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If the angle between the vector $\overrightarrow{A}<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>\overrightarrow{B}$ is  $\theta$, the value of the product $\left(\overrightarrow{B}\times \overrightarrow{A}\right).\overrightarrow{A}$ is equal to:
1. $B{A}^2<mspace\; width="1em"></mspace>\cos \theta$
2. $B{A}^2<mspace\; width="1em"></mspace>\sin \theta$
3. $B{A}^2<mspace\; width="1em"></mspace>\sin \theta \cos \theta$
4. zero

Two forces are such that the sum of their magnitudes is \(18~\text{N}\) and their resultant is perpendicular to the smaller force and the magnitude of the resultant is \(12~\text{N}\). Then the magnitudes of the forces will be:
1. \(12~\text{N}, 6~\text{N}\)
2. \(13~\text{N}, 5~\text{N}\)
3. \(10~\text{N}, 8~\text{N}\)
4. \(16~\text{N}, 2~\text{N}\)

If the magnitude of the sum of two vectors is equal to the magnitude of the difference between the two vectors, the angle between these vectors is:
1. \(90^{\circ}\)
2. \(45^{\circ}\)
3. \(180^{\circ}\)
4. \(0^{\circ}\)

The resultant of two vectors A and B is perpendicular to the vector A and its magnitude is equal to half the magnitude of vector B. The angle between A and B is -
                               
1. $120°$
2.  $150°$
3.  $135°$
4.  None of these

What is the resultant of three coplanar forces: $300<mspace\; width="1em"></mspace>\mathrm{N}$ at $0°$, $400<mspace\; width="1em"></mspace>\mathrm{N}$ at $30°$ and $400<mspace\; width="1em"></mspace>\mathrm{N}$ at $150°$?
1.  $500<mspace\; width="1em"></mspace>\mathrm{N}$
2.  $700<mspace\; width="1em"></mspace>\mathrm{N}$
3.  $1100<mspace\; width="1em"></mspace>\mathrm{N}$
4.  $300<mspace\; width="1em"></mspace>\mathrm{N}$

For the figure -
 
1.  A+B=C
2.  B+C=A
3.  C+A=B
4.  A+B+C=0

The two vectors $\mathrm{A}=2\hat{\mathrm{i}}+\hat{\mathrm{j}}+3\hat{\mathrm{k}}$ and $\mathrm{B}=7\hat{\mathrm{i}}-5\hat{\mathrm{j}}-3\hat{\mathrm{k}}$ are -
1.  parallel
2.  perpendicular
3.  anti-parallel
4.  None of these

A vector A points, vertically upward and, B points towards north. The vector product $\mathrm{A}\times \mathrm{B}$ is -
1.  along west
2.  along east
3.  zero
4.  vertically downward

The vector having a magnitude of 10 and perpendicular to the vector $3\hat{\mathrm{i}}-4\hat{\mathrm{j}}$ is- 
1. $4\hat{\mathrm{i}}-3\hat{\mathrm{j}}$
2. $5\sqrt{2}<mspace\; width="1em"></mspace>\hat{\mathrm{i}}-5\sqrt{2}<mspace\; width="1em"></mspace>\hat{\mathrm{j}}$
3. $8\hat{\mathrm{i}}+6\hat{\mathrm{j}}$
4.  $8\hat{\mathrm{i}}-6\hat{\mathrm{j}}$

If \(\overrightarrow{A}={2}\hat{i}+\hat{j}\;{\&}\;\overrightarrow{B}=\hat{i}{-}\hat{j},\)  then the components of \(\overrightarrow {A}\) along with \(\overrightarrow {B}\) & perpendicular to \(\overrightarrow {B}\) respectively will be:
1. \(\frac{\hat{i} - \hat{j}}{2} ,~\frac{3}{2}\left(\hat i+\hat j\right)\)
2. \(\frac{\hat{i} - \hat{j}}{2} ,~-\frac{2}{3}\left(\hat i+\hat j\right)\)
3. \(\frac{\hat{i} - \hat{j}}{2} ,~-\frac{3}{2}\left(\hat i-\hat j\right)\)
4. \(\frac{\hat{i} - \hat{j}}{2} ,~\frac{2}{3}\left(\hat i-\hat j\right)\)

Which of the following represented to \(U-x\) graph of \(U=\dfrac{1}{2} K \left(\right. A^{2}   -   x^{2} \left.\right)   ?   \left(\right. K > 0 \left.\right)\)
1. 
2. 
3. 
4. 

If curve between acceleration ($\mathrm{\alpha }$) and position (x) is a straight line as shown. Then acceleration is

$1.<mspace\; width="1em"></mspace>\frac{40}{3}-\frac{8}{3}\mathrm{x}$
$2.<mspace\; width="1em"></mspace>\frac{46}{3}-\frac{8}{3}\mathrm{x}$
$3.<mspace\; width="1em"></mspace>\frac{5}{6}-\frac{8}{3}\mathrm{x}$
$4.<mspace\; width="1em"></mspace>\frac{1}{3}-\frac{5}{2}\mathrm{x}$

Which of the following graphs best represents the straight line \(y=-2x+5\text{?}~\)

1.		2.
3.		4.

1. \(2P_0 - \frac{P_0V}{V_0}\)
2. \(3P_0 - \frac{P_0V}{V_0}\)
3. \(P_0 - \frac{P_0V}{V_0}\)
4. \(4P_0 - \frac{P_0V}{V_0}\)

The parabola y = x${}^2$ + 2x is represented by
1. 
2. 
3. 
4.

The relationship y = $\frac{3}{\mathrm{x}}$ is best represented as 
1. 
2. 
3. 
4. 

The parabola y = x${}^2$ + 1 is represented by
1. 
2. 
3. 
4. 
 

The slope of a curve between y and x changes from 0 to -5 as x changes from 0 to 5. Which of the following curve best represents the above mentioned curve?
1. 
2. 
3. 
4. 

Which of the following graph has a positive, decreasing slope?
1. 
2. 
3. 
4. 

The slope of a curve is initially positive, then becomes zero, and thereafter becomes negative. Which of the following graphs best represents this behaviour?
 

1.		2.
3.		4.