Question 1: Palette 1/127

Allen MCQ

As $\theta$ increases from $0^{\circ}$ to $90^{\circ}$ , the value of $\sin \theta : -$

A

Increases

B

Decreases

C

Remains constant

D

First decreases then increases.

Question 2: Palette 2/127

Allen MCQ

If $\sin \theta = \frac{\sqrt{2}}{\sqrt{3}}$ and $\theta$ lies in the first quadrant, the value of $\tan \theta$ is:

A

$\sqrt{2}$

B

$\frac{1}{\sqrt{2}}$

C

$\frac{\sqrt{3}}{\sqrt{2}}$

D

$\frac{1}{2}$

Question 3: Palette 3/127

Allen MCQ

Find $\theta$ for which $\sin \theta = \cos \theta$ , if $180^{\circ} < \theta < 360^{\circ}$

A

$135^{\circ}$

B

$315^{\circ}$

C

$225^{\circ}$

D

$150^{\circ}$

Question 4: Palette 4/127

Allen MCQ

If $\sin\theta_{1} + \sin\theta_{2} + \sin\theta_{3} = 3$ then value of $\cos\theta_{1} + \cos\theta_{2} + \cos\theta_{3}$ is :-

A

3

B

0

C

-3

D

1

Question 5: Palette 5/127

Allen MCQ

The greatest value of the function $7 \sin\theta - 24 \cos\theta$ is

A

12

B

13

C

25

D

17

Question 6: Palette 6/127

Allen MCQ

The length of hypotenuse of a right angle triangle exceeds the length of its base by 2 cm and exceeds twice the length of altitude by 1 cm. Find length of each side of the triangle.

A

6, 8, 10

B

7, 24, 25

C

8, 15, 17

D

7, 40, 41

Question 7: Palette 7/127

Allen MCQ

If $x = at^4$ and $y = bt^3$ . Find $\frac{dy}{dx}$

A

$\frac{4a}{3bt}$

B

$\frac{3b}{4at}$

C

$\frac{3a}{4bt}$

D

$\frac{4b}{3at}$

Question 8: Palette 8/127

Allen MCQ

A metallic disc is being heated. Its area at any time t is given by $A = 5t^{2} + 4t + 8$ . Calculate rate of increase in area at t = 3s.

A

$30 \, m^{2}/s$

B

$34 \, m^{2}/s$

C

$28 \, m^{2}/s$

D

$20 \, m^{2}/s$

Question 9: Palette 9/127

Allen MCQ

The side of a square is increasing at the rate of 0.1 cm/s. The rate of increase of perimeter w.r.t. time is :

A

0.2 cm/s

B

0.4 cm/s

C

0.6 cm/s

D

0.8 cm/s

Question 10: Palette 10/127

Allen MCQ

A particle moves along the straight line $3y = x + 5$ . Which coordinate changes at a faster rate?

A

x-coordinate

B

y-coordinate

C

Both x and y coordinates

D

Data insufficient.

Question 11: Palette 11/127

Allen MCQ

The slope of graph as shown in figure at points 1, 2 and 3 is $m_1$ , $m_2$ and $m_3$ respectively then

A

$\mathrm{m}_1 > \mathrm{m}_2 > \mathrm{m}_3$

B

$\mathrm{m}_1 < \mathrm{m}_2 < \mathrm{m}_3$

C

$\mathrm{m}_1 = \mathrm{m}_2 = \mathrm{m}_3$

D

$\mathrm{m}_1 = \mathrm{m}_3 > \mathrm{m}_2$

Question 12: Palette 12/127

Allen MCQ

Magnitude of slope of the shown graph.

A

First increases then decreases

B

First decreases then increases

C

Increases

D

Decreases

Question 13: Palette 13/127

Allen MCQ

Calculate the area enclosed under the curve $f(x) = x^2$ between the limits $x = 2$ and $x = 3$

A

5

B

$\frac{19}{3}$

C

$\frac{17}{3}$

D

8

Question 14: Palette 14/127

Allen MCQ

Find the value of $\int_{0}^{4}|(1-x)|.dx$

A

zero

B

1

C

4

D

5

Question 15: Palette 15/127

Allen MCQ

The equation of a curve is given as $y = x^{2} + 2 - 3x$ . The curve intersects the y-axis at

A

(1, 0)

B

(2, 0)

C

(0, 2)

D

No where

Question 16: Palette 16/127

Allen MCQ

Two particles A and B are moving in XY-plane. Their positions vary with time t according to relation: $x_{A}(t)=3t,\quad x_{B}(t)=6$ $y_{A}(t)=t,\quad y_{B}(t)=2+3t^{2}$ Distance between two particles at t=2 is:

A

12

B

13

C

5

D

$\sqrt{12}$

Question 17: Palette 17/127

Allen MCQ

The distance between points $(a + b, b + c)$ and $(a - b, c - b)$ is :-

A

$2\sqrt{a^{2} + b^{2}}$

B

$2\sqrt{b^{2} + c^{2}}$

C

$2\sqrt{2}b$

D

$\sqrt{a^{2} - c^{2}}$

Question 18: Palette 18/127

Allen MCQ

A dog is at point A(0, 3, 4)m and cat is at B(5,3,-8)m The dog is free to move but cat is fixed. The minimum distance travelled by dog to catch the cat is :-

A

25m

B

12m

C

13m

D

20m

Question 19: Palette 19/127

Allen MCQ

A particular straight line passes through origin and a point whose abscissa is equal to ordinate. The equation of such straight line is:

A

y = x

B

y = 2x

C

y = -4x

D

y = - $\frac{x}{4}$

Question 20: Palette 20/127

Allen MCQ

If $y = x^{2} + 2x - 3$ , then y-x graph is :-

A

B

C

D

Question 21: Palette 21/127

Allen MCQ

If y = |x - 1|, then y - x graph is :-

A

B

C

D

Question 22: Palette 22/127

Allen MCQ

Frequency f of a simple pendulum depends on its length $\ell$ and acceleration g due to gravity according to the following equation $f = \frac{1}{2\pi}\sqrt{\frac{g}{\ell}}$ . Graph between which of the following quantities is a parabola?

A

f on the ordinate and $1 / \ell$ on the abscissa

B

f on the ordinate and $\sqrt{\ell}$ on the abscissa

C

$f^2$ on the ordinate and $\ell$ on the abscissa

D

$f^2$ on the ordinate and $1 / \ell$ on the abscissa

Question 23: Palette 23/127

Allen MCQ

The sum of the series $1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \cdots\cdots\infty$ is :-

A

$\frac{8}{7}$

B

$\frac{6}{5}$

C

$\frac{2}{3}$

D

$\frac{3}{2}$

Question 24: Palette 24/127

Allen MCQ

In the given figure, each box represents a function machine. A function machine illustrates what it does with the input. Which of the following statements is correct?

