution : B

From the diagram, both A and D have a magnitude of 2 units and are facing opposite directions.

Question 8

Is a vector necessarily changed if it is rotated through an angle?

True

False

Can't Say

None of These

SOLUTION

Solution : B

If a vector is rotated by any angle which is not a multiple of $360^{\circ}$ or $2 π$ radians, then it is different. But if rotated through a multiple of $360^{\circ}$ , it remains the same. As it is simply making full circles, the direction will be the same as the initial direction.

Question 9

Which of the given 2 vectors are same?

(A) & (C)

both option (A) & (B)

None of these

SOLUTION

Solution : B

For 2 vectors to be equal their magnitude and direction has to be same.

Option A: says vector A and E surely they are pointed in the same direction but if we see magnitude wise the vector A has a magnitude of 2 units or it is only 2 boxes long, while vector E has magnitude of 3 units, so vector A & E can't be same.

Option B: says vector C & B, they are surely pointing in the same direction are their magnitudes also same.

Vector C has a unit of $2 \sqrt{2}$ units and so does vector B.

So option B is correct.

Here we conclude that we can translate a vector anywhere on the 3D space, it wouldn't change it as long as I keep the magnitude of the vector same and keep it pointing in the same direction.

Question 10

If the river is flowing to your left, In which general direction must you swim to avoid being eaten by the crocodiles on both the sides?

It doesn't matter how the river is flowing, I can swim straight towards the other bank

I must swim exactly against the river ie. towards the right

I must swim in some direction between left and straight

I must swim somewhere between right and straight

SOLUTION

Solution : D

You must swim somewhere between right and straight.

Question 11

Given two vectors a vector and b vector where b makes an angle theta with the positive direction of a as shown. Find the magnitude of the resultant according to triangle law in this case.

I tried and i think have the answer in the first attempt.

I am trying but I am stuck

I tried and did not get the answer initially but after a few attempts I think I have the right answer now.

I didn't try and don't want to do it on my own. I want to watch you doing it and spoon feed me like a baby

SOLUTION

Solution : C

Question 12

You have to go to building B from A and it's raining heavily. You want to get as less wet as possible. Will only running fast help you or can running slow also work?

Running fast is the only solution.

Yes, Running slow might help sometimes.

C. First run fast then slow.

D. First run slow then fast.

SOLUTION

Solution : B

Running slow can also work sometimes. Watch the next video to understand why.

Question 13

Which of the given vector is a negative vector?

Vector A

Vector B

There is no such thing as Negative Vector

None of these

SOLUTION

Solution : C

We can assign any random direction to be positive and then all the vectors directing towards that direction will be represented with a positive sign and the vectors directing opposite to it will be accompanied with a negative sign. We define such signs for our convenience and there is no positive or negative vector in absolute terms.

Question 14

If you take 3 steps towards North then 4 steps towards East.
Then Find the Resultant.

A. 5 in North West direction

B. 5 in North East direction

C. 5 towards North

D. 5 towards South

SOLUTION

Solution : B

Watch the next video for solution.

Question 15

If multiple vectors cancel out then what do we get ?

A. 0

B. 0 vector

C. Unit vector

D. Can not be determined

SOLUTION

Solution : B

0 vector. Watch the next video to refine this concept.

Free Objective Test 02 Practice Test - 11th and 12th

Question 1

SOLUTION

Question 2

SOLUTION

Question 3

SOLUTION

Question 4

SOLUTION

Question 5

SOLUTION

Question 6

SOLUTION

Question 7

SOLUTION

Question 8

SOLUTION

Question 9

SOLUTION

Question 10

SOLUTION

Question 11

SOLUTION

Question 12

SOLUTION

Question 13

SOLUTION

Question 14

SOLUTION

Question 15

SOLUTION

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