If $\overrightarrow{A}\times \overrightarrow{B}=\overrightarrow{C}+\overrightarrow{D}$,then which of the following statement is correct?

What is the maximum value of 5sinθ – 12cosθ?

Find $\frac{\mathrm{dy}}{\mathrm{dx}}$ , if $\mathrm{y} = {\mathrm{t}}^3+\hspace{0.17em}1$ and  $\mathrm{x} = {\mathrm{t}}^2 + 3$.

The volume flow rate of water flowing out of a tubewell is given by $\mathrm{Q} = (3{\mathrm{t}}^2 - 4\mathrm{t} \hspace{0.17em}+1) {\mathrm{m}}^3/\sec$.What volume of water will flow out of the tubewell in the third second if the volume flow rate is defined as Q =$\frac{\mathrm{dV}}{\mathrm{dt}}$?

A thin wire bent to form a circle and carrying a current I has a magnetic moment M. The shape of the wire is changed to a square and it carries the same current. It will have a magnetic moment

A scalar quantity is one that:

The position of a particle in a rectangular co-ordinate system is (3, 2, 5). Then its position vector will be:

A force of 5N acts on a particle along a direction making an angle of $60°$ with vertical. Its vertical component will be:

$\overrightarrow{\mathrm{A}}$ is a vector with magnitude A, then the unit vector $\hat{\mathrm{A}}$ in the direction of $\overrightarrow{\mathrm{A}}$ is

If $\overrightarrow{\mathrm{A}}=2\hat{\mathrm{i}}+4\hat{\mathrm{j}}-5\hat{\mathrm{k}}$, then the direction cosines of the vector are:

(direction cosines (or directional cosines) of a vector are the cosines of the angles between the vector and the three +ve coordinate axes.)

The vector that must be added to the vector $\hat{\mathrm{i}}-3\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ and $3\hat{\mathrm{i}}+6\hat{\mathrm{j}}-7\hat{\mathrm{k}}$ so that the resultant vector is a unit vecotr along the y-axis is

Surface area is:

A force F applied at a 30° angle to the x-axis has the following X and Y components:

Angular momentum is

If $\overrightarrow{\mathrm{P}}=\overrightarrow{\mathrm{Q}}$ , then which of the following is NOT correct?

Which of the following is a scalar quantity

There are two force vectors, one of 5N and the other of 12N. At what angle should the two vectors be added to get the resultant vector of 17N, 7N, and 13N, respectively:

If $\overrightarrow{\mathrm{A}}=4\hat{\mathrm{i}}-3\hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{B}}=6\hat{\mathrm{i}}+8\hat{\mathrm{j}}$ then magnitude and direction of $\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}$ will be

If a particle moves from point P(2,3,5) to point Q(3,4,5). Its displacement vector be

If vectors $\hat{\mathrm{i}}-3\hat{\mathrm{j}}+5\hat{\mathrm{k}}$ and $\hat{\mathrm{i}}-3\hat{\mathrm{j}}-\mathrm{\alpha }\hat{\mathrm{k}}$ are equal vectors, then the value of $\mathrm{\alpha }$ is:

A plane is revolving around the earth with a speed of 100 km/hr at a constant height from the surface of the earth. The change in the velocity as it travels half-circle is:

A particle moves from position null to $(11\hat{\mathrm{i}}+11\hat{\mathrm{j}}+15\hat{\mathrm{k}})$ due to a uniform force of $(4\hat{\mathrm{i}}+\hat{\mathrm{j}}+3\hat{\mathrm{k}})$N. If the displacement is in m, then the work done will be: (Given: \(W=\vec{F}.\vec{S}\))

If for two vectors $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$, $\overrightarrow{\mathrm{A}}\times \overrightarrow{\mathrm{B}}=0$, then the vectors:

When $\overrightarrow{\mathrm{A}}.\overrightarrow{\mathrm{B}}=-\left|\mathrm{A}\right|\left|\mathrm{B}\right|$, then

The dot product of two mutual perpendicular vector is:

Current in a circuit is given by $i =3t^2+2t$. Find charge that crosses a cross-section from time t=0 to t=2 sec.

Let $\mathrm{\theta }$ be the angle between vectors $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$. Which of the following figures correctly represents the angle $\mathrm{\theta }$?

If the angle between the two forces increases, the magnitude of their resultant:

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

4.2. Which one of the following statements is true?