A

$z = (2x + 3)^{2}$

B

$z = 2(x + 3)$

C

$z = \sqrt{2x + 3}$

D

$z = \sqrt{2(x + 3)}$

Question 25: Palette 25/127

Allen MCQ

Which of the following statements is false:

A

Mass, speed and energy are scalars

B

Momentum, force and torque are vectors

C

Distance is a vector while displacement is a scalar

D

A scalar has only magnitude whereas as a vector has both magnitude and direction

Question 26: Palette 26/127

Allen MCQ

A physical quantity which has a direction and obeys triangle law of vector addition:

A

must be a vector

B

may be a vector

C

must be a scalar

D

none of the above

Question 27: Palette 27/127

Allen MCQ

The forces, which meet at one point and their lines of action lie in one plane, are called:

A

non-concurrent and non-coplanar forces

B

non-concurrent and coplanar forces

C

concurrent and non-coplanar forces

D

concurrent and coplanar forces

Question 28: Palette 28/127

Allen MCQ

Which of the following physical quantities is not an axial vector?

A

angular velocity

B

angular momentum

C

velocity

D

torque

Question 29: Palette 29/127

Allen MCQ

The direction of the angular velocity vector is along:

A

Along the tangent of circular path

B

Along the direction of radius vector

C

Opposite to the direction of radius vector

D

Along the axis of rotation

Question 30: Palette 30/127

Allen MCQ

If $\hat{\mathbf{n}}$ is a unit vector in the direction of the vector $\vec{\mathbf{A}}$ , then:

A

$\hat{\mathbf{n}} = \frac{\vec{\mathbf{A}}}{|\vec{\mathbf{A}}|}$

B

$\hat{\mathbf{n}} = \vec{\mathbf{A}} |\vec{\mathbf{A}}|$

C

$\hat{\mathbf{n}} = \frac{|\vec{\mathbf{A}}|}{\vec{\mathbf{A}}}$

D

None of the above

Question 31: Palette 31/127

Allen MCQ

In the given figure, $\vec{a} + \vec{b} + \vec{c}$ is

A

$2\vec{a}$

B

$2\vec{b}$

C

$2\vec{c}$

D

$\vec{a} + \vec{b}$

Question 32: Palette 32/127

Allen MCQ

Vector sum of two forces of 10N and 5N can be:

A

4N

B

18N

C

12N

D

2N

Question 33: Palette 33/127

Allen MCQ

The vector sum of the forces of 10 newton and 8 newton cannot be:

A

2N

B

8N

C

18N

D

20N

Question 34: Palette 34/127

Allen MCQ

Which of the following pair of forces can give a resultant force of 2 N?

A

1 N and 2 N

B

1 N and 5 N

C

2 N and 5 N

D

1 N and 4 N

Question 35: Palette 35/127

Allen MCQ

Two vectors of equal magnitude have a resultant equal to either of them in magnitude. The angle between the vector is:

A

$60^{\circ}$

B

$90^{\circ}$

C

$105^{\circ}$

D

$120^{\circ}$

Question 36: Palette 36/127

Allen MCQ

$\vec{R} = \vec{a} +\vec{b}$ , where $\vec{R},\vec{a}$ and $\vec{b}$ are non-zero vector. If $R = a = b$ , the angle between $\vec{R}$ and $\vec{a}$ is :-

A

$\frac{\pi}{3}$

B

$\frac{2\pi}{3}$

C

$\frac{\pi}{4}$

D

$\frac{\pi}{6}$

Question 37: Palette 37/127

Allen MCQ

If resultant of two vectors $\vec{a}$ and $\vec{b}$ shown in the figure is $\sqrt{7}b$ , then value of $\frac{b}{a}$ is :-

A

$\frac{1}{2}$

B

1

C

2

D

3

Question 38: Palette 38/127

Allen MCQ

If $\vec{A} +\vec{B} = \vec{C}$ and $A + B = C$ , then the angle between $\vec{A}$ and $\vec{C}$ is :

A

0

B

$\frac{\pi}{4}$

C

$\frac{\pi}{2}$

D

$\pi$

Question 39: Palette 39/127

Allen MCQ

Two vectors $\vec{A}$ and $\vec{B}$ are such that $\vec{A} + \vec{B} = \vec{C}$ and A - B = C. Which of the following statements, is correct?

A

$\vec{A}$ is parallel to $\vec{B}$

B

$\vec{A}$ is anti-parallel to $\vec{B}$

C

$\vec{A}$ is perpendicular to $\vec{B}$

D

$\vec{A}$ and $\vec{B}$ are equal in magnitude

Question 40: Palette 40/127

Allen MCQ

In vector diagram shown in figure where $\left(\vec{R}\right)$ is the resultant of vectors $(\vec{A})$ and $(\vec{B})$ . If $R = \frac{B}{2}$ , then value of angle $\theta$ is :

A

$30^{\circ}$

B

$45^{\circ}$

C

$60^{\circ}$

D

$75^{\circ}$

Question 41: Palette 41/127

Allen MCQ

The resultant of $\vec{A}$ and $\vec{B}$ makes an angle $\alpha$ with $\vec{A}$ and $\beta$ with $\vec{B}$ , then:

A

$\alpha < \beta$

B

$\alpha < \beta$ if A < B

C

$\alpha < \beta$ if A > B

D

$\alpha < \beta$ if A = B

Question 42: Palette 42/127

Allen MCQ

If two forces of equal magnitude acting on a particle. The angle between forces is $60^{\circ}$ . The resultant force on the particle is:

A

at an angle of $30^{\circ}$ with each force.

B

at an angle of $45^{\circ}$ with one of the force

C

at an angle of $15^{\circ}$ with one of the force

D

at an angle lying between $45^{\circ}$ to $60^{\circ}$

Question 43: Palette 43/127

Allen MCQ

The resultant of $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{B}$ . What is the angle between $\vec{A}$ and $\vec{B}$ ?

A

$\cos^{-1}\left(\frac{A}{B}\right)$

B

$\cos^{-1}\left(-\frac{B}{A}\right)$

C

$\sin^{-1}\left(\frac{A}{B}\right)$

D

$\sin^{-1}\left(-\frac{A}{B}\right)$

Question 44: Palette 44/127

Allen MCQ

The resultant of two forces make $30^{\circ}$ and $60^{\circ}$ angles with them and has magnitude 40 N. The magnitudes of two vectors are:

A

$20\sqrt{3}N, 20N$

B

$30N, 20\sqrt{3}N$

C

40N, 30N

D

$3\sqrt{3}N, 40\sqrt{3}N$

Question 45: Palette 45/127

Allen MCQ

Given that $\vec{\mathrm{P}} +\vec{\mathrm{Q}} = \vec{\mathrm{P}} -\vec{\mathrm{Q}}$ . This can be true when:

A

$\vec{\mathrm{P}} = \vec{\mathrm{Q}}$

B

$\vec{\mathrm{Q}} = \vec{0}$

C

Neither $\vec{\mathrm{P}}$ nor $\vec{\mathrm{Q}}$ is a null vector

D

Data Insufficient

Question 46: Palette 46/127

Allen MCQ

The resultant of $\vec{A} \& \vec{B}$ is $\vec{R}_1$ . On reversing the vector $\vec{B}$ , the resultant becomes $\vec{R}_2$ . What is the value of $2(R_1^2 + R_2^2)$ ?

A

$4(A^2 + B^2)$

B

$A^2 - B^2$

C

$2(A^2 + B^2)$

D

$2(A^2 - B^2)$

Question 47: Palette 47/127

Allen MCQ

If vectors $\vec{A}$ and $\vec{B}$ are such that $|\vec{A}+\vec{B}|=\left|\vec{A}\right|=\left|\vec{B}\right|$ , then $|\vec{A}-\vec{B}|$ may be equated to

A

$\frac{\sqrt{3}}{2}|\vec{A}|$

B

$|\vec{A}|$

C

$\sqrt{2}|\vec{A}|$

D

$\sqrt{3}|\vec{A}|$

Question 48: Palette 48/127

Allen MCQ

If the difference of two unit vectors is a unit vector, then the magnitude of their sum is:

A

$\sqrt{2}$

B

$\sqrt{3}$

C

$\frac{1}{\sqrt{2}}$

D

$\sqrt{5}$

Question 49: Palette 49/127

Allen MCQ

In the given figure, O is the centre of the regular pentagon ABCDE. Five forces each of magnitude $F_{0}$ are acted as shown in the figure. The resultant force is :-

A

$5\mathrm{F}_0$

B

$5\mathrm{F}_0\cos 72^{\circ}$

C

$5\mathrm{F}_0\sin 72^{\circ}$

D

zero

Question 50: Palette 50/127

Allen MCQ

Two vectors $\vec{A}$ and $\vec{B}$ lie in a plane, another vector $\vec{C}$ lies in the same plane, then the resultant of these three vectors i.e. $\vec{A} + \vec{B} + \vec{C}$ :

A

may be zero

B

cannot be zero

C

lies in the plane containing $\vec{A}$ & $\vec{B}$

D

Both 1 & 3

Question 51: Palette 51/127

Allen MCQ

Which of the following sets of concurrent forces may be in equilibrium?

A

$F_{1} = 3N$ , $F_{2} = 5N$ , $F_{3} = 1N$ , $F_{4} = 10N$

B

$F_{1} = 3N$ , $F_{2} = 5N$ , $F_{3} = 9N$ , $F_{4} = 4N$

C

$F_{1} = 3N$ , $F_{2} = 5N$ , $F_{3} = 6N$ , $F_{4} = 15N$

D

$F_{1} = 3N$ , $F_{2} = 5N$ , $F_{3} = 15N$ , $F_{4} = 5N$

Question 52: Palette 52/127

Allen MCQ

Five forces 2N, $\sqrt{3}$ N, 5N, $\sqrt{3}$ N and 2N respectively act at a particle P as shown in the figure. The resultant force on the particle P is.

A

10 N making angle $60^{\circ}$ with x-axis.

B

10 N making angle $60^{\circ}$ with y-axis.

C

20 N along y-axis

D

None of these

Question 53: Palette 53/127

Allen MCQ

If $\vec{a}+\vec{b}+\vec{c}=0$ . The angle between $\vec{a}$ and $\vec{b}$ , $\vec{b}$ and $\vec{c}$ are $150^{\circ}$ and $120^{\circ}$ , respectively. Then, the magnitude of vectors $\vec{a}$ , $\vec{b}$ and $\vec{c}$ are in ratio of:-

A

1:2:3

B

$1:2:\sqrt{3}$

C

$\sqrt{3}:2:1$

D

$2:\sqrt{3}:1$

Question 54: Palette 54/127

Allen MCQ

The magnitudes of vectors $\vec{A},\vec{B}$ and $\vec{C}$ are respectively 7, 24 and 25 units and $\vec{A}+\vec{B}=\vec{C}$ , then the angle between $\vec{A}$ and $\vec{B}$ is:

A

0

B

$\pi/3$

C

$\pi/2$

D

$\pi/4$

Question 55: Palette 55/127

Allen MCQ

If vectors $\vec{P}, \vec{Q}$ and $\vec{R}$ have magnitudes 5, 12 and 13 units and $\vec{P} + \vec{Q} = \vec{R}$ , the angle between $\vec{P}$ and $\vec{R}$ is:

A

$\cos^{-1}\left(\frac{5}{12}\right)$

B

$\cos^{-1}\left(\frac{5}{13}\right)$

C

$\cos^{-1}\left(\frac{12}{13}\right)$

D

$\cos^{-1}\left(\frac{2}{13}\right)$

Question 56: Palette 56/127

Allen MCQ

If the vectors $\left(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}\right)$ and $3\hat{i}$ form two sides of a triangle, then $3^{rd}$ side of the triangle can be:

A

$\sqrt{18}$ unit

B

$\sqrt{6}$ unit

C

$\frac{3}{\sqrt{2}}$ unit

D

both (1) & (2)

Question 57: Palette 57/127

Allen MCQ

The minimum number of vectors of equal magnitude required to produce a zero resultant is:

A

2

B

3

C

4

D

more than 4

Question 58: Palette 58/127

Allen MCQ

How many minimum number of coplanar vectors having different magnitudes can be added to give zero resultant?

A

2

B

3

C

4

D

5

Question 59: Palette 59/127

Allen MCQ

How many minimum number of vectors in different planes can be added to give zero resultant?

A

2

B

3

C

4

D

5

Question 60: Palette 60/127

Allen MCQ

What happens, when we multiply a vector by 2?

A

direction reverses and unit changes

B

direction remains same and magnitude is doubled

C

direction remains unchanged and unit changes

D

none of these

Question 61: Palette 61/127

Allen MCQ

What is the maximum number of components into which a vector can be split?

A

2

B

3

C

4

D

Infinite

Question 62: Palette 62/127

Allen MCQ

What is the maximum number of rectangular components into which a vector can be split in its own plane?

A

2

B

3

C

4

D

Infinite

Question 63: Palette 63/127

Allen MCQ

What is the maximum number of rectangular components into which a vector can be split in space?

A

2

B

3

C

4

D

∞

Question 64: Palette 64/127

Allen MCQ

The unit vector along $\hat{\mathrm{i}} - 2\hat{\mathrm{j}}$ is:

A

$\frac{\hat{\mathrm{i}} - 2\hat{\mathrm{j}}}{\sqrt{5}}$

B

$\hat{\mathrm{i}} +\hat{\mathrm{j}}$

C

$\frac{\hat{\mathrm{i}} + \hat{\mathrm{j}}}{\sqrt{2}}$

D

$\frac{\hat{\mathrm{i}} - \hat{\mathrm{j}}}{\sqrt{5}}$

Question 65: Palette 65/127

Allen MCQ

If $\vec{\mathrm{A}} +\vec{\mathrm{B}}$ is a unit vector along y-axis and $\vec{\mathrm{A}} = \hat{\mathrm{i}} -\hat{\mathrm{j}} +\hat{\mathrm{k}}$ , then what is $\vec{\mathrm{B}}?$

A

$\hat{\mathrm{j}} +\hat{\mathrm{k}}$

B

$\hat{\mathrm{j}} -\hat{\mathrm{k}}$

C

$\hat{\mathrm{i}} +\hat{\mathrm{j}} +\hat{\mathrm{k}}$

D

$2\hat{\mathrm{j}} -\hat{\mathrm{i}} -\hat{\mathrm{k}}$

Question 66: Palette 66/127

Allen MCQ

If a unit vector is represented by $0.3\hat{i}-0.4\hat{j}+ck$ , then the value of 'c' is:

A

$\sqrt{0.75}$

B

$\sqrt{0.25}$

C

$\sqrt{0.01}$

D

$\sqrt{0.39}$

Question 67: Palette 67/127

Allen MCQ

$\hat{\mathbf{e}}_{\mathrm{r}}$ is unit vector along radius of a circle shown in figure. $\hat{\mathbf{e}}_{\mathrm{r}}$ can be represented as :-

A

$\cos \theta \hat{\mathrm{i}} +\sin \theta \hat{\mathrm{j}}$

B

$\sin \theta \hat{\mathrm{i}} +\cos \theta \hat{\mathrm{j}}$

C

$\cos \theta \hat{\mathrm{i}} -\sin \theta \hat{\mathrm{j}}$

D

$-\cos \theta \hat{\mathrm{i}} +\sin \theta \hat{\mathrm{j}}$

Question 68: Palette 68/127

Allen MCQ

Forces 7N, 24N, 25N act at a point in mutually perpendicular directions. The magnitude of the resultant force is:

A

19 N

B

13 N

C

26 N

D

$25\sqrt{2}$ N

Question 69: Palette 69/127

Allen MCQ

The angle that the vector $\vec{\mathrm{A}} = 2\hat{\mathrm{i}} +3\hat{\mathrm{j}}$ makes with x-axis is:

A

$\tan^{-1}(3 / 2)$

B

$\tan^{-1}(2 / 3)$

C

$\sin^{-1}(2 / 3)$

D

$\cos^{-1}(3 / 2)$

Question 70: Palette 70/127

Allen MCQ

What vector must be added to the other vectors $\hat{\mathrm{i}} - 2\hat{\mathrm{j}} + 2\hat{\mathrm{k}}$ and $2\hat{\mathrm{i}} + \hat{\mathrm{j}} - \hat{\mathrm{k}}$ , so that the resultant may be a unit vector along y-axis?

A

$2\hat{\mathrm{i}} + \hat{\mathrm{j}} - \hat{\mathrm{k}}$

B

$-3\hat{\mathrm{i}} + 2\hat{\mathrm{j}} - \hat{\mathrm{k}}$

C

$-2\hat{\mathrm{i}} - \hat{\mathrm{j}} - \hat{\mathrm{k}}$

D

$3\hat{\mathrm{i}} - 2\hat{\mathrm{j}} - \hat{\mathrm{k}}$

Question 71: Palette 71/127

Allen MCQ

The unit vector parallel to the resultant of the vectors $\vec{A} = 4\hat{i} + 3\hat{j} + 6\hat{k}$ and $\vec{B} = 2\hat{i} - 3\hat{j} + 2\hat{k}$ is:

A

$\frac{1}{10}\left[8\hat{i} + 6\hat{k}\right]$

B

$\frac{1}{10}\left[6\hat{i} + 8\hat{k}\right]$

C

$\frac{1}{10}\left[6\hat{i} + 6\hat{k} + 6\hat{j}\right]$

D

$\frac{1}{10}\left[6\hat{j} + 8\hat{k}\right]$

Question 72: Palette 72/127

Allen MCQ

If $\vec{a}=2\hat{i}+2\hat{j}-\hat{k}$ and $\vec{b}=\hat{i}+\hat{j}+\hat{k}$ . Find a vector $\vec{c}$ which is parallel to $\vec{a}$ but has magnitude three times that of $\vec{b}$ .

A

$\vec{c}=3\hat{i}+3\hat{j}+3\hat{k}$

B

$\vec{c}=2\sqrt{3}\hat{i}+2\sqrt{3}\hat{j}-\sqrt{3}\hat{k}$

C

$\vec{c}=6\hat{i}+6\hat{j}-3\hat{k}$

D

$\vec{c}=3\hat{i}+6\hat{j}-6\hat{k}$

Question 73: Palette 73/127

Allen MCQ

The velocity of a particle is $\vec{v} = (\hat{i} + \hat{j} - \hat{k})m/s$ . A force of $10\sqrt{3}N$ parallel to velocity in vector form is:

A

$(10\hat{i} + 10\hat{j} - 10\hat{k})N$

B

$(\hat{i} + \hat{j} - \hat{k})10\sqrt{3}N$

C

$(\hat{i} + \hat{j} - \hat{k})N$

D

None of these

Question 74: Palette 74/127

Allen MCQ

The direction cosines of a vector $\sqrt{2}\hat{\mathrm{i}} +\sqrt{2}\hat{\mathrm{j}} +\hat{\mathrm{k}}$ are:-

A

$\frac{\sqrt{2}}{\sqrt{5}},\frac{\sqrt{2}}{\sqrt{5}},\frac{1}{\sqrt{5}}$

B

$\frac{1}{\sqrt{5}},\frac{1}{\sqrt{5}},\frac{1}{5}$

C

$\frac{1}{5},\frac{1}{5},\frac{1}{\sqrt{5}}$

D

$\frac{1}{\sqrt{5}},\frac{1}{\sqrt{5}},\frac{1}{\sqrt{5}}$

Question 75: Palette 75/127

Allen MCQ

Vector $\vec{P}$ makes angles $\alpha, \beta \& \gamma$ with the X, Y and Z axes respectively, then $\cos^{2}\alpha + \cos^{2}\beta + \cos^{2}\gamma =$

A

0

B

1

C

2

D

3

Question 76: Palette 76/127

Allen MCQ

Find the direction cosines of vector $(\vec{a}-\vec{b})$ , if $\vec{a}=2\hat{i}+3\hat{j}+\hat{k}$ and $\vec{b}=2\hat{i}+2\hat{j}+3\hat{k}$

A

$0,\frac{1}{\sqrt{5}},\frac{-2}{\sqrt{5}}$

B

0, 0, 0

C

$\frac{1}{\sqrt{5}},\frac{-2}{\sqrt{5}},\frac{2}{\sqrt{5}}$

D

1, 1, -1

Question 77: Palette 77/127

Allen MCQ

Three forces are acting on a particles as shown in the figure. To have the resultant forces only along the y-direction, the magnitude of the minimum additional force needed is :-

A

0.866 N

B

1.732 N

C

0.5 N

D

4 N

Question 78: Palette 78/127

Allen MCQ

The force $\vec{\mathrm{F}} = (\hat{\mathrm{i}} +\mathrm{b}\hat{\mathrm{j}} +3\hat{\mathrm{k}})\mathrm{N}$ is rotated through an angle $\alpha$ , then it becomes $\{2\hat{\mathrm{i}} +(2\mathrm{b} - 1)\hat{\mathrm{j}} +\hat{\mathrm{k}}\} \mathrm{N}$ The value of b is :-

A

2

B

$-\frac{2}{3}$

C

$\frac{2}{3}$

D

Both (1) and (2)

Question 79: Palette 79/127

Allen MCQ

If $\vec{P}\cdot\vec{Q}=-PQ$ , then angle between $\vec{P}$ and $\vec{Q}$ is:

A

$0^{\circ}$

B

$180^{\circ}$

C

$45^{\circ}$

D

$60^{\circ}$

Question 80: Palette 80/127

Allen MCQ

A force $\vec{\mathrm{F}} = (2\hat{\mathrm{i}} + 3\hat{\mathrm{j}})\mathrm{N}$ acts on a body and displaces it by $\vec{S} = (3\hat{\mathrm{i}} + 4\hat{\mathrm{j}})\mathrm{m}$ . The work done $(W = \overline{F} \cdot \overline{S})$ by the force is:

A

10J

B

12J

C

18J

D

25J

Question 81: Palette 81/127

Allen MCQ

A force $(2\hat{i}+2\hat{j})$ N displaces an object through a distance $(2\hat{i}-3\hat{j})$ m. The work $(W=\vec{F}\cdot\vec{S})$ done is:

A

-2J

B

12J

C

5J

D

13J

Question 82: Palette 82/127

Allen MCQ

A force of 14 N acts on a particle along the vector $(3\hat{i}+2\hat{j}-6\hat{k})$ . If the particle displaces from $(0,0,0)$ to $(2,4,-2)$ , the work $(W=\vec{F}\cdot\vec{S})$ done by force on the particle is :-

A

10J

B

52J

C

-48J

D

14 J

Question 83: Palette 83/127

Allen MCQ

If a vector $(2\hat{i}+3\hat{j}+8\hat{k})$ is perpendicular to the vector $(4\hat{i}-4\alpha\hat{j}+\alpha\hat{k})$ , then the value of $\alpha$ is:

A

-1

B

1/2

C

-1/2

D

2

Question 84: Palette 84/127

Allen MCQ

The vector $\vec{\mathrm{P}} = a\hat{\mathrm{i}} + a\hat{\mathrm{j}} + 3\hat{\mathrm{k}}$ and $\vec{\mathrm{Q}} = a\hat{\mathrm{i}} - 2\hat{\mathrm{j}} - \hat{\mathrm{k}}$ are perpendicular to each other. The positive value of a is:

A

3

B

2

C

1

D

zero

Question 85: Palette 85/127

Allen MCQ

A vector perpendicular to $(4\hat{i}+3\hat{j})$ may be:

A

$4\hat{i}+3\vec{j}$

B

$7\hat{k}$

C

$6\hat{i}$

D

$3\hat{i}+4\hat{j}$

Question 86: Palette 86/127

Allen MCQ

Let $\vec{A} = \hat{i} A\cos \theta -\hat{j} A\sin \theta$ , be any vector. Another vector $\vec{B}$ which is normal to $\vec{A}$ is :

A

$\hat{\mathrm{i}} B\cos \theta +\hat{\mathrm{j}} B\sin \theta$

B

$\hat{\mathrm{i}} B\sin \theta +\hat{\mathrm{j}} B\cos \theta$

C

$\hat{\mathrm{i}} B\sin \theta -\hat{\mathrm{j}} B\cos \theta$

D

$\hat{\mathrm{i}} A\cos \theta -\hat{\mathrm{j}} A\sin \theta$

Question 87: Palette 87/127

Allen MCQ

If $\hat{\mathbf{n}} = a\hat{\mathbf{i}} + b\hat{\mathbf{j}}$ is perpendicular to the vector $(\hat{\mathbf{i}} - \hat{\mathbf{j}})$ , then the value of $a$ and $b$ may be:

A

1, 0

B

-2, 0

C

3, 0

D

$\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}$

Question 88: Palette 88/127

Allen MCQ

The vector sum of two forces is perpendicular to their vector difference. In that case, the force:

A

Are equal to each other.

B

Are equal to each other in magnitude.

C

Are not equal to each other in magnitude.

D

Cannot be predicted.

Question 89: Palette 89/127

Allen MCQ

Given that A = B and $\vec{A} \perp \vec{B}$ . What is the angle between $(\vec{A} + \vec{B})$ and $(\vec{A} - \vec{B})$ ?

A

$30^{0}$

B

$60^{0}$

C

$90^{0}$

D

$180^{0}$

Question 90: Palette 90/127

Allen MCQ

A parallelogram is formed with $\vec{a}$ and $\vec{b}$ as the sides. Let $\vec{d}_{1}$ and $\vec{d}_{2}$ be the diagonals of the parallelogram. The value of $a^{2} + b^{2}$ is :-

A

$d_{1}^{2} + d_{2}^{2}$

B

$\frac{d_{1}^{2} + d_{2}^{2}}{2}$

C

$(d_{1} + d_{2})^{2}$

D

$d_{1}^{2} + d_{2}^{2} + d_{1}d_{2}$

Question 91: Palette 91/127

Allen MCQ

The angle between the two vectors $\vec{A} = 3\hat{i} +4\hat{j} +5\hat{k}$ and $\vec{B} = 6\hat{i} +8\hat{j} +10\hat{k}$ will be:

A

$0^{\circ}$

B

$180^{\circ}$

C

$90^{\circ}$

D

$45^{\circ}$

Question 92: Palette 92/127

Allen MCQ

What is the angle between $\vec{A}$ and the resultant of $(\vec{A} + 2\hat{B})$ and $(2\vec{A} - 2\hat{B})$ ?

A

$0^{\circ}$

B

$\tan^{-1}\left(\frac{A}{B}\right)$

C

$\tan^{-1}\left(\frac{B}{A}\right)$

D

$\tan^{-1}\left(\frac{A - B}{A + B}\right)$

Question 93: Palette 93/127

Allen MCQ

The angle between vectors $(\hat{\mathrm{i}}+\hat{\mathrm{j}})$ and $(\hat{\mathrm{i}}+\hat{\mathrm{k}})$ is:

A

$90^{\circ}$

B

$180^{\circ}$

C

$0^{\circ}$

D

$60^{\circ}$

Question 94: Palette 94/127

Allen MCQ

The angle between $2\hat{i}+\hat{j}+2\hat{k}$ and $\hat{i}-\hat{j}+\hat{k}$ is :-

A

$30^{\circ}$

B

$60^{\circ}$

C

$\cos^{-1}\left(\frac{1}{\sqrt{3}}\right)$

D

$\cos^{-1}\left(\frac{2}{3}\right)$

Question 95: Palette 95/127

Allen MCQ

What is the projection of $3\hat{i} + 4\hat{k}$ on the z-axis?

A

3

B

4

C

5

D

zero

Question 96: Palette 96/127

Allen MCQ

What is the projection of $\vec{B}$ on $\vec{A}$ ?

A

$\vec{A}.\vec{B}$

B

$\vec{A}.\hat{B}$

C

$\vec{B}.\hat{A}$

D

$\hat{A}.\hat{B}$

Question 97: Palette 97/127

Allen MCQ

If $\hat{\mathrm{i}},\hat{\mathrm{j}}$ and $\hat{\mathrm{k}}$ are unit vectors along X, Y & Z axis respectively, then tick the wrong statement:

A

$\hat{\mathrm{i}}\times \hat{\mathrm{i}} = \vec{0}$

B

$\hat{\mathrm{i}}\times \hat{\mathrm{j}} = \hat{\mathrm{k}}$

C

$\hat{\mathrm{i}}.\hat{\mathrm{j}} = 1$

D

$\hat{\mathrm{i}}\times \hat{\mathrm{k}} = -\hat{\mathrm{j}}$

Question 98: Palette 98/127

Allen MCQ

The magnitude of the vector product of two vectors $\vec{A}$ and $\vec{B}$ may be:

A

Equal to 0

B

Less than AB

C

Equal to AB

D

All of above

Question 99: Palette 99/127

Allen MCQ

If $\vec{\mathrm{P}}\times \vec{\mathrm{Q}} = \vec{\mathrm{R}}$ , then which of the following statements is true?

A

$\vec{\mathrm{R}}\bot \vec{\mathrm{P}}$

B

$\vec{\mathrm{R}}\bot \vec{\mathrm{Q}}$

C

$\vec{\mathrm{R}}\bot (\vec{\mathrm{P}} +\vec{\mathrm{Q}})$

D

All of above

Question 100: Palette 100/127

Allen MCQ

Two vectors $\vec{P}$ and $\vec{Q}$ are inclined to each other at angle $\theta$ . Which of the following is the unit vector perpendicular to $\vec{P}$ and $\vec{Q}$ ?

A

$\frac{\vec{P}\times\vec{Q}}{P.Q}$

B

$\frac{\hat{P}\times\hat{Q}}{\sin\theta}$

C

$\frac{\vec{P}\times\vec{Q}}{|\vec{P}\times\vec{Q}|}$

D

Both 2 and 3

Question 101: Palette 101/127

Allen MCQ

Which of the following vector identities is false?

A

$\vec{P} + \vec{Q} = \vec{Q} + \vec{P}$

B

$\vec{P} \times \vec{Q} = \vec{Q} \times \vec{P}$

C

$\vec{P}. \vec{Q} = \vec{Q}. \vec{P}$

D

$\vec{P} \times \vec{Q} = -(\vec{Q} \times \vec{P})$

Question 102: Palette 102/127

Allen MCQ

What is the value of $\left(\vec{\mathrm{A}} +\vec{\mathrm{B}}\right)\times \left(\vec{\mathrm{A}} -\vec{\mathrm{B}}\right)$ ?

A

$-2(\vec{\mathrm{A}}\times \vec{\mathrm{B}})$

B

$2(\vec{\mathrm{B}}\times \vec{\mathrm{A}})$

C

$\vec{0}$

D

both 1 and 2

Question 103: Palette 103/127

Allen MCQ

The angle between vectors $(\vec{A} \times \vec{B})$ and $-(\vec{B} \times \vec{A})$ is:

A

$\pi$ rad

B

$\frac{\pi}{2}$ rad

C

$\frac{\pi}{4}$ rad

D

zero

Question 104: Palette 104/127

Allen MCQ

A vector $\vec{A}$ points vertically upward and $\vec{B}$ points towards south. The vector product $\vec{A} \times \vec{B}$ is

A

zero

B

along west

C

along east

D

vertically downward

Question 105: Palette 105/127

Allen MCQ

If $\frac{3}{4}|\vec{A}\times\vec{B}|=|\vec{A}.\vec{B}|$ , then the angle between $\vec{A}$ and $\vec{B}$ will be:

A

$30^{\circ}$

B

$45^{\circ}$

C

$60^{\circ}$

D

$53^{\circ}$

Question 106: Palette 106/127

Allen MCQ

If $\vec{A} = 3\hat{\mathrm{i}} +4\hat{\mathrm{j}}$ and $\vec{B} = 6\hat{\mathrm{i}} +8\hat{\mathrm{j}}$ and A and B are the magnitudes of $\vec{A}$ and $\vec{B}$ , then which of the following is true?

A

$\vec{A}\times \vec{B} = \vec{0}$

B

$\frac{A}{B} = 2$

C

$\vec{A}.\vec{B} = 48$

D

$A = 10$

Question 107: Palette 107/127

Allen MCQ

Two non zero vectors $\vec{A}$ and $\vec{B}$ are such that $\left|\vec{A}+\vec{B}\right|=\left|\vec{A}-\vec{B}\right|$ . Then select correct alternative

A

$\vec{A}.\vec{B}=0$

B

$\vec{A}\times\vec{B}=\vec{0}$

C

$\vec{A}=\vec{0}$

D

$\vec{B}=\vec{0}$

Question 108: Palette 108/127

Allen MCQ

A vector $\vec{\mathrm{F}}_1$ is along the positive Y-axis. If its vector product with another vector $\vec{\mathrm{F}}_2$ is zero then $\vec{\mathrm{F}}_2$ may be :-

A

$4\hat{\mathrm{j}}$

B

$-(i + \hat{j})$

C

$(i + \hat{k})$

D

$-4\hat{i}$

Question 109: Palette 109/127

Allen MCQ

If $\vec{A} \times \vec{B} = \vec{0}$ and $\vec{B} \times \vec{C} = \vec{0}$ , then the angle between $\vec{A}$ and $\vec{C}$ may be:

A

$\pi$

B

$\frac{\pi}{4}$

C

$\frac{\pi}{2}$

D

None

Question 110: Palette 110/127

Allen MCQ

The vector $\vec{B}=6\hat{i}+2\hat{j}+S\hat{k}$ is parallel to the vector $\vec{A}=3\hat{i}+\hat{j}+2\hat{k}$ if S=

A

1

B

4

C

6

D

8

Question 111: Palette 111/127

Allen MCQ

If three vectors satisfy the relation $\vec{A}.\vec{B}=0$ and $\vec{A}.\vec{C}=0$ , then $\vec{A}$ can be parallel to

A

$\vec{C}$

B

$\vec{B}$

C

$\vec{B}\times\vec{C}$

D

$\vec{B}.\vec{C}$

Question 112: Palette 112/127

Allen MCQ

For a body, angular velocity $\vec{\omega} = \hat{\mathrm{i}} - \hat{\mathrm{j}} + \hat{\mathrm{k}}$ and radius vector $\vec{r} = \hat{\mathrm{i}} + \hat{\mathrm{j}} + \hat{\mathrm{k}}$ , then its velocity $(\vec{v} = \vec{\omega} \times \vec{r})$ is:

A

$-5\hat{\mathrm{i}} + 2\hat{\mathrm{j}} + 3\hat{\mathrm{k}}$

B

$-5\hat{\mathrm{i}} + 2\hat{\mathrm{j}} + 3\hat{\mathrm{k}}$

C

$-2\hat{\mathrm{i}} + 2\hat{\mathrm{k}}$

D

$-5\hat{\mathrm{i}} - 2\hat{\mathrm{j}} - 3\hat{\mathrm{k}}$

Question 113: Palette 113/127

Allen MCQ

Find unit vector perpendicular to the plane of $\vec{a} = 2\hat{i} - 2\hat{j} +\hat{k}$ and $\vec{b} = \hat{i} +2\hat{j} +2\hat{k}$

A

$\frac{2}{3}\hat{\mathrm{i}} +\frac{1}{3}\hat{\mathrm{j}} +\frac{2}{3}\hat{\mathrm{k}}$

B

$-\frac{2}{3}\hat{\mathrm{i}} -\frac{1}{3}\hat{\mathrm{j}} -\frac{2}{3}\hat{\mathrm{k}}$

C

$-\frac{2}{3}\hat{\mathrm{i}} -\frac{1}{3}\hat{\mathrm{j}} +\frac{2}{3}\hat{\mathrm{k}}$

D

$\frac{2}{3}\hat{\mathrm{i}} +\frac{2}{3}\hat{\mathrm{j}} -\frac{1}{3}\hat{\mathrm{k}}$

Question 114: Palette 114/127

Allen MCQ

If vectors $\vec{A} = \cos \omega t\hat{i} +\sin \omega t\hat{j}$ and $\vec{B} = \cos \frac{\omega t}{2}\hat{i} +\sin \frac{\omega t}{2}\hat{j}$ are functions of time, then the value of $t$ at which they are orthogonal to each other is:

A

$t = 0$

B

$t = \frac{\pi}{4\omega}$

C

$t = \frac{\pi}{2\omega}$

D

$t = \frac{\pi}{\omega}$

Question 115: Palette 115/127

Allen MCQ

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is :-

A

$0^{\circ}$

B

$90^{\circ}$

C

$45^{\circ}$

D

$180^{\circ}$

Question 116: Palette 116/127

Allen MCQ

A particle moving with velocity $\vec{V}$ is acted by three forces shown by the vector triangle PQR. The velocity of the particle will:

A

increase

B

decrease

C

remain constant

D

change according to the smallest force $\overrightarrow{QR}$

Question 117: Palette 117/127

Allen MCQ

If $\vec{\mathrm{F}} = 2\hat{\mathrm{i}} +\hat{\mathrm{j}} -\hat{\mathrm{k}}$ and $\vec{\mathrm{r}} = 3\hat{\mathrm{i}} +2\hat{\mathrm{j}} -2\hat{\mathrm{k}}$ , then the scalar and vector products of $\vec{\mathrm{F}}$ and $\vec{\mathrm{r}}$ have the magnitudes respectively as:

A

$5,\sqrt{3}$

B

$4,\sqrt{5}$

C

$10,\sqrt{2}$

D

$10,2$

Question 118: Palette 118/127

Allen MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Current has magnitude as well as direction but still not considered as vector.
Reason (R): Current do not follow vector algebra.
In the light of the above statements,
choose the most appropriate answer from the options given below:

A

Both (A) and (R) are true and (R) is the correct explanation of (A).

B

Both (A) and (R) are true and (R) is NOT the correct explanation of (A).

C

(A) is true but (R) is false.

D

(A) is false but (R) is true.

Question 119: Palette 119/127

Allen MCQ

Two vectors $\vec{A} \& \vec{B}$ have equal magnitude equal to $Z$ . If angle between $\vec{A} \& \vec{B}$ is $60^{\circ}$ then match the following: Match the Column-I with Column-II

Column-I	Column-II
(A) $|\vec{A}+\vec{B}|$ (B) $|\vec{A}-\vec{B}|$ (C) $\vec{A}\cdot\vec{B}$ (D) $|\vec{A}\times\vec{B}|$	(P) $\frac{\sqrt{3}}{2}Z^2$ (Q) $Z$ (R) $\sqrt{3}Z$ (S) None

A

A-R, B-S, C-Q, D-P

B

A-R, B-Q, C-S, D-P

C

A-P, B-Q, C-R, D-S

D

A-Q, B-P, C-S, D-P

Question 120: Palette 120/127

Allen MCQ

Match the following

Column-I	Column-II
(A) $\vec{a} +\vec{b} = \vec{c}$ (B) $\vec{a}-\vec{c}=\vec{b}$ (C) $\vec{\mathbf{b}} -\vec{\mathbf{a}} = \vec{\mathbf{c}}$ (D) $\vec{a} +\vec{b} +\vec{c} = \vec{0}$	(P) (Q) (R) (S)

A

(A)-(S), (B)-(R), (C)-(P), (D)-(Q)

B

(A)-(R), (B)-(S), (C)-(Q), (D)-(P)

C

(A)-(P), (B)-(Q), (C)-(R), (D)-(S)

D

(A)-(S), (B)-(R), (C)-(Q), (D)-(P)

Question 121: Palette 121/127

Allen MCQ

Given below are two statements: Statement I : Resultant of 2 forces of magnitude 4N and 5N can be 2N in magnitude. Statement II: $\left|\vec{a}\right|-\left|\vec{b}\right|\leq\left|\vec{a}+\vec{b}\right|\leq\left|\vec{a}\right|+\left|\vec{b}\right|$ In the light of the above statements, choose the most appropriate answer from the options given below :

A

Both statement I and statement II are correct.

B

Statement I is correct and statement II is incorrect.

C

Statement I is incorrect and statement II is correct.

D

Both statements I and statements II are incorrect.

Question 122: Palette 122/127

Allen MCQ

Given below are two statements : Statement I : Two null vector have same direction. Statement II: $\vec{A} \times \vec{B}$ lies in the plane of $\vec{A} + \vec{B}$ . In the light of the above statements, choose the most appropriate answer from the options given below:

A

Both statement I and statement II are correct.

B

Statement I is correct and statement II is incorrect.

C

Statement I is incorrect and statement II is correct.

D

Both statements I and statements II are incorrect.

Question 123: Palette 123/127

Allen MCQ

Which of the following is correct :
(i) $\vec{A} \cdot \vec{B}$ is a vector quantity
(ii) $\vec{A} \times \vec{B}$ is perpendicular to plane of $\vec{A} + \vec{B}$
(iii) For two orthogonal vectors $\vec{A} \cdot \vec{B} = 0$
(iv) If vectors are parallel or antiparallel, then $\vec{A} \times \vec{B} = \vec{0}$

A

(i) only

B

(i) & (ii)

C

(iii) & (iv) only

D

(ii), (iii) & (iv)

Question 124: Palette 124/127

Allen MCQ

Given below are two statements: Statement-I : For every small angle $\theta$ , we may use approximation $\sin\theta \approx \theta \approx \tan\theta$ . Statement-II : For very small angle $\theta$ , the hypotenuse and the base become approximately of the same length.

A

Statement-I is true, Statement-II is true; Statement-II is a correct explanation for Statement-I.

B

Statement-I is true, Statement-II is true; Statement-II is not a correct explanation for Statement-I.

C

Statement-I is true, Statement-II is false.

D

Statement-I is false, Statement-II is true.

Question 125: Palette 125/127

Allen MCQ

Refer the given figure and identify correct statement(s)
(A) Distance of A from x-axis is $5\sqrt{3}$ cm.
(B) Distance of B from x-axis is 6 cm.
(C) Distance of A from y-axis is 5 cm.
(D) Distance of B from y-axis is 8 cm.

A

A, C

B

A, D

C

A, B, C

D

A, B, C, D

Question 126: Palette 126/127

Allen MCQ

Three forces $\vec{F}_{1}$ , $\vec{F}_{2}$ and $\vec{F}_{3}$ are represented as shown. Each of them is of equal magnitude. Match the Column-I(Combination), with Column-II (Approximate Direction)

Column-I	Column-II
(A) $\vec{\mathrm{F}}_1 + \vec{\mathrm{F}}_2 + \vec{\mathrm{F}}_3$ (B) $\vec{\mathrm{F}}_1 - \vec{\mathrm{F}}_2 + \vec{\mathrm{F}}_3$ (C) $\vec{\mathrm{F}}_1 - \vec{\mathrm{F}}_2 - \vec{\mathrm{F}}_3$ (D) $\vec{\mathrm{F}}_2 - \vec{\mathrm{F}}_1 - \vec{\mathrm{F}}_3$	(P) (Q) (R) (S)

A

$\mathrm{A} \rightarrow \mathrm{R}, \mathrm{B} \rightarrow \mathrm{Q}, \mathrm{C} \rightarrow \mathrm{P}, \mathrm{D} \rightarrow \mathrm{S}$

B

$\mathrm{A} \rightarrow \mathrm{Q}, \mathrm{B} \rightarrow \mathrm{P}, \mathrm{C} \rightarrow \mathrm{R}, \mathrm{D} \rightarrow \mathrm{S}$

C

$\mathrm{A} \rightarrow \mathrm{Q}, \mathrm{B} \rightarrow \mathrm{R}, \mathrm{C} \rightarrow \mathrm{P}, \mathrm{D} \rightarrow \mathrm{S}$

D

$\mathrm{A}\rightarrow \mathrm{S},\mathrm{B}\rightarrow \mathrm{P},\mathrm{C}\rightarrow \mathrm{R},\mathrm{D}\rightarrow \mathrm{Q}$

Question 127: Palette 127/127

Allen MCQ

Which of the following statement is/are true? (a) Two vectors of unequal magnitude can add up to zero. (b) Three vectors of unequal magnitude can add up to zero, if they lie in a plane. (c) Three vectors of unequal magnitude can added up to zero, if they do not lie in same plane.

A

Only a

B

a, b and c

C

only b

D

only